text:
\section{Preliminaries}\label{sec: 1}
The counterfactual quantum communication \cite{SLAZ:13:PRL,AV:19:PRA} is based on the single-particle nonlocality and quantum measurement theory.  A quantum state usually collapses back to its initial state if the time between repeated measurements is short enough \cite{IHBW:90:PRA}. This \ac{QZ} effect  has been demonstrated to achieve the \ac{IFM}  where the the state of a photon acts as an unstable quantum state corresponding to the presence of the absorptive object \cite{KWHZK:95:PRL}. We begin with detailed state transformations of the \ac{CCT} protocol for general input states and then briefly review the overall actions of the \ac{QZ} and  \ac{CQZ} gates \cite{ZJS:18:SR,ZJS:19:SR} that are invoked to devise  \ac{CCT}.

\subsection{\ac{CCT}}

 Alice and Bob start the protocol with the initial composite state $\ket{\psi_0}_\mathrm{AB}=\ket{\psi}_\mathrm{A}\ket{\psi}_\mathrm{B}$ where $\ket{\psi}_\mathrm{A}$ and $\ket{\psi}_\mathrm{B}$ are given in (6) and (7) of the main text, respectively. Bob applies the CNOT operation locally where Bob's qubit acts as a control and the ancillary qutrit is a target (see Fig.~1 in the main text). It transforms $\ket{\psi_0}_\mathrm{AB}$ to
\begin{align}
\ket{\psi_1}_\mathrm{ABC}
	=
	\ket{\psi}_\mathrm{A}
	\left(
		\gamma
		\ket{00}_\text{BC}
		+
		\delta
		\ket{11}_\text{BC}
	\right).\label{eq:psi 1}
\end{align}

The counterfactual Toffoli gate $\M{T}$ transforms $\ket{\psi_1}_\mathrm{ABC}$ to
\begin{equation}
\begin{aligned}
\ket{\psi_2}_{\text{ABC}}
	&
	=
	\gamma
	\ket{\psi}_\mathrm{A}
	\ket{00}_\text{BC}
	\\
	&\hspace{0.35cm}+
	\delta
	\big(
		\alpha
		\ket{01}_\text{AB}
		+
		\beta
		\ket{10}_\text{AB}
	\big)
	\ket{1}_\text{C}.
\end{aligned}
\label{eq:psi 2}
\end{equation}
Then, the local operation $\M{V}_1\hspace{-0.05cm}\left(\M{U}\right)$ at Bob's side transforms
$\ket{\psi_2}_{\text{ABC}}$ to
\begin{align}
\begin{aligned}
\ket{\psi_3}_{\text{ABC}}
	&
	=
	\gamma
	\ket{\psi}_\mathrm{A}
	\ket{00}_\text{BC}
	\\
	&
	\hspace{0.35cm}
	+
	\delta
	\alpha
	e^{-\iota\left(\varphi+\phi\right)/2}
	\cos\left(\theta/2\right)
	\ket{001}_{\text{ABC}}
	\\
	&\hspace