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Sliptrick Records Welcome Finnish Slackers STONER KINGS
8th August 2019 Power of Metal News 0
Joining the ranks at Sliptrick Records this week:
Stoner Kings (FIN) Stoner Rock | Stoner Metal | Heavy Rock | Riff Rock
Stoner Kings is the brainchild of band frontman, vocalist and songwriter, Michael "StarBuck" Majalahti, who is the self-proclaimed, most accomplished professional wrestler in history from Northern Europe. The band was formed in 2000, after Michael came back from a disenfranchising experience of a disheartening UK wrestling tour, looking to focus his efforts elsewhere. Michael had moved from his homeland of Canada to Finland in the summer of 1996, when he started writing music and picked up playing guitar to pass the time. Many of the songs that ended up on Stoner Kings' debut Brimstone Blues were created around this era, between 1996-2000.
The band strove forward and under an augmented line-up released a second album in early 2006 after finishing recordings in late 2005. This sophomore effort would come to be known as Fuck The World, which served as a backlash to all of the spite issued forth by the critics of the band, who just couldn't get over their name. Between late 2006 and early 2007, Stoner Kings went through some tumultuous line-up changes. Everyone, save StarBuck, exited the band to be replaced by new players.
By the autumn of 2008 and after 3 singles, this latest line-up of Stoner Kings had dissolved and Michael decided to hang up the gloves indefinitely. It took eight years for the itch to make a comeback and became so undeniable that Michael contacted his old drummer J-J and talked to him about regrouping under a new line-up. Rude Rothsten from the 2007-2008 incarnation of Stoner Kings joined on bass once again and the new guitarist would be a young musician named Joonas Vepsä.
Stoner Kings's comeback gig was in November 2016 in Helsinki at On The Rocks. From that moment forward, the band set out to both gig regularly and at the same time work on new songs. The group hit the studio one year later in the autumn of 2017 to compile a set of songs for their third album. This process would take one year, as they recorded the yet-to-be-released album that came to be called Alpha Male between the autumn of 2017 and the autumn of 2018, a process that was performed in three separate recording and mixing blocks. Now ready to see the light of day, Alpha Male will be released via Sliptrick Records soon!
Stoner Kings are:
Michael "StarBuck" Majalahti – Vocals |
J-J Kontoniemi – Drums |
Rude Rothstén – Bass |
Joonas Vepsä – Guitar
Band links: Facebook | Instagram | On Sliptrick
Sliptrick Records
Stoner Kings
Prog Rockers MAGIC PIE Share New Single "P&C"!
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Lost in Thought - Renascence
Marillion – F*** Everyone And Run (F E A R)
Anciients - Voice Of The Void
Atheist - Unquestionable Presence (re-release)


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University of Santa Cruz Arboretum and Botanic Garden.
Freed orange styles ending in the yellow stigmas.
The orange styles are uncurling from the anther.
Flowers opening from back to front.
Such gorgeous plants! Thos one is blooming in 9B in early December.
Photo courtesy of and copyright of Fiona in South Lake, Western Australia.
University of Santa Cruz Arboretum and Botanic Garden. Copyright of Ferd Bergholz of Scotts Valley, California.
Copyright of and photo courtesy of Karlo Taliana from Sydney, Australia.
Photo courtesy of and copyright of Brian Freeman, from Victor Harbor, South Australia.
Grafted as a standard. Copyright of and photo courtesy of Deb Mc from Melbourne, Victoria, Australia.


You spend a good amount of time practicing your golf game and see yourself as a good practice player. On the practice putting green, you're rolling in putts and have proved to yourself you have decent putting skills. On the driving range you're hitting the ball really well.
Overall, you know you have the skills to shoot lower scores than you have been but you just haven't been able to do it yet. When you get out onto the golf course, things don't go as well as you'd like or maybe you had a good round going and things fell apart quickly.
Stop letting your mental game ruin your skill and ability to perform well on the golf course. You have the skill to shoot lower scores! You need to master the mental game to see these skills come to fruition. Order our eBook: The Golf Mental Game Blueprint today and begin implementing the lessons and strategies taught.
You've asked, we've delivered! After many high school golf coaches have reached out to us at GolfPracticeGuides.com, we decided to write this detailed guide to coaching high school golf for you to use to coach your team.
If you'd like bonuses, stop by our website shop page FoyGolfAcademy.com. These are an extra cost we've separated to keep the price of this eBook lower for coaches.
If you have any questions, feel free to email us for assistance. Let's get started helping you learn how to be that awesome high school golf coach who players love and succeed together with during the season. You're doing an awesome thing by being a coach and helping beginners learn the sport. Thank you!


There is one thing common amongst globally recognized hotel brands: they create memories for their guests. Their guests are loyal. Their guests have an emotional bond with these brands. This is because these brands evoke very strong images and connections which result in positive memory. I feel very fortunate indeed to be associated with Sheraton, one of the most recognized hotel brands in the world, and a member of the great team at the Sheraton Grande Taipei Hotel.
There is satisfactory service and then there is memorable service. Memorable service does not have to require a big effort. A concierge arranging to deliver your passport at once – when you left it in the hotel room and need it at the airport – is memorable service; but so is finding out what that movie was that I saw half of last night and can't remember which channel it was on.
There was one occasion when I have seen a guest reach the door of our hotel, look at the heavy rain, and wince. An associate quickly went over with an umbrella and offered it to him. That got a smile and solved the problem before the guest needed to ask. Hotels with memorable service understand this.
Satisfactory service can be achieved by having the right procedures and the right scripts. But memorable service comes only when we have trained employees to listen to guests and think about what those guests really want. Most often, it is about minute personal touches. Sometimes memorable service is just about recognizing what a guest wants before they actually thought it out themselves and giving it to them first.
At Sheraton, our associates strive to genuinely share a generosity of spirit with each other and with our guests, our associates believe in our core values and truly live our brand positioning "The World's Gathering Place." We also appreciate the power of customer loyalty and seek out opportunities to create memorable experiences that will drive that loyalty.
Previous:Glion's Azerbaijani alumni contribute to their country's booming tourism economy.


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Mayoral hopeful Vallas calls possible $10B Emanuel pension payoff 'irresponsible'
By Bill Ruthhart
Mayoral challenger Paul Vallas, shown speaking May 2, 2018, is criticizing Mayor Rahm Emanuel over a plan to borrow as much as $10 billion to shore up the city's ailing pension funds. (Erin Hooley/Chicago Tribune)
A plan under consideration by Mayor Rahm Emanuel to borrow as much as $10 billion to shore up the city's ailing pension funds would be an "irresponsible" bet that could jeopardize the city's economic future, mayoral challenger Paul Vallas said Tuesday.
Vallas, the former CEO of Chicago Public Schools and a onetime city budget director, took aim at the borrowing proposal. Emanuel's financial advisers say the plan could save future taxpayers hundreds of millions of dollars, but some finance experts have described it as risky.
"I just think it's fiscally irresponsible. Why do it? Because it's about politics, not about sound fiscal policy," Vallas said. "By doing the borrowing, it really allows you to defer big tax increases. … And depending on how you structure the financing, you could have an easy four to five years without a lot of pressure to raise significant revenue."
Saying that City Hall hasn't always been transparent with its finances, Vallas called on aldermen to hold formal hearings on the pension borrowing plan and to hire an independent firm to detail the risks involved.
The borrowing idea first was floated earlier this month by Emanuel's close friend and confidant Michael Sacks, CEO of Chicago-based asset management firm GCM Grosvenor. At an annual conference for buyers and raters of city debt, Sacks described a scenario in which the city could issue as much as $10 billion in so-called pension obligation bonds.
Under the strategy, the city would borrow the money at relatively low interest rates and use it to reduce the city's $28 billion in public employee pension debt. The pension funds would then invest that borrowed money and ideally earn returns that outpace the interest the city would have to pay on the new debt.
City Chief Financial Officer Carole Brown has said it's an idea she has to consider, since the move could save hundreds of millions of dollars down the road.
READ MORE: After Vallas calls event to push for more Chicago ambulances, Emanuel adds five of them »
Vallas said he believes Emanuel is considering the approach so he can campaign without having to address the possibility of another round of large property tax increases. The mayor already has issued record property tax hikes during his tenure to prop up the pension funds.
Issuing pension obligation bonds would be a first for Chicago, which for years shortchanged four city worker pension funds and is now playing catch-up. Sacks' pitch on the concept has sparked mixed reactions among investors across the nation.
Brown has said the city would expect to earn 7 percent interest on the new money, if it were invested in the pension funds, which would outpace the interest rates on the bonds. Vallas on Tuesday, though, stressed the risk involved, saying the city would lose economic flexibility in a down market with so much of its money dedicated to bond holders.
[Most read] Column: Donald Trump's Inauguration Day letter to Joe Biden: An exclusive (very real) draft »
"You're going to have, in effect, a city budget where the overwhelming vast majority of your revenues is dedicated to bond holders, and when things go south, if we hit a recession or an economic downturn, the impact can be catastrophic," Vallas said. "The projections that you're going to be able to do this and generate 7 percent from the investment fund and that's going to exceed your borrowing costs, I just think that numbers are not justified based on past history."
Asked what he would do instead to shore up the pension funds, Vallas did not give a specific answer. Instead, he said he would release his full financial and budget plan in the coming weeks that he said would include specifics on how to raise more money for the funds.
Tuesday's comments by Vallas are the latest in a series of barbs between the schools guru and Emanuel on city finances.
In February, as Vallas was weighing a run, Emanuel slammed him as the "architect of kicking the can down the road," to which Vallas responded by calling the mayor a liar. On Tuesday, Emanuel's City Hall spokesman issued a statement accusing Vallas of setting "Chicago's finances on fire" when he was budget director and CPS CEO.
The mayor has attacked Vallas for having a role in skipping CPS pension payments and eliminating a property tax specifically earmarked for teacher pensions. While CPS skipped some payments on Vallas' watch, the teachers pension fund was still sound when he left the district in 2001. Vallas has blamed his successors for not keeping the city's commitments on fully funding the pensions.
"Paul ought to take a deep breath and ask himself why wouldn't the financial team study every sound option to save taxpayers money and strengthen pension funds for retirees?" Emanuel spokesman Adam Collins said.
bruthhart@chicagotribune.com
Twitter @BillRuthhart
Chicago's mayoral race on display as Emanuel, opponents politick at Bud Billiken parade »
Paul Vallas
Chicago City Hall
City watchdog says Animal Care and Control employee sexually assaulted 2 co-workers while off duty, supervisor did not report to higher-ups
The Spin: Biden calls for unity, end to 'uncivil war' | Twitter captivated by Obama-Harris picture on historic day | Trump bows out, vows 'we'll be back'

redpajama_set_name: RedPajamaCommonCrawl


VideoSlots.com is an online casino that recently announced a fresh content supply deal with Wazdan, a developer based in Malta. The deal will see a range of video slots from Wazdan integrated within the VideoSlots.com domain.
European Gaming Media and Events published a press release which communicated that VideoSlots.com – operated by Panda Media Limited – has signed the new deal in a bid to offer the very best content "from the industry's most trusted providers". The deal means that is will be adding "a wide range of slot titles" to an already impressive range of over 3,000 games.


