I would argue in a slightly different vein than the other (good) answers. Technically, you don't need to know how quantum physics works at all, to write hard science fiction that uses it. The only thing you need to know is what it can do. Or rather what people that understand it believe it will be able to do in the future.
There is of course the engineering-porn side of hard scifi with its endless infodumps, but in general those do not advance the story and are somewhat rightfully considered a bad habit. There are also stories that hinge on how a very specific concept in engineering or physics is implemented precisely, but there are many times as much that don't.
For most people, technology is just a tool. To answer your question, I need know that the words I am typing right now will appear on this page where you can read them after I press the big button at the bottom. I do not need to be able to program, or to know how a computer works, or the internet, or how to set up a server, I only need to know what actions I can take and what effects they have. And even though in fact I actually know all this, I rarely feel the need to tell people about it if they don't explicitly ask or it somehow helps me to make a point.
The same is true for the characters in your novel. To them their quantum-whatever-device might be an every day object, so they are used to it and don't reflect on its inner workings. Or some Q'ish science boffin might hand them this brand new device, telling them that they shouldn't even try to understand how it works, it's way above their paygrade, but in recognition of that it's been made foolproof. 634
Just press that button and thing happens.
What makes your story hard science fiction is that the existence of such a device in the future is plausible. Leave it to the reader to figure out the details if they want to. In fact you can get away with more this way than if you explain everything. It is much harder to prove that something cannot be done than that something cannot be done in this very specific way. Equally, any plotholes of the "why didn't they construct device X using the same technology as in device Y" are less likely to occur if you don't know the details of Y that might prevent this.
So just grab some popular science magazine or read around on wikipedia about proposed technologies related to your plot and figure out what proponents say that they can do and what critics say their problems are. Then find some place in between and use them for your story.
To take your quantum physics example, if you read around a bit in science news, you will find people talking about quantum computers and quantum encryption. Of the former people apparently think that they might be able to crack any classical encryption, but right now they are big experimental device requiring clean rooms and special cooling and so on. Of the latter they think that it is uninterceptable, but you need a line of sight or a direct fiber connection to exchange "entangled particles" or whatever that is (I am being deliberately obtuse here).
This is already enough material to spawn a mid 21st century hard scifi spy story: Agent 008 obtains an encrypted storage device with important information from the last remnants of resistance in now fully occupied Hong Kong and somehow has to get it back home for decryption by the agencies quantum computers, all without it being intercepted. His quantum encrypted satellite line is way to slow for this amount of data, all fast modes of communication are watched and the borders are closed. How can he get the storage device out of the country without causing an international incident? How long does he have until his opponents notice what a treasure he is carrying? 209