As we start this morning, I have only 40 minutes in which to acquaint you with a marvelous new remedy for the general contractors, or the subcontractors, with whom we work. I say that I am going to "acquaint you" with this new remedy, the "Stop Order Law," because I have found during the last 18 months that extremely few lawyers have yet "had their hands dirty" with a Stop Order. From talking to construction law practitioners, I have found that only about 15% of them have actually dealt with one of these new Stop Orders since the statute became effective on August 21, 1998. I predict that we are going to see more and more of these Stop Orders as our economy slows down. I think we had better learn how they work.
To put this new remedy in context, let me take you back to the way things were about 10 years ago. In 1990, if you were a subcontractor and had not been paid your 2nd and 3rd payment applications to the General, you had only Choice A or Choice B, the latter with two variations. Choice A was to forget about your lien and file a suit in contract against your contracting party. Choice B was that you could lien the apartment project job for all that you had put into it, your "enhancing" of the owner's premises, minus whatever you had been paid. Your variation on Choice B then was to leave the job or not to leave the job that you had liened! Your mechanics lien would very likely be behind a whopping big first mortgage which, in those days, was likely to be 95% of the top value of a working apartment project. So, when most of the subs walked off for non-payment and the appraisers moved in so as to value the "pile of sticks and pipes" for the lender, the 5% owner's equity just "evaporated." You, the sub, now had a lien, but the project (and likely the owner) were headed for bankruptcy or a foreclosure sale.
The first lender would make a credit bid in a foreclosure or a bankruptcy sale of a project and, simply put, no artisan could hope that his lien could bring him any significant sum. In the event that there were to be some "nubbin" of equity left, the fact that the lienor-claimants could not then get an award of their attorneys' fees would "chew up" the possibility of their recovering much for their liens.
The sub's only hope was that the project which he was liening was not yet "far gone" economically. If that were the case, the sub could count on some title company spokesperson's contacting him to say that "everyone else" was settling out for 30% of their claimed lien-amount so as to permit the defunct owner to "sell and transfer free of liens" on the project. If the sub would not cooperate, then 20 other subcontractors would hate his guts for having blocked the only way for them all to get any significant money out of the failed project.
Only "once in a blue moon" would a subcontractor be so lucky as to hear that the project was not as I have described it above. On the best of those occasions, one heard that one's lien had been "bonded off" with a §32-1004 "150% of lien amount" bond. In such few cases, the lucky sub would be allowed to "chase the cash" represented by the § 33-1004 bond – rather than chasing a chance of bidding in at a courthouse-steps auction foreclosure sale or a bankruptcy court sale concerning the title to (the equity in) a troubled apartment project.
In a nutshell, the great expense of preparing, then recording a notice of lien, then suing upon the lien, then fighting off the economic failure of the project, and (likely) the economic failure of the owner, simply made the mechanics lien law an illusory remedy. Having a poor remedy made the subs and generals "easy prey" for an owner's threatened bankruptcy or a first lien "blowout" foreclosure. The contractors had a bad legal position – and it blighted their business posture.
California, the Concept Behind the "Stop Order"
I do not plan to dwell on how "they" do it in other States, whose laws our Legislature so often looks to when we are making social policy. Suffice it to say that California Civil Code §3103 contained the seeds of what was enacted here in Arizona some 18 months ago in 1998.
The core of the Stop Order is a simple concept: the unpaid contractor ought to be able to chase cash, rather than chase an equity in real estate, equity which is very often just an elusive figment of bankers' imaginations.
It is, however, crucial for you to understand that the new Stop Order does not apply to two classes of work: (a) to government work (non-"private" work per § 33-1053) and (b) to owner-occupant dwellings per § 33-1002.
Let's take those two exclusion areas separately. For government work, the contractors are protected by the Little Miller Act, §34-222. There, the contractors already can chase the cash! As to private owner-occupant residences, subs never even had any lien rights on such residences. A.R.S. § 33-1002. Only Generals who had a signed contract with the owner could lien owner-occupant residences. The Legislature was in no mind to extend this new remedy to those two situations, i.e. to the Miller Act covered work nor to the owner-occupant residence.
To understand the new remedy, you need only think of it as sort of a form of "garnishment" designed to help artisans, designed to permit them to "garnish" construction loan funds in the hands of the lender, or the owner. As we will see, this remedy will let the contractor "chase the cash," instead of resorting to his illusory remedy of liening the project and trying to obtain relief from its equity.
(a) Contents of the SON: A stop order notice served on the Owner or Lender must be verified – and it must contain the five items listed in A.R.S. § 33-1051: (i) description of the labor, materials, or tools furnished. (ii) the person requesting such. (iii) the value of what was furnished and promised to be furnished. (iv) the amount of payment received. (v) the name and address of the stop order claimant.
As Exhibit B, I have given you a form of Stop Order Notice which is being used today by one of the lien services here in Phoenix. Please note that a copy of the bond should be attached if it is a Bonded Stop Order Notice ("BSON").
You can deliver a stop order notice early in the job, whenever you are unpaid and you want to "garnish" money flowing along the lender-owner-general chain above you so as to be sure that you will get paid. THE KEY IS THAT ONCE YOU SERVE IF YOU FAIL TO SUE UPON YOUR NOTICE BY THREE MONTHS AFTER YOUR LIEN RECORDING PERIOD EXPIRES, then you are too late to sue on your Stop Order Notice. See A.R.S. § 33-1063. Once that 90 days period (after the lien recording period) has lapsed, an SON, if you served one, is void and of no effect. § 33-1063(B). See Exhibit C, my timeline for SON's and liens.
Section 33-1058 says that upon receipt of a SON the lender may (and on receipt of a BSON the lender shall) withhold from construction funds the amount needed to pay the claim. What I have found to be a practical problem is that lenders "take their own sweet time" in telling the party serving the SON or BSON whether or not the lender had some funds available which have been "trapped" by the service of the SON or BSON. I believe that the reason that lenders are often slow to admit that funds have been reached and segregated is that they are not sure if 10 more SON's might be coming in to them and, if so, what money will be available to cover all the SON's eventually received.
(c) Bonding: As you all may know, if you serve a prejudgment garnishment, you have to provide a bond against the risk that yours might be a wrongful garnishment.
Well, in much the same vein, to have an automatic "garnishment" result from a contractor's service of a SON, it has to be a bonded SON ("BSON") that one serves. See § 33-1058. The bonds, by the way, seem to be really cheap.
I sometimes have to "pinch myself" regarding the unbonded stop orders. I rather wonder why one would "bother" serving an unbonded stop order notice. As is made clear in A.R.S. § 33-1058(A), an unbonded notice is like a "letter to mom." The lender, if he wishes, can ignore it and continue using up loan funds. However, I can imagine few instances where lenders, whose fees and interest after all are paid by the owners, will, out of the goodness of their hearts, elect to "recognize" an unbonded stop order notice and proceed to withhold loan funds to cover the stop order claim by a subcontractor.
(d) Service: Under § 33-1056, there are strict requirements on how one serves an owner (personally, or through substituted service made on someone living at his residence). There's no indication of what you do when the owner is a corporation or an LLC. There are, likewise, strict requirements about serving a lender; you must serve the Manager or "other responsible officer" at the branch or the office of the Lender that actually manages the construction monies in question. If you are calling around to get that information from the lender, you will want to keep a record as to who on the lender's staff told you it was the North Sunnyslope office or who the manager there was.
Well, no one would expect that the contractors could get this dandy new remedy without there being some "buried hazards" placed inside the statute.
If you were a lender, you would like to be able to process the payments on a troubled construction job in such a way that you could know at given intervals that you had the fund-flow "under control." You would want to be able to project what SON's might do to your fund balance. If you were a lender, you would not want last minute SON's from six contractors, for three months of payment applications each to hit you suddenly when the job (and the funds for the job) were nearly at completion. The way that the lenders can do that testing of the financial status of the job is by what I call "periodic sweeps."
In §§ 33-1054 and -1055(A), it states that any owner or lender can send out to a contractor a "DEMAND FOR SERVICE OF STOP NOTICE PURSUANT TO A.R.S. §§ 33-1054 and -1055." The owner or lender's bold-faced typed message to your contractor clients should be a "red-flag" whenever such a notice comes in the mail. If the contractor fails to respond by serving on the lender a stop order notice by the 30th day after the mailing to him, then he cannot later serve any stop order notice for "the work" which the owner described in the owner's "demand for stop notice." Thus, I predict that when lenders get down close to the last installment of their construction loan pay-out, they will routinely send out these "sweep" demands for stop orders. If you respond, then they know exactly what debts exist that may lay claim on their funds. If you don't respond, they can safely ignore you as regards the project's loan funds. Uneducated contractors will carelessly lose their chance to "chase the cash," leaving those contractors with just their lien remedies.
(a) If a rash of stop order notices hits a lender, it does not mean that the first to serve gets 100% and that other later claimants may get 50% or zero. Under § 33-1060, all stop order claimants will receive a pro-rata share. In other words, stop order notice claimants are put on a "parity" and the "garnished funds" are doled out in pro rata shares. See A.R.S. § 33-1000. It is this vague feature, I believe, of the SON law that slows down lender responses to SON's.
(b) Rather like § 33-420 regarding false liens, § 33-1061 says that the contractor who willfully serves a false stop order notice, will be subjected to severe penalties. He forfeits all lien rights, all stop order "garnishment" rights, and he gets hit with § 33-420's $5,000 or actual damages, which ever is greater!
(c) Note that there are really three responses that a contractor might receive from a lender after service of a BSON: (i) "we got your notice and bond and we have segregated and are holding all the funds which you claimed"; (ii) "too late, when your notice reached us, we had paid out so much of the loan proceeds that we now hold nothing (or a very small portion) of what you claimed"; or (iii) "hallelujah, there is a § 33-1003 bond in lieu of liens recorded on this job – and we are refusing your BSON because you can go chase that cash." See § 33-1057(B).
You will be pleased to learn that, similar to § 33-998, allowing attorneys' fees in lien-foreclosure suits, the new stop order law has provided for attorneys' fees awards in its § 33-1066. There is also a separate interest provision related to funds trapped by a BSON, so as to discourage lenders from holding such trapped funds for long periods.
No longer does the subcontractor who fears the general contractor's shaky finances, have to worry that, when the General "goes down," the sub will be caught up in a lien-enforcement game in which the sub can only rarely win payment for what he's actually spent on the job. No longer does the sub have to chase the equity in the troubled project, knowing all the time that it is an illusory pursuit.
The new stop order notice remedy allows a sub (or a General) on a troubled project to chase the cash by serving the owner or lender with BSON's which act somewhat like bonded prejudgment garnishments of construction loan funds. This new remedy can accelerate the subs (or a General's) getting paid. The new remedy is timed so that, if one watches the timeline, Exhibit C, one can "test the waters" by serving bonded stop order notices; see if one gets a favorable response from the "garnished party"; see if payment in full is received before the lien period expires; record one's lien while then commencing suit upon a BSON; and seek to foreclose that lien if the pro-rata share of a construction loan's proceeds remaining does not cover 100% of the value which one has put into the job.
In a nutshell, the BSON remedy is speedier, more reliable, and, since it's a "chase of the cash," it is likely to benefit the contractors far more than a lien claim.
The lien remedy then remains as a "backup" remedy, one that can supplement the BSON remedy, if one has commenced so late in the process that loan proceeds are essentially exhausted before the BSON's reach the lender.
All contractors need to be vigilant in scanning their mail for a § 33-1054 and -1055 "Demand for Service of Stop Notice Pursuant to A.R.S. §§ 33-1054 or -1055." To fail to timely respond (in 30 days) is to abandon all possibility of using stop order notices on that job.


Hit and Run Baton Rouge Lawyer - Hit by drunk driver?
Hit by a Drunk or Negligent Driver in Louisiana?
Intoxicated drivers are a great danger to both pedestrians and other drivers. They are known to cause some of the most horrifying accidents, and leave victims with devastating injuries. Such accidents can result in serious back and neck injuries and even death. It can be impossible to avoid a collision with a drunk driver that has lost control of their faculties. Call (225) 307-0088.
You need a lawyer with extensive experience to help you recover for losses sustained in an accident caused by a drunk driver. Such a lawyer will understand the full extent of harm suffered and how your injuries could negatively affect your quality of life.
There are a number of things that you have to prove in order to obtain damages. First, your lawyer has to prove that the driver was intoxicated to a level where the driver lost physical and mental control. Secondly, the intoxication should be the direct cause of the injuries suffered by the victims. The injuries should also have been caused by the driver's negligence or carelessness.
There are cases where a DUI conviction can be used as evidence of negligent driving but you don't need that to sue. A driver's intoxication is not assumed to be the cause of an accident but proof that the driver was intoxicated or impaired can be enough to assign fault.
There are also situations where the victims have been held partially liable for causing an accident involving a drunk driver. The victim may have been speeding or did not obey traffic laws when their car collided with that of a drunk driver. In such cases the amount of compensation the plaintiff gets is reduced.
In fatal accidents with a drunk driver where a person is killed, the deceased's family can pursue a wrongful death claim. They may seek damages such as loss of future financial support and others.


After working at video post-production houses in Cincinnati and Seattle for many years, Lucy started her own studio in 2009. She enjoys taking projects from concept to completion with on-time, on-budget, creative solutions. Lucy has extensive experience designing and animating graphics for television and corporate video including show opens/graphics packages, promos, commercials, informational graphics and multiscreen presentations.
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Designer | Motion Graphics Artist.
As a designer and animator, Josh enjoys the creative process from branding, illustration and storyboarding to the final animation. He loves the way timing, movement and music can complement each other to evoke emotions and tell a complete story through film and video.


– CANADA, Vancouver – Sonoro Metals Corp., (TSX:SMO | OTCQB:SMOFF | FRA:23SP) today announced the appointment of Neil Maedel to the Company's Board of Directors and his assumption of duties as Executive Director, Corporate Finance. To accommodate the appointment of Mr. Maedel, director Ronald Husband has resigned from the Board, but will continue to act as an advisor to the Board. In addition, Sonoro has appointed Katharine Regan as Corporate Secretary of the Company.


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\section{Introduction}\label{sec:intro}

A common computer consists of a fixed number of gates that process classical information by performing classical operations on input data, strings of bits.
A single computer can be used for many different tasks simply by changing its program.
Indeed, common computer can be programmed to perform arbitrary classical manipulations on the input data, although the execution time depends on its computational speed.
This \emph{universality}, making it a very versatile device, is arguably the most important feature of a computer.

A quantum computer presumably consists of \emph{quantum gates} that are used to implement desired quantum operations on a quantum input, for instance \emph{qubits}. It's suspected, that large scale quantum computers should surpass their classical counterparts with superior speed and hence revolutionize the world by opening for study a whole class of computational tasks that ordinary computers simply cannot grasp efficiently, such as factorization of large integers and simulation of quantum systems.
However, there is, besides the practical issues of actually building one, a major theoretical problem with quantum computer, namely its universality.

Contrary to classical computing, where it is possible to design a universal gate array that can be \emph{deterministically programmed} to implement any arbitrary function on a given classical input data, in quantum case no such universality holds.
Indeed, it was proven by Nielsen and Chuang in \cite{NiCh97}, that to program a quantum gate array to realize any two different \emph{unitary channels}, being the mathematical representatives of quantum gates, requires orthogonal programming vectors. A cardinality argument leads to impossibility of implementing all unitary channels even in an infinite dimensional separable Hilbert space. The existence of imperfect, that is probabilistic, universally programmable quantum gate arrays has, however, been confirmed and studied in \cite{NiCh97,HiBuZi01,HiZiBu06}.

Another useful device would be a \emph{quantum multimeter} that could be programmed to measure any quantum observable.
Also this universally programmable device is feasible only if some error is accepted or the implementation is probabilistic \cite{DuBu02,FiDuFi02,DaPe05,PerezGarcia06}.
It turns out  that the reason for this is very similar to the impossibility result on unitary channels: the programming of a multimeter to realize any two different \emph{sharp observables} demands orthogonal programming vectors.
This orthogonality result can however be alleviated -- so that different sharp observables can be programmed with non-orthogonal programming vectors -- assuming that classical \emph{post-processing} of the measurement statistics is allowed \cite{ZiBu05}.

As we will show, all the previously mentioned no-go results have natural formulations in the context of quantum theory of measurement.
This wider framework also reveals their inherent connections and opens up some immediate generalizations.

Our study is organised as follows.
In section \ref{sec:prelim} we start by introducing some preliminary concepts and mathematical machinery.
In section \ref{sec:prog} we study the limitations of deterministic programmability of quantum channels and observables.
We start by first studying the programmability of sharp observables and show that the programming vectors for any two different sharp observables are necessarily orthogonal, whenever post-processing is not allowed.
We show that this result directly implies that also two different unitary channels require orthogonal programming vectors, giving an alternative proof for the well-known result first proven in \cite{NiCh97}, yet in a more general context.
We also note further limitations: the programming of a sharp observable and an \emph{extreme observable} require orthogonal programming vectors. The same result holds also for a unitary and an extreme channel. In fact, the programming limitations of sharp observables and unitary channels are somewhat analogous: a difference arises only when post-processing of the measurement statistics is allowed.
In the final section \ref{sec:eff} we develop the concept of \emph{effectiveness} for deterministic programming by giving bounds for a programming protocol to be efficient.

\section{Preliminaries}\label{sec:prelim}

In this section we fix notations and recall the basic concepts needed in our investigation.
Let $\hi$ be a complex separable Hilbert space with either finite or countably infinite dimension.
We denote by $\lh$ the set of \emph{bounded linear operators}, by $\trh$ the set of \emph{trace class operators} and by $\ph$ the set of \emph{projections} on $\hi$. We identify the set of \emph{quantum states} as $\sh = \{\rho \in \trh \, | \, \rho \geq 0, \tr{\rho}=1\}$. In particular a state $\rho$ is called \emph{pure}, or equivalently a \emph{vector state}, if $\rho \in \sh \cap \ph$, that is $\rho = P[\varphi] = |\varphi\rangle\langle\varphi|$ for some unit vector $\varphi \in \hi$.

\subsection{Observables}

Let $\Omega$ be a nonempty set and $\Sigma \subset 2^\Omega$ a $\sigma$-algebra.
We denote by $\mc{O}$ the set of quantum \emph{observables} on $(\Omega,\Sigma)$, i.e., the mappings $\Eo: \Sigma \rightarrow \lh$ that are positive, $\sigma$-additive and normalized so that $\Eo(\Omega)=\id_\hi$.
The operators $\Eo(X)$, $X\in \Sigma$, in the range of an observable $\Eo$ are called \emph{effects}.
If $\Eo(\{x_i\})\neq 0$ for some finite number of points $x_1,\ldots,x_N$ and $\sum_{i=1}^N \Eo(\{x_i\})=\id_\hi$, then we say that $\Eo$ has $N$-outcomes, or is \emph{$N$-valued}.
We often denote $\Eo(x) \equiv \Eo(\{x\})$ when there is no risk of confusion.

A special class of observables are those whose range consists of projections.
We say that an observable $\Ao$ is \emph{sharp} if all its effects are projections, that is, $\Ao(X)^2 = \Ao(X)$ for every $X \in \Sigma$.

Every observable $\Eo$ has a \emph{Naimark dilation} into a sharp observable, i.e., there exist a Hilbert space $\hik$, a sharp observable $\Ao:\Sigma\to\lk$ and an isometric linear map $W:\hi\to\hik$ such that
\begin{equation}
\Eo(X) = W^* \Ao(X) W
\end{equation}
for all $X\in\Sigma$; see e.g. \cite{CBMOA03}.
Since $W$ is an isometric linear map, $W^*W=\id_\hi$ and $WW^*$ is the projection onto $W(\hi)\subset\hik$.

We recall the following characterisation of sharp observables; see e.g.  \cite{LaYl04} for a proof.

\begin{proposition}\label{prel:sharp}
Let $\Eo$ be an observable and $(\hik,\Ao,W)$ its Naimark dilation.
The following are equivalent:
\begin{itemize}
\item[(i)] $\Eo$ is a sharp observable.
\item[(ii)] $\Eo(X\cap Y) = \Eo(X)\Eo(Y)$ for all $X,Y\in\Sigma$.
\item[(iii)] $[\Ao(X),WW^*]=0$ for all $X\in\Sigma$.
\end{itemize}
\end{proposition}

The set $\mc{O}$ is a convex set, and a convex combination $\lambda \Eo + (1-\lambda) \Fo$ of two observables $\Eo$ and $\Fo$ corresponds to their mixing.
The extremal elements of $\mc{O}$, i.e., the observables that cannot be expressed as convex mixtures of other observables, are called \emph{extreme observables}.
All sharp observables are extreme, but it is known that there are also other extreme observables \cite{PSAQT82}.
For instance, in a finite $d$-dimensional Hilbert space we can construct an extreme observable with $N$ outcomes for each $N=d,\ldots,d^2$ \cite{HaHePe12}, but any sharp observable has at most $d$ outcomes.
A complete characterisation of extreme observables is given in \cite{Pellonpaa11}.

\subsection{Channels}

Quantum channels are devices performing quantum state transformations.
Mathematically, a linear mapping $\Ec: \trh \rightarrow \trh$ is a quantum channel if it is \emph{completely positive} and \emph{trace-preserving} (Schr\"{o}dinger picture), or equivalently, if its dual map $\Ec^*: \lh \rightarrow \lh$ is completely positive and \emph{unital}, meaning that $\Ec^*(\id_\hi)=\id_\hi$ (Heisenberg picture).

A unitary operator $U:\hi\to\hi$ defines a \emph{unitary channel} $\Uc$ by $\Uc (T) = UT U^*$ for all $T \in \trh$, or $\Uc^* (B) = U^* B U$ for all $B \in \lh$ in the Heisenberg picture.
The unitary channels are exactly the \emph{reversible channels}, i.e., those channels that have an inverse map which is a channel.
One of the important properties of unitary channels is that they are \emph{multiplicative}, namely
\begin{equation}\label{eq:unitary}
\Uc^* (BC) = U^* B U \, U^* C U = \Uc^* (B)\Uc^* (C)
\end{equation}
for all $B,C \in \lh$.

Every channel $\Ec$ has a \emph{Stinespring dilation}, i.e., there exist a Hilbert space $\hik$ and an isometric linear map $W:\hi\to\hi\otimes\hik$ such that
\begin{equation}\label{prel:stines}
\Ec(T) = \ptr{WTW^*}
\end{equation}
for all $T\in\trh$, or equivalently
\begin{equation}
\Ec^*(B) = W^* B \otimes \id_\hik W
\end{equation}
for all $B\in\lh$; see e.g. \cite{CBMOA03}.

The following properties of unitary channels will be needed later.

\begin{proposition}\label{prel:unitary}
Let $\Uc^*:\lh\rightarrow\lh$ be a unitary channel and $(\hik,W)$ its Stinespring dilation.
Then $\Uc^*$ satisfies the following equivalent conditions:
\begin{itemize}
\item[(i)] $\Uc^*$ is multiplicative.
\item[(ii)] $\Uc^*(P)$ is a projection for each projection $P\in\ph$.
\item[(iii)]  $[B\otimes \id_\hik, W W^*]=0$ for all $B\in \lh$.
\end{itemize}
\end{proposition}

\begin{proof}
We have already seen that $\Uc^*$ is multiplicative, so we only need to prove that the conditions (i)--(iii) are equivalent.
The implications (i)$\Rightarrow$(ii) and (iii)$\Rightarrow$(i) are straightforward to verify.
In the following we prove that (ii)$\Rightarrow$(iii).

Assume (ii). For each $P \in \ph$, we then have
\begin{eqnarray}
W^* P \otimes \id_\K W &=& W^* P \otimes \id_\K W W^* P \otimes \id_\K W \nonumber \\
\Rightarrow W W^* P \otimes \id_\K W W^* &=& \left( W W^* P \otimes \id_\K W W^* \right)^2
\end{eqnarray}
implying that $W W^* P \otimes \id_\K W W^*$ is a projection.
Since both $W W^*$ and $P \otimes \id_\K$ are projections, then by \cite[Lemma 2.2.1]{LaYl04} we have $\left[W W ^*, P \otimes \id_\K \right]=0$ for all $P \in \ph$.
By the linearity and continuity of the mapping $B\mapsto \left[W W^*, B \otimes \id_\K \right]$ we get $\left[W W^*, B \otimes \id_\K \right]=0$ for all $B \in \lh$.
\end{proof}

The set of all channels $\mc{C}$ is a convex set and the extremal elements of $\mc{C}$ are called \emph{extreme channels}.
All multiplicative channels are extreme, but there exist also other extreme channels.
For instance, fix a unit vector $\varphi\in\hi$ and define a channel by $\mc{E}^*(B)=\ip{\varphi}{B\varphi} \id_\hi$.
This channel is clearly not multiplicative, but it is easy to verify that it is extreme.
The corresponding Schr\"{o}dinger channel $\Ec$ is known as a \emph{complete state space contraction}, since $\Ec(\rho) = P[\varphi]$ for all states $\rho \in \sh$.

\subsection{Measurement models}\label{sec:memo}

Every physical measurement is based on the same general concept: the observed system is brought into contact with some measuring apparatus and the value of the measured observable is read from the apparatus' pointer scale.

\begin{figure}
\includegraphics[width=0.9\textwidth]{mnt.png}
\caption{Measurement schematics: Initial state of the system ($\rho\in \sh$) is interacting with the initial probe state of the measurement apparatus $(\xi \in \sk)$ via measurement coupling ($\mc V: \mc T(\hi \otimes \K)\rightarrow \mc T(\hi \otimes \K)$). The measurement statistics of the pointer observable ($\Zo(X) \in \lk$) acting on the combined state ($\mc V(\rho\otimes\xi) \in \mc S (\hi \otimes \K)$) actualize the statistics of the measured observable $(\tr{\Eo(X) \, \rho})$. }\label{fig:mnt}
\end{figure}

Mathematically, a \emph{measurement model} is a 4-tuple $\langle \K, \Zo,\mc V, \xi \rangle$, where $\K$ is the Hilbert space associated to the apparatus, $\Zo: \Sigma \rightarrow \lk$ is the \emph{pointer observable}, $\mc V: \trhk \rightarrow \trhk$ is the channel describing the \emph{measurement interaction} between the system and the apparatus and $\xi \in \sk$ is the initial \emph{probe state}.
The measurement statistics produce the measured observable $\Eo$ via the \emph{probability reproducibility condition}
\begin{eqnarray}
\tr{\Eo(X) \, \rho} = \tr{\id_\hi \otimes \Zo(X) \, \mc V(\rho \otimes \xi) } \, ,
\end{eqnarray}
which is required to hold for all initial system states $\rho \in \sh$ and $X\in \Sigma$; see Fig. \ref{fig:mnt}. In other words, the measured observable is
\begin{eqnarray}\label{obs:repro}
\Eo(X) = \ptr{\mc V^*\left(\id_\hi \otimes \Zo(X)\right) \, \id_\hi \otimes \xi} \, .
\end{eqnarray}

Following the terminology of \cite{OQP97}, we say that a measurement model is \emph{normal} when the pointer observable is sharp, the interaction is given by a unitary channel ($\mc V(\rho \otimes \xi) = G \rho \otimes \xi G^*$ for some unitary operator $G$ on $\hi\otimes\K$) and the initial probe state is pure ($\xi = P[\phi]$ for some unit vector $\phi \in \K$). In such a case we write the measurement model shortly as $\langle \K, \Zo, G, \phi \rangle$.
The measured observable induced by a normal measurement model $\langle \K, \Zo, G, \phi \rangle$ is
\begin{equation}\label{eq:naimark-memo}
\Eo(X) = W_\phi^*\,  G^*(\id_\hi \otimes \Zo(X))G \, W_\phi \, ,
\end{equation}
for all $X\in \Sigma$, where $W_\phi(\varphi)=\varphi\otimes \phi$ for all $\varphi\in\hi$.
It is a fundamental result of quantum measurement theory that every observable has a normal measurement model \cite{Ozawa84}.
We say that \eqref{eq:naimark-memo} is a \emph{measurement dilation} of $\Eo$.
It is obviously a special kind of Naimark dilation of $\Eo$. Using Prop. \ref{prel:sharp} one easily confirms that the sharpness of $\Eo$ is equivalent to $\left[ G^*(\id_\hi \otimes \Zo(X))G, W_\phi W_\phi ^* \right]=0$ for all $X\in \Sigma$.

Measurement processes can be used to model not only any observable but also an arbitrary quantum channel.
Namely, a measurement model $\langle \K, \Zo, \Vc, \xi \rangle$ induces a channel
\begin{equation}\label{chan:repro-s}
\Ec(\rho) = \ptr{\Vc(\rho \otimes \xi)} \, .
\end{equation}
Note that the pointer observable plays no role in \eqref{chan:repro-s}.
The corresponding Heisenberg channel is given by
\begin{eqnarray}\label{chan:repro}
\Ec^*(B) = \ptr{\Vc^*(B\otimes \id_\K) \, \id_\hi \otimes \xi} \, .
\end{eqnarray}
As in the case of observables, every channel has a normal measurement model $\langle \K, \Zo, G, \phi \rangle$, and in that case \eqref{chan:repro} takes the form
\begin{equation}\label{eq:stinespring-2}
\Ec^*(B) = W_\phi^*\,  G^*(B \otimes \id_\K) G \,W_\phi \, , \quad B\in\lh \, .
\end{equation}
This is obviously a special kind of Stinespring dilation of $\Ec^*$ and by Prop. \ref{prel:unitary}, if $\mc E^*$ is a unitary channel, then $\left[G^*(B\otimes \id_\K)G, W_\phi W_\phi^* \right]=0$ for all $B \in \lh$.

We end this subsection with a simple observation related to the measurement models of extreme  observables and channels.
Suppose that an observable $\Eo$ has a measurement model $\langle \K, \Zo, \Vc, \xi \rangle$ where the probe state $\xi$ is mixed.
We write the probe state $\xi$ as a convex decomposition $\xi = \sum_{i} \lambda_i P[\phi_i]$, and then
\begin{eqnarray}
\Eo & = &  \ptr{\mc V^*\left(\id_\hi \otimes \Zo(X)\right) \, \id_\hi \otimes \xi} \\
&=& \sum_{i} \lambda_i  \, \ptr{\Vc^*(\id_\hi \otimes \Zo) \, \id_\hi \otimes P[\phi_i]} \nonumber \\
&=&  \sum_{i} \lambda_i \, \Eo_i \, ,
\end{eqnarray}
where $\Eo_i$ are some observables.
If $\Eo$ is extreme, then $\Eo_i=\Eo$ for each $i$,
and hence $\Eo$ has a measurement model $\langle \K, \Zo, \Vc, \phi_i \rangle$, where the probe state is pure.
An analogous argument is valid for the extreme channels.
We summarize this observation in the following proposition, earlier noted in \cite{DaPe05}.

\begin{proposition}\label{prop:ext}
Let $\mc D$ be an extreme observable/channel having a measurement model $\langle \K, \Zo, \mc V, \xi \rangle$.
Then $\mc D$ has a measurement model $\langle \K, \Zo, \mc V, \xi' \rangle$, where  $\xi'$ is a pure state.
\end{proposition}

\section{Programmable quantum multimeters}\label{sec:prog}

\subsection{Multimeters}

Generally speaking, \emph{multimeters} are measurement settings that can be programmed to implement any observable/channel from a specified set.
The programming is done by changing some part of the measurement model: the probe state, the pointer observable, or the interaction.
Usually the easiest to physically realize, and thus the most interesting set of programmable multimeters, are those in which the initial probe state is changed.
In the rest of our investigation we reserve the term 'programming' for this state-programming scenario only.
Therefore, a multimeter is a measurement model in which we do not specify the pointer state, \emph{i.e.} a 3-tuple $\langle \K, \Zo, \Vc \rangle$.
This is a  \emph{normal multimeter} if $\Zo$ is sharp and $\Vc$ is unitary.

From an abstract point of view a quantum multimeter is a specific kind of function that maps quantum states into observables or channels.
This function must be physically realizable, meaning that it should be induced from a measurement process.
The essential fact is that all functions from states to either channels or observables are not physically realizable in this way.
For instance, it is easy to construct a bijective function between pure qubit states and qubit unitary channels.
However, there is no programmable multimeter capable of implementing all qubit unitary channels \cite{NiCh97} nor all sharp qubit observables \cite{DaPe05}.

\subsection{Programming quantum observables}\label{sec:probs}

In this subsection we study the programmability of quantum observables.
We denote the set of programmable observables with a given multimeter $\mc{M}$ by $\mc{O}_\mc{M}$.
The analysis done in articles \cite{DuBu02,FiDuFi02,DaPe05} indicates that $\mc{O}_\mc{M}$ is always a proper subset of $\mc{O}$, meaning that a fixed multimeter cannot be used to program all observables.
Here we elaborate this result by showing that different sharp observables demand orthogonal programming vectors, proving that $\mc{O}_\mc{M}$ can contain at most $\dim\K$ sharp observables.
Note that due to Proposition \ref{prop:ext} the programming protocols of all extreme observables can be restricted to vector states.

\begin{proposition}\label{obs:programming}
Let $\mc{M}=\langle \hik, \Zo, \Vc \rangle$ be a multimeter and suppose that two different sharp observables $\Ao_1$ and $\Ao_2$ can be programmed with vector states $\phi_1$ and $\phi_2$, respectively.
Then $\phi_1$ and $\phi_2$ are orthogonal.
\end{proposition}

\begin{proof}
We fix disjoint sets $X,Y\in\Sigma$ such that $\Ao_1(X) \Ao_2(Y) \neq 0$.
These kind of sets exist, for if $\Ao_1(X) \Ao_2(Y)=0$ holds for all disjoint sets $X,Y\in\Sigma$, then
\begin{eqnarray}
\Ao_1(X) = \Ao_1(X) \Ao_2(\Omega) = \Ao_1(X) \Ao_2(X) = \Ao_1(\Omega) \Ao_2(X) = \Ao_2(X) \, ,
\end{eqnarray}
contradicting $\Ao_1\neq\Ao_2$.

The condition $\Ao_1(X) \Ao_2(Y) \neq  0$ means that the projections $\Ao_1(X)$ and $\Ao_2(Y)$ are non-orthogonal.
Hence, there exist unit vectors $\varphi_1$ and $\varphi_2$ in $\hi$ such that $\Ao_1(X)\varphi_1=\varphi_1$, $\Ao_2(Y)\varphi_2=\varphi_2$ and $\ip{\varphi_1}{\varphi_2}\neq 0$.
Since $X$ and $Y$ are disjoint, we have $\Ao_1(Y)\varphi_1= 0$ and $\Ao_2(X)\varphi_2= 0$.

Denote $\Fo = \Vc^*(\id_\hi \otimes \Zo)$.
Then
\begin{eqnarray}
\ip{\varphi_1 \otimes \phi_1}{\Fo(Y) \varphi_1 \otimes \phi_1} = \ip{\varphi_1}{\Ao_1(Y) \varphi_1} = 0
\end{eqnarray}
and
\begin{eqnarray}
\ip{\varphi_2 \otimes \phi_2}{\Fo(Y) \varphi_2 \otimes \phi_2} = \ip{\varphi_2}{\Ao_2(Y) \varphi_2} =1,
\end{eqnarray}
from which it follows that $\Fo(Y) \varphi_1 \otimes \phi_1 = 0$ and $\Fo(Y) \varphi_2 \otimes \phi_2 =  \varphi_2 \otimes \phi_2$.
Using these two equations we obtain
\begin{eqnarray}
0 &=& \ip{\Fo(Y) \varphi_1 \otimes \phi_1}{\varphi_2 \otimes \phi_2} = \ip{\varphi_1 \otimes \phi_1}{\Fo(Y) \varphi_2 \otimes \phi_2} \nonumber \\
&=& \ip{\varphi_1 \otimes \phi_1}{\varphi_2 \otimes \phi_2} = \ip{\varphi_1}{\varphi_2}\ip{\phi_1}{\phi_2} \, ,
\end{eqnarray}
proving that $\ip{\phi_1}{\phi_2}=0$.
\end{proof}

A stronger version of Prop. \ref{obs:programming} holds when the multimeter is assumed to be normal.

\begin{proposition}\label{obs:ex} Let $\mathcal{M}= \langle \K, \Zo, G \rangle$ be a normal multimeter and suppose two different observables, a sharp observable $\Ao$ and an extreme observable $\Eo$, can be programmed with vector states $\phi$ and $\phi'$, respectively.
Then $\phi$ and $\phi'$ are orthogonal.
\end{proposition}

\begin{proof}
Assume $\ip{\phi}{\phi'}\neq 0$.
Then $\phi'$ can be written as $\phi'=\alpha \phi + \beta \eta$, where $\ip{\phi}{\eta}=0$ and $\alpha,\beta \in \C\setminus\{0\}$ satisfy $|\alpha|^2 + |\beta|^2 = 1$.
We have
\begin{equation}
W_{\phi'}= \alpha W_{\phi} + \beta W_{\eta} \, , \quad W^*_{\phi'}= \bar{\alpha} W^*_{\phi} + \bar{\beta} W^*_{\eta} \, ,
\end{equation}
and
\begin{equation}
W_{\phi}^* W_{\eta}= \ip{\phi}{\eta} \id =0 = W_{\eta}^*  W_{\phi} \, .
\end{equation}

Denote $\Zo'(X)=G^*\left(\id_\hi\otimes\Zo(X)\right) G$ for all $X\in\Sigma$.
We recall from Prop. \ref{prel:sharp} that the sharpness of $\Ao$ is equivalent to $[\Zo'(X), W_{\phi} W_{\phi}^*]=0$ for all $X\in\Sigma$.
Therefore,
\begin{equation}
W_{\phi}^* \Zo'(X) W_{\eta} = W^*_{\phi}W_{\phi} \left( W_{\phi}^* \Zo'(X) W_{\eta} \right) = W^*_{\phi} \Zo'(X) W_{\phi}  W_{\phi}^*W_{\eta} = 0 \, .
\end{equation}
It follows that
\begin{eqnarray}
\Eo(X) &=& W_{\phi'}^* \Zo'(X) W_{\phi'} \nonumber \\
&=& |\alpha|^2 W_{\phi}^* \Zo'(X) W_{\phi} + \bar{\alpha} \beta W_{\phi}^* \Zo'(X) W_{\eta} \nonumber \\
& &+\alpha \bar{\beta} W_{\eta}^* \Zo'(X) W_{\phi}+ |\beta|^2 W_{\eta}^* \Zo'(X) W_{\eta} \nonumber \\
&=& |\alpha|^2 \Ao(X) + |\beta|^2 \Fo(X),
\end{eqnarray}
where $\Fo$ is an observable induced by the measurement $\langle \K, \Zo, G, \eta \rangle$.
This contradicts the extremality of $\Eo$, hence $\ip{\phi}{\phi'} \neq 0$ must be false. \qed
\end{proof}

One may wonder if two extreme observables require orthogonal program states.
This is not the case as the following example illustrates.

\begin{example}
Covariant phase space observables have an important role in quantum mechanics \cite{CSWTG00}.
It is well known that every covariant phase space observable rises as an operator density defined by the \emph{Weyl operators} $W(q,p)=e^{\frac{i q p}{2}} e^{-i q P} e^{i p Q}$, $q,p\in \mathbb{R}$ and a state $\xi \in \sk$ in the form
\begin{eqnarray} \label{density}
\Eo^\xi(Z)=\frac{1}{2\pi} \int_Z W(q,p)\, \xi \, W(q,p)^* dq \, dp,
\end{eqnarray} for all $Z \in \mc B(\mathbb{R}^2)$.
It is easy to see that $\Eo^\xi$ is extremal in the set of all covariant phase space observables if and only if $\xi=P[\phi]$ for some unit vector $\phi\in \K$, and furthermore it has been shown in \cite{HePe12} that $\Eo^\xi$ is extremal in the set of all observables on $\mathbb{R}^2$ if and only if $\ip{\phi}{W(q,p)\phi}\neq 0$ for all $q,p\in \mathbb{R}$.
It follows that, for example, every Gaussian state $\phi_{a,b}(x)=N \text{exp}(-\frac{a}{2} x^2 + b x )$, where $a>0$, $b \in \mathbb{R}$ and $N$ is an appropriate normalizing constant, induces some extremal covariant phase space observable via (\ref{density}).

A physically feasible normal measurement model for such observables, based on \emph{eight port homodyne detection}, is described in \cite{KiLa07}.
In this particular model the vector state $P[\phi]$ of $\Eo^{P[\phi]}$ is regarded as the initial probe state. The above considerations show that two extremal observables do not necessarily require orthogonal vector states for programming since for example $\phi_{a,b}$ and $\phi_{c,d}$ are non-orthogonal for all $a,c>0$, $b,d\in \mathbb{R}$.
\end{example}

In the statement of Prop. \ref{obs:ex}, one can require that $\Eo$ is merely an extreme element of $\mc{O}_{\mc{M}}$ rather than of $\mc{O}$.
The proof is still valid without any changes.
Therefore, Prop. \ref{obs:ex} gives some indication on what the set $\mc{O}_{\mc{M}}$ looks like.
In the case where the maximal amount of sharp observables can be programmed, the structure of $\mc{O}_{\mc{M}}$  is particularly simple.

\begin{proposition}\label{obs:basis}
Let $\dim \K<\infty$.
Suppose one can program $n=\dim \K$ sharp observables $\Ao_1,\ldots,\Ao_n$, with a normal multimeter $\mathcal{M}$.
Then $\mc{O}_{\mc{M}}$ is the convex hull of the set $\{\Ao_1,\ldots,\Ao_n \}$.
\end{proposition}

\begin{proof}
The programming vectors $\phi_1,\ldots,\phi_n$ form an orthonormal basis of $\hik$.
Every unit vector $\psi\in\hik$ has a basis expansion $\psi = \sum_{i=1}^n \ip{\phi_i}{\psi} \phi_i$.
A similar calculation as in the proof of Prop. \ref{obs:ex} shows that the observable $\Eo$ obtained by using $\psi$ as a program state is
\begin{equation}
\Eo = \sum_{i=1}^n \mo{\ip{\phi_i}{\psi}}^2 \Ao_i \, .
\end{equation}
hence a mixture of the observables $\Ao_1,\ldots,\Ao_n$.

Every mixed program state $\xi$ has a convex decomposition into pure states, $\xi = \sum_{i} \lambda_i P[\psi_i]$.
The resulting observable $\Eo$ is a mixture of the observables corresponding to the pure states $P[\psi_i]$.
Thus, every observable in $\mc{O}_{\mc{M}}$ is a mixture of the observables $\Ao_1,\ldots,\Ao_n$.
\end{proof}

\subsection{Programming quantum channels}

As in the case of programming observables there is no multimeter which could be deterministically programmed to realize all channels, meaning that the set of programmable channels $\mc{C}_{\mc{M}}$ with a given multimeter $\mc{M}$ is always a proper subset of $\mc{C}$.
A special case in which the multimeter is assumed to be normal was first analysed by Nielsen and Chuang who showed that, when such a multimeter is programmed to realize two different unitary channels, the programming vectors must be orthogonal \cite{NiCh97}.

In this subsection we generalize this result for general (non-normal) multimeters capable of realizing two different unitary channels.
Again Proposition \ref{prop:ext}, together with the extremality of unitary channels, shows that one only needs to consider pure programming states.
We remind that, since the pointer observable plays no role in the channel programming scenarios, the corresponding entry in the measurement model is simply omitted; the programmable multimeter is given by a pair $\langle \K, \mc V \rangle$.
Often in the literature this also known as programmable \emph{gate array} or  \emph{processor}.

\begin{proposition}\label{chan:programming}
Let $\mathcal{M}=\langle \hik, \Vc \rangle$ be a multimeter and suppose that two different unitary channels $\Uc_1$ and $\Uc_2$ can be programmed with vector states $\phi_1$ and $\phi_2$, respectively.
Then $\phi_1$ and $\phi_2$ are orthogonal.
\end{proposition}

\begin{proof}
Suppose $\ip{\phi_1}{\phi_2}\neq 0$.
Since $\Uc_1 \neq \Uc_2$, there exists a projection $P\in\ph$ such that $\Uc_1(P) \neq \Uc_2(P)$.
We fix a sharp observable $\Ao$ such that $\Ao(X)=P$ for some $X\in\Sigma$.
For instance, $\Ao$ can be a two-valued observable consisting of projections $P$ and $\id_\hi-P$.
Further, we fix a measurement model $\langle \K_0, \Zo, \Vc_0, \eta \rangle$ for $\Ao$, where the program state $\eta$ can be chosen pure.
Then the concatenated multimeter in Fig. \ref{fig:concatenation} implements different sharp observables $\Ao_1=\Uc_1^*(\Ao)$ and $\Ao_2=\Uc_2^*(\Ao)$ with non-orthogonal programming vectors $\phi_1\otimes \eta$ and $\phi_2\otimes \eta$, respectively.
This contradicts Prop. \ref{obs:programming}, and hence $\ip{\phi_1}{\phi_2}\neq 0$ must be false.
\end{proof}

\begin{figure}
\includegraphics[width=0.95\textwidth]{mnt3.png}
\caption{An illustration of a concatenation of a multimeter $\langle \K, \mc V \rangle$ and an $\Ao$-measurement $\langle \K_0, \Zo, \mc V_0, \eta \rangle$ used in proposition  \ref{chan:programming}.}
\label{fig:concatenation}
\end{figure}

As in the case of observables, a stronger version of Prop. \ref{chan:programming} is obtained when the multimeter is assumed to be normal.
The proof is analogous to that of Prop. \ref{obs:ex}.

\begin{proposition}\label{chan:ex}
Let $\mathcal{M}= \langle \hik, G \rangle$ be a normal multimeter and suppose two different channels, a unitary channel $\Uc$ and an extreme channel $\Ec$, can be programmed with vector states $\phi$ and $\phi'$, respectively.
Then $\phi$ and $\phi'$ are orthogonal.
\end{proposition}

\begin{proof}
Assume $\ip{\phi}{\phi'}\neq 0$.
Then $\phi'$ can be written as $\phi'=\alpha \phi + \beta \eta$, where $\ip{\phi}{\eta}=0$ and $\alpha,\beta \in \C\setminus\{0\}$ satisfy $|\alpha|^2 + |\beta|^2 = 1$.
We recall from Prop. \ref{prel:unitary} that the unitarity of the channel $\Uc$ implies $[G^* (B\otimes \id_\hik)G, W_\phi W_\phi^*]=0$ for all $B\in \lh$.
It follows that
\begin{equation}
W_{\phi}^*  G^*(B\otimes \id_\hik)G W_{\eta} =  0 \, ,
\end{equation}
and hence
\begin{eqnarray}
\Ec^*(B) &=& W_{\phi'}^*  G^*(B \otimes \id_\hik)G  W_{\phi'} \nonumber \\
&=& |\alpha|^2 \Uc^*(B) + |\beta|^2 \Fc^*(B) \, ,
\end{eqnarray}
where $\Fc$ is a channel.
This contradicts the extremality of $\Ec$, thus $\ip{\phi}{\phi'} \neq 0$ must be false.
\end{proof}

The next example shows that sheer extremality of the channels is not enough to imply orthogonality of the programming states.

\begin{example}
Choose two non-orthogonal unit vectors $\varphi,\varphi'\in\hi$.
The corresponding complete state space contractions are extreme channels, and they can be programmed with a normal multimeter $\langle \hi, G_{\text{SWAP}}\rangle$ and non-orthogonal program states $\varphi$ and $\varphi'$, respectively.
Here $G_{\text{SWAP}}$ is the 'swap' unitary operator defined as
\begin{equation*}
G_{\text{SWAP}} \psi_1\otimes\psi_2 = \psi_2 \otimes \psi_1 \, .
\end{equation*}
\end{example}

The proof of the following result is the same as the proof of Prop. \ref{obs:basis} with obvious changes, so we omit it.

\begin{proposition}
Let $\dim \K<\infty$.
Suppose one can program $\dim \K=n$ unitary channels $\Uc_1,\ldots,\Uc_n$, with a normal multimeter $\mathcal{M}$.
Then $\mc{C}_\mc{M}$ is the convex hull of the set $\{\Uc_1,\ldots,\Uc_n \}$.
\end{proposition}

\begin{example}\label{ex:push} An example of a normal multimeter in previous proposition is the "push-a-button" multimeter for which $G = \sum_{i=1}^n U_i \otimes P[\phi_i]$. Indeed we have $\mc U_i(\rho) = \ptr{G (\rho \otimes P[\phi_i]) G^*}$ for every $i=1,...,n$. We shall return to this multimeter in the last section \ref{sec:eff}.
\end{example}

\subsection{Post-processing assisted programming of quantum observables}

\emph{Post-processing} is classical information processing of the obtained measurement statistics: merging together, relabeling and weighting measurement outcomes in a stochastic manner.
Mathematically post-processing is described by a classical-to-classical channel $\Lambda$ between probability measures on measurable spaces $(\Omega, \Sigma)$ and $(\Omega', \Sigma')$.

\begin{figure}[h]
\includegraphics[width=1.0\textwidth]{postprocessing.png}
\caption{Post-processing is a classical manipulation of measured statistics described by a classical-to-classical channel $\Lambda$. }\label{fig:postpr}
\end{figure}

In particular this channel $\Lambda$ maps measurement statistics of the measured observable $\Eo:\Sigma\rightarrow\lh$ into those of another \emph{fuzzy} observable $\Eo':\Sigma'\rightarrow\lh$ via $\Lambda(\tr{\Eo(\cdot) \, \rho}) = \tr{\Eo'(\cdot) \, \rho}$, for all $\rho \in \sh$; see Fig. \ref{fig:postpr}.
Under certain technical assumptions (see \cite{JePuVi08} for details), the action of the channel $\Lambda$ can be equivalently described by a \emph{Markov kernel}, i.e., a map $k: (\Omega,\Sigma') \rightarrow \left[0,1\right]$ such that
\begin{itemize}
\item[(i)] $k(x, \cdot)$ is a probability measure for every $x\in \Omega$,
\item[(ii)] $k(\cdot, X)$ is measurable for every $X \in \Sigma'$,
\end{itemize}
acting via formula $\Eo'(X) = \int k(x, X) \, d\Eo(x)$.
The properties of post-processing have been studied for example in \cite{MaMu90a,BuDaKePeWe05,Heinonen05,JePu07}.

Post-processing can be taken as an additional component of a measurement model, so that a measurement model is understood as a 5-tuple $\langle \K, \Zo, \mc V, \xi,k \rangle$.
If post-processing is included in programming, then the programmability of quantum observables changes.
For instance, jointly measurable observables can be implemented without changing the probe state at all; we just fix a measurement model for their joint observable and post-process the measurement statistics by calculating the marginals.

Surprisingly, different sharp observables may not require orthogonal programming states if post-processing is allowed.
In the following we present an example of a measurement model capable of programming three sharp spin-observables, $\So_i(\pm) = \frac{1}{2}(\id_{\C^2} \pm \sigma_i)$, $i=1,2,3$, with non-orthogonal programming vectors. Here $\sigma_i$, $i=1,2,3$, are the conventional \emph{Pauli spin operators}.
The example is a more explicit version of the one constructed in \cite{ZiBu05}.

\begin{example}
Let the apparatus Hilbert space be $\K= \C^4$ with orthonormal basis $\{|i \rangle \, | \, i=0,1,2,3\}$ and define the (non-orthogonal) programming vectors $\phi_i = \frac{1}{\sqrt{2}}(|0 \rangle+|i \rangle)$, $i=1,2,3$. One easily checks that $G = \sum_{j,k=0}^3 \frac{1}{2} \sigma_j \sigma_k \sigma_j \otimes |j \rangle \langle k |$, where $\sigma_0 = \id_{\C^2}$, is an unitary operator on $\C^2 \otimes \C^4$.
A straightforward calculation shows that the effects of the measured observable in the model $\langle \K, \Zo, G, \phi_i\rangle$, where $\Zo(j)=|j\rangle\langle j |$, are given by $\Eo_i(j) = \frac{1}{4}\left( \id_{\C^2} + \sigma_j \sigma_i \sigma_j\right)$. Using three different post-processings we get
\begin{eqnarray}
\begin{array}{lr}
\So_1(+) = \Eo_1(0)+\Eo_1(1)\, , & \So_1(-) = \Eo_1(2)+\Eo_1(3) \\
\So_2(+) = \Eo_2(0)+\Eo_2(2)\, , & \So_2(-) = \Eo_2(1)+\Eo_2(3) \\
\So_3(+) = \Eo_3(0)+\Eo_3(3)\, , & \So_3(-) = \Eo_3(1)+\Eo_3(2)
\end{array}.
\end{eqnarray}

More generally, define a unit vector $\phi_{(\alpha, \vec{a})} \in \K$ to be $\phi_{(\alpha, \vec{a})} = \left(\alpha |0\rangle +\sum_{i=1}^3 a_i |i\rangle \right)$, where $\alpha \in \mathbb{R}$ and $\vec{a}=(a_1,a_2,a_3)\in\mathbb{R}^3$ satisfy the normalization $\alpha^2 + \sum_i a_i^2 = 1$. Programming of the above multimeter with $\phi_{(\alpha, \vec{a})}$ induces an observable $\Eo_{(\alpha, \vec{a})}(j) = \frac{1}{4}\left(\id_{\C^2} + 2 \alpha\, \sigma_j (\vec{a} \cdot \vec{\sigma}) \sigma_j\right),$ which is easily proven using the property $\{\sigma_j, \sigma_k\} = 2\delta_{jk} \id_{\C^2}$ for $j,k =1,2,3$. In particular the choise $\alpha = 1/\sqrt{2}, a_i = 1/\sqrt{6},$ $i=1,2,3$ induces a \emph{symmetric informationally complete} observable $\Eo(j)= \frac{1}{4}(\id_{\C^2} + \frac{1}{\sqrt{3}} \sum_i \sigma_j \sigma_i \sigma_j )$.
\end{example}

The previous example illustrates that some sharp observables can indeed be programmed with non-orthogonal programming vectors if post-processing is allowed.
The explanation for this is simple: although post-processing should be viewed as classical processing of information, it effectively alters the pointer observable.
To see this, let $\langle \K, \Zo, \mc V, \phi, k \rangle$ be a measurement model for $\Eo$, where $k: (\Omega, \Sigma) \rightarrow \left[0,1\right]$ is a Markov kernel.
Using the formula \eqref{obs:repro}, linearity and continuity we have
\begin{eqnarray}
\Eo(X) &=& \int k(x, X) \, \ptr{ \mc V^*( \id_\hi \otimes d\Zo(x)) \, \id_\hi \otimes P[\phi]}\nonumber \\
&=&\ptr{ \mc V^*( \id_\hi \otimes \left(\int k(x, X)\, d\Zo(x)\right)) \id_\hi \otimes P[\phi]} \nonumber \\
&=& \ptr{ \mc V^*( \id_\hi \otimes \Zo'(X) ) \, \id_\hi \otimes P[\phi]},
\end{eqnarray}
where  $\Zo'(X) = \int k(x, X) \, d\Zo(x)$.
This shows that $\langle \K, \Zo,\mc  V, \phi, k \rangle$ and $\langle \K, \Zo', \mc V, \phi \rangle$ are equivalent as measurements of $\Eo$.
But because the pointer is no longer kept fixed (if the Markov kernel is changed), the derivation in Prop. \ref{obs:programming} leading to the orthogonality of programming vectors does not hold anymore.

We note that if the pointer observable is altered arbitrarily, then all observables acting on a given Hilbert space can be implemented with a single a measurement model \cite{HeMiRe14}.
It is, however, left as a open question whether there exists a universal state-programmable multimeter capable of measuring every observable when post-processing is allowed.

Since the post-processing only affects the pointer observable, it is obvious that the programmability of channels does not change even if post-processing is allowed.

\section{Efficiency of a Quantum Multimeter}\label{sec:eff}

In this section we shortly study the effectiveness of quantum multimeters and give limits to efficient programming. Throughout the section we assume that post-processing is not allowed.

As discussed in Sec. \ref{sec:memo}, a normal measurement model $\langle \K, \Zo, G, \phi \rangle$ constitutes a special type of Naimark dilation of the measured observable $\Eo$, called a measurement dilation of $\Eo$.
Different measurement dilations of a given observable can be arranged by the dimensions of the auxiliary Hilbert spaces.
This gives us a natural quantification of effectiveness: \emph{the smaller} the apparatus' dimension, \emph{the more efficient} the measurement.

It has been shown in \cite{Pellonpaa14} that the minimal dimension of the apparatus $\K$ corresponding to the minimal measurement dilation of a $N$-valued (sharp) observable is $\dim \K =N$ and such a minimal measurement can always be found.
For readers convenience we present here a slightly different proposition proving this fact.

\begin{proposition}\label{prop:minimal}
Let $\Ao$ be a $N$-valued sharp observable.
\begin{itemize}
\item[(a)] There exists a normal measurement model $\langle \K, \Zo, G, \phi \rangle$ of $\Ao$ with $\dim \hik  = N$.
\item[(b)] Any measurement model $\langle \K, \Zo, \mc V, \xi \rangle$ of $\Ao$ satisfies $\dim \hik  \geq N$.
\end{itemize}
\end{proposition}

\begin{proof}
\begin{itemize}
\item[(a)]
Let $\K$ be a Hilbert space with $\dim \K = N$ and fix an orthonormal basis $\{\varphi_j \}_{j=1}^N$ for $\hik$.
For each $j=1,...,N$, define a unitary operator $G_j$ on $\hik$ as
\begin{eqnarray}
G_j \varphi_k = \left\lbrace
\begin{array}{ll}
\varphi_1, & \quad j=k \\
\varphi_k, & \quad j\neq k\neq 1\\
\varphi_j, & \quad k=1
\end{array} \right. .
\end{eqnarray}
Further, define $G = \sum_j \Ao(j) \otimes G_j^*$, which is a unitary operator on $\hi\otimes\hik$.
By choosing the pointer observable as $\Zo(k) = |\varphi_k\rangle\langle\varphi_k|$ and the initial probe state as $\phi=\varphi_1$, we get
\begin{eqnarray}
W^*_{\phi} \, G^*\left( \id_\hi \otimes \Zo(k)\right) G \, W_{\phi} &=& \sum_j | \ip{G_j \varphi_k}{\varphi_1}|^2 \, \Ao(j)\nonumber \\
&=& \Ao(k) \, ,
\end{eqnarray}
proving that $\langle \K, \Zo, G, \phi \rangle$ is a measurement model of $\Ao$.
\item[(b)]
Let $\langle \K, \Zo, \mc V, \xi \rangle$ be a measurement model of $\Ao$.
We first note that the pointer observable $\Zo$ must be $N$-valued (though not necessarily sharp) and the probe state can be chosen pure, $\xi = |\phi\rangle\langle\phi|$.
Since $\Ao$ is sharp, there exist orthonormal vectors $\varphi_1,\ldots,\varphi_N$ such that $\Ao(j) \varphi_i = \delta_{ij} \varphi_j$.
Then the probability reproducibility condition gives
\begin{eqnarray}
\delta_{ij} = \tr{\Ao(j)\, P[\varphi_i]} &=& \tr{\id_\hi \otimes \Zo(j) \, \mc V (P[\varphi_i]\otimes \xi) } \nonumber \\
&=&\tr{\Zo(j) \, \hptr{ \mc V(P[\varphi_i]\otimes\xi)}} \nonumber \\
&=&\tr{ \Zo(j) \, \zeta_i},
\end{eqnarray}
where $\zeta_i = \hptr{\mc V(P[\varphi_i]\otimes \xi)}$.
It follows that $\Zo(j) \zeta_i = \delta_{ij} \, \zeta_j$, and therefore
\begin{eqnarray}
\zeta_i  \, \zeta_j = \zeta_i  \, \Zo(j) \zeta_j = (\Zo(j) \zeta_i)^* \, \zeta_j = \delta_{ij}  \, \zeta_j^2,
\end{eqnarray}
meaning that the supports of the operators $\zeta_i$ and $\zeta_j$ are orthogonal as subspaces whenever $i\neq j$.
We thus have $N$ orthogonal subspaces in $\hik$, so $\dim\hik \geq N$.
\end{itemize}
\end{proof}

Obviously this sets further limitations to the programming scenarios of sharp observables in addition to those seen in \ref{sec:probs}. We summarize these observations in the following proposition.

\begin{proposition}
Programming of different sharp observables $\Ao_1,\ldots,\Ao_n$, with $N_i$ values, respectively, can be done only if the apparatus $\K$ satisfies $\dim \K \geq \max \{ n, N_1,...,N_n \}.$
\end{proposition}

\begin{example}
Let $\Ao_1$ and $\Ao_2$ be sharp spin-observables.
Since the effects $\Ao_1(\pm)$ and $\Ao_2(\pm)$ are rank-1 projections in a two dimensional Hilbert space, there exists a unitary operator $R$ on $\C^2$ such that  $\Ao_2 =  R^* \Ao_1 R$.
Now let $\phi_1$ and $\phi_2$ be any pair of orthonormal vectors and define a unitary operator $G = G_{\text{SWAP}} (\id_{\C^2} \otimes P[\phi_1] + R \otimes P[\phi_2])$.
One easily verifies that $\langle \C^2, \Ao_1, G\rangle$ is a multimeter that can be programmed to measure $\Ao_1$ and $\Ao_2$ with vectors $\phi_1$ and $\phi_2$, respectively.
This shows that at least in this particular case the minimal programming dimension can indeed be reached.
\end{example}
 \begin{figure}[h]\label{fig:push}
\includegraphics[width=1.0\textwidth]{pushabutton3.png}
\caption{Illustration of the "push-a-button" programming protocol. Minimal measurement devices for each observable are bundled together and one simply chooses beforehand which one to use.}
\end{figure}
An inefficient way of programming $n$ observables is to have minimal measurements $\langle \K_j, \Zo_j, G_j, \phi_j\rangle$ for each observable $\Ao_j$ individually and simply to select beforehand which one should be performed (see Fig. \ref{fig:push}) .
Mathematically this ''push-a-button'' protocol is described by a programmable multimeter $\langle \K, \Zo, G \rangle$ and programming vectors $\Phi_i, \ i=1,...n$ where
\begin{eqnarray*}
\K=\otimes_{j=1}^n \K_j  \otimes \C^n \\
\Zo=\left( \otimes_{j=1}^n \Zo_{j} \right)\otimes \id_{\C^n} \\
G=\left( \sum_{i=1}^n G_i \otimes_{j\neq i}^n \id_j   \otimes |i\rangle\langle i | \right) \\
\Phi_i = \left( \otimes_{j=1}^n \phi_j \right) \otimes |i\rangle
\end{eqnarray*}

The size of this "push-a-button" -multimeter is $\dim \K = n \cdot \Pi_{i=1}^n N_i$. We take this trivial programming scenario, which nevertheless can always be performed for any finite set of (sharp) observables, as the upper bound of effectiveness of a multimeter.
We conclude that in every interesting programming protocol capable of programming sharp observables $\Ao_i$, $i=1,...,n$, the size of the apparatus $\dim \K$ satisfies the bounds
\begin{eqnarray}
\max\{n,N_1,...,N_n\} \leq \dim \K \leq n \cdot \Pi_{i=1}^n N_i.
\end{eqnarray}

\begin{proposition}
Let $\Ao_1,\ldots,\Ao_n$ be sharp observables with $N_1,\ldots,N_n$ values, respectively.
There exists a normal multimeter $\langle \K, \Zo, G \rangle$ with $\dim \K=n \cdot \max\{N_1,...,N_n\}$ capable of realizing each of the $\Ao_i$ $i=1,...,n$.
\end{proposition}

\begin{proof}
Denote $d= \max\{N_1,...,N_n\}$. Let $\K = \K_1 \otimes \K_2$ with $\dim \K_1=d$ and $\dim \K_2=n$, and fix some orthonormal bases $\{\phi_k\}_{k=1}^d \subset \K_1$ and $\{\eta_l \}_{l=1}^n  \subset \K_2$. Define the unitaries $G_j: \K_1 \rightarrow \K_1$, $j=1,...,d$, as in Prop. \ref{prop:minimal}.
Extend every observable $\Ao_l$ to be ''$d$-valued'' by adding zero-effects, if necessary, and define the coupling to be
\begin{equation}
G= \sum_{j=1}^d \sum_{l=1}^n   \Ao_l(j) \otimes G_j^* \otimes P[\eta_l] \, .
\end{equation}
Finally, choose the pointer observable to be $\Zo(k)= |\phi_k\rangle\langle\phi_k| \otimes \id_{\K_2}$. Then
\begin{eqnarray}
&& \ptr{ G^*\left( \id_\hi \otimes \Zo(k)\right) G \, \id_\hi \otimes P[\phi_1 \otimes \eta_i] } \nonumber \\
&=& \sum_{j,j',l,l'} \Ao_l(j) \Ao_{l'}(j')\, \tr{|G_j \phi_k \rangle\langle G_{j'} \phi_k| \, P[\phi_1]} \,  \tr{ P[\eta_{l}] \, P[\eta_{l'}] \, P[\eta_i]} \nonumber \\
&=& \Ao_i(k).
\end{eqnarray}
This shows, that if one chooses $\Phi_i=\phi_1\otimes \eta_i$, then for every $i=1,...,n$ $\langle \K, \Zo, G, \Phi_i \rangle$ is an $\Ao_i$-measurement.
\end{proof}

Following the methods introduced above one can also study the effectiveness of channel programming. Since one can induce an arbitrary unitary channel $\mc U^* (B) = U^* B U$ from a normal measurement model $\langle \K, G, \phi\rangle$ using a unitary coupling $G = U \otimes \id_\K$, we note that $\min \dim \K =1$.
Interestingly enough, from the point of view of deterministic programming this means that the ''push-a-button'' realization of $n$ unitary channels (see Ex. \ref{ex:push}) is actually the most efficient protocol one can have. This implies that when engineering unitary quantum gate arrays, it's sufficient to build every gate individually and bundle those into an array respecting the ''push-a-button'' protocol.

\section{Conclusions and discussion}\label{sec:discussion}

The fundamental limitations on the deterministic programming of sharp observables or unitary channels are essentially the same.
We have shown how these two scenarios are connected and can be put into a common framework by using the general theory of quantum measurements. In particular, we have generalized the orthogonality result from Nielsen and Chuang, in which the programmable multimeter/gate array is described by a unitary channel, to a completely general case in which the channel is arbitrary. We emphasize, that the original no-go theorem of perfectly precise programmable quantum gate array by Nielsen and Chuang would hold also in this case via dilating the channel into a unitary one. The drawback in this dilation approach is that it doesn't address the orthogonality in the context of original space. Our results clarify this aspect.

This article deals with qualitative aspects of quantum programming, namely the orthogonality of the programming vectors of sharp observables and unitary channels. A quantitative study on the connection between the distance of programming states and the distinction of programmed devices will be the subject of a separate investigation.
It would also be interesting to answer whether or not a deterministically programmable multimeter capable of measuring every quantum observable is possible, if post-processing is allowed.

\section*{Acknowledgements}

This work has been supported by the Academy of Finland (grant no. 138135). M.T. acknowledges financial support from the University of Turku Graduate School (UTUGS).
The authors are grateful to Jussi Schultz for his comments on an earlier version of this manuscript. M.T. would also like to acknowledge Erkka Haapasalo for many useful discussions.

redpajama_set_name: RedPajamaArXiv


text:
Q: Keep running Jupyter notebook if VPN is disconnected I use a company VPN like many others for work. We have Jupyterhub installed on the Kubernetes cluster accessed via ip_address:port. The ip_adress can only be accessed if VPN is connected.
My company's VPN disconnects after 9 hours. The jupyter notebooks running on the hub also stop running. How do I keep the notebooks running even after I reconnect VPN?

redpajama_set_name: RedPajamaStackExchange


I had the honour of judging the Canada's Smarted and Canada's Greenest IT awards along with James Alexander, CEO of the Quest for Canada's Smartest IT (@JamesFAlexander) and Shirley Blayney, General Business Solutions Manager at IBM. There were some fabulous nominations. I was happy to see how Canadian organizations are providing advanced business solutions while taking care of the planet.
The Quest for Canada's Smartest IT is a competition that recognizes Canadian companies using technology to help their business, the environment and their communities. 2011 marks the second year of our wildly successful competition.
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The awards ceremony will be held Thursday, 17 November in Toronto. I will be presenting the Canada's Smartest IT Award.
You can register now and participate in celebrating Smart IT/Green IT at no charge. There is a door charge if you can't register in advance.


Join Super Barbie in the make-up room and help her find some missing items. They are all somewhere in the room, you just have to look carefully. They are tiny objects and that's why Super Barbie has so much difficulty in finding them. Help her with your skills and she will be very thankful. Have a great time playing this new skill game with Super Barbie!


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Defense analysts see unmanned weaponry as the future of warfare, but critics question oversight.
ABOARD USS GEORGE H.W. BUSH – A drone the size of a fighter jet took off from the deck of an American aircraft carrier for the first time Tuesday in a test flight that could eventually open the way for the U.S. to launch unmanned aircraft from just about any place in the world.
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Still, defense analysts say drones are the future of warfare.
The new Joint Strike Fighter jet "might be the last manned fighter the U.S. ever builds. They're so expensive, they're so complex, and you put a human at risk every time it takes off from a carrier," said James Lewis, senior fellow at the Center for Strategic and International Studies in Washington.
While the X-47B isn't intended for operational use, it will help Navy officials develop future carrier-based drones. Those drones could begin operating by 2020, according to Rear Adm. Mat Winter, the Navy's program executive officer for unmanned aviation and strike weapons.
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Developed by Northrop Grumman under a 2007 contract at a cost of $1.4 billion, the X-47B is capable of carrying weapons. The X-47B can reach an altitude of more than 40,000 feet and has a range of more than 2,100 nautical miles.


text:
Q: sqlcmd won't work on ubuntu despite standard installation and usage I followed the instructions on the MS site and installed tools including sqlcmd.
I followed the examples, with several variants
sqlcmd -H 12.34.56.78,1234 -U $user -P $passwd -d $database -Q "SELECT * FROM blodge"

sqlcmd -S 12.34.56.78,1234 -U $user -P $passwd -d $database -Q "SELECT * FROM blodge"

sqlcmd -S tsp:12.34.56.78,1234 -U $user -P $passwd -d $database -Q "SELECT * FROM blodge"

and got errors like

Sqlcmd: Error: Microsoft ODBC Driver 17 for SQL Server : Login failed for user 'muggins'..

and

Sqlcmd: Error: Microsoft ODBC Driver 17 for SQL Server : Protocol error in TDS stream.
  Sqlcmd: Error: Microsoft ODBC Driver 17 for SQL Server : Client unable to establish connection due to prelogin failure.

[Note I have changed URL, etc, above.  Also, I checked that all the login details are correct]
Thanks for any help [open to alternatives to sqlcmd also!]
P.S. I have tested the connection from the GUI MySQL client
PPS Ubuntu 18.04

A: The correct format is the second one:
sqlcmd -S 12.34.56.78,1234 -U $user -P $passwd -d $database -Q "SELECT * FROM blodge"

The default SQL Server port is 1433, but as you seem to reach SQL Server ("Login failed for user.."), double check your username/password or try to leave out the -P parameter from the command so you see if you get the password prompt.


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Pieter Crijnse Volmarijn, né en 1629 et décédé en 1679 à Rotterdam, est un peintre siècle d'or néerlandais.

Selon le RKD, il est élève de Hendrick Martensz Sorgh et Nicolaus Knüpfer et travaille à Utrecht. Il est peut-être le fils ou le neveu de Crijn Hendricksz Volmarijn.

Notes et références

Liens externes

 Pieter Crijnse Volmarijn sur Artnet

Naissance en 1629
Naissance à Rotterdam
Naissance dans les Provinces-Unies
Décès en avril 1679
Décès à Rotterdam
Décès dans les Provinces-Unies
Peintre néerlandais du XVIIe siècle
Peintre de l'âge d'or néerlandais

redpajama_set_name: RedPajamaWikipedia


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Waving away the protests of Dr. Will Hamilton, legendary singer Anita Jane Wells fakes an illness to con her young protégé, singing star Lyndsay
Rose, into flying to Missouri to take over her Christmas show in Branson. Anita Jane claims she's a Christmas angel, doing this for Lyndsay's own
good so she won't spend another Christmas alone. Once he sees her distress for Anita Jane, Will tells Lyndsay the truth, and the duo plot to make
Anita Jane's recuperative time absolutely miserable. But you can't hinder a Christmas angel's scheme, as Lyndsay and Will discover in this romantic comedy.
Q & A with Veda Boyd Jones regarding An Ozark Christmas Angel:
Q: This book is set in Branson, Missouri. Why?
A: I speak in Branson each May at the 6th grade Lit Fest, and each year the school provides special tickets to the authors, so I've been to several of the shows on the strip. Branson is a fascinating place with a combination small town and the glitz and lights of the strip. When I thought of giving a cameo role to characters (Callie and Morgan) from a previous romance, I needed a musical setting. Branson came to mind, and I built the story around a country music star. Callie and Morgan are only on a handful of pages, but it was fun to include them for anyone who has read the earlier e-book, Mountain Love Song.
Q: Have you ever stayed at Big Cedar Lodge that you used in the book?
A: Yes, I've stayed in one of the cabins, so I could use that experience and put the wood-burning fireplace and the hunting cabin atmosphere in the story.
Q: In the story, Lyndsay forgets the 'deathday' of her husband. Do you feel this is something people should forget?
A: Birthday and deathday are the bookends of a life. I like celebrating the beginning of life, but not the end. Human nature tends to make us remember the hard times, and I'll admit, I remember the death days of loved ones, but I try to focus on the life lived instead of the ending. I stuck that in there as a message that we should enjoy each day, and not let one be tainted by what happened years earlier.
Q: There's quite a bit of deception in An Ozark Christmas Angel, and yet a surprise ending. How did you think of this?
A: I wanted the reader to think she/he had figured out why Anita Jane manipulated Lyndsay into going to Branson to do her show, but I had a little fun with it. I really didn't know I'd twist it up a bit until I wrote the ending.


THE IRISH public warmly greeted the words of Minister for Transport, Tourism and Sport Shane Ross when he confirmed the entire FAI board would resign from their positions in July, however, since this news emerged it has become clear that in a further act of sly japery the board wrote their resignations in slowly disappearing ink.
The disappearing ink used only lasted 3 hours before completely fading from the resignation letters which goes some way to account for the fact John Delaney is currently only offering to temporarily step aside from his Executive Vice President role while various inquiries are being conducted.
When the FAI board was asked by a journalist if this meant Delaney would not be receiving his new and as yet still undisclosed EVP salary while not actively working, they fell about the room laughing and encouraged the journalist to try a career in stand up, they were that funny.
To heap more misery and stress of Delaney, leading groups of scientists have requested permission to run tests on the FAI's former CEO in a bid to find out if he would be the only human being capable of surviving a nuclear holocaust even if he was just metres from the initial blast zone.


An elevated take on the classic sneakers from childhood. The Diego Low Top Sneaker takes it up a notch with a Vibram sole and beautiful leather upper. Wear it to work or while on vacation, it's as versatile as it is comfortable. All Nisolo sneakers come equipped with two types of laces, both cotton and waxed cotton, to fit your style. Handmade in an ethical factory in León, Mexico.
If you prefer a more roomy fit, we recommend ordering true to size. However, we recommend sizing down a half size if you plan to wear thin socks or no socks as the sneaker does run bit large.


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Browse 69 market data Tables and 66 Figures spread through 146 Pages and in-depth TOC on "Robotic Process Automation Market - Global Forecast to 2022"
The robotic process automationmarket for the healthcare and pharmaceuticals industry is expected to grow at the highest CAGR between 2017 and 2022. The healthcare and pharmaceuticals industry is highly information-dependent, as it involves medical records of patients, credentials of patients, information on claims processing, revenue cycle management, etc. In this regard, robotic process automation not only helps reduce operational costs but also ensures greater accuracy. The interactive solutions offered by robotic process automationhelp efficiently manage data, reduce medical transportation costs, lower appointment scheduling errors, and so on.
Robotic process automation tools held the largest market share in 2016 owing to its capability of eliminating repeatable and predictable human interactions with business applications by mimicking the way people interact with applications through a user interface and also by following simple rules to make decisions. Tool-based lifecycle management can be divided into requirement definition, initial design, application development, testing, deployment, and release and maintenance. It also involves tracking and documenting changes throughout the process of the application.
The robotic process automation market for North America held the largest share among all the regions under study in 2016 and is expected to dominate the market between 2017 and 2022. In the US, BFSI has been leveraging robotics process automation to improve business processes since 2010. Due to the high degree of flexibility and scalability of the solution, as well as greater data processing and workflow management capabilities, there is widespread deployment of robotic process automation in the BFSI space. The growth of robotic process automation in Canada is driven by the ramp-up of the banking and financial industry. Human resource outsourcing, business process outsourcing, and contact center outsourcing have seen tremendous growth in Canada in recent times. The growth of the robotic process automation market in Mexico is driven by the booming manufacturing industry. New factories and manufacturing units are being built in Mexico, requiring proper supply chain management to be implemented to reduce costs. Inventory management, purchase order, stocking goods, and economic order quantity management require automated processes—backed by software bots.
The report profiles the most promising players in the robotic process automation market. The competitive landscape of the market presents an interesting picture of strategies adopted by a large number of players. Nice Systems Ltd. (Israel), Automation Anywhere (US), Blue Prism Group Plc (UK), Celaton Ltd. (UK), IPSoft, Inc. (US), Pegasystems Inc. (US), Redwood Software (US), UiPath SRL (UK), Verint Systems Inc. (US), and Xerox Corporation (US) are few dominant players in the robotic process automation market.
Don't miss out on business opportunities in Robotic Process Automation Market. Speak to our analyst and gain crucial industry insights that will help your business grow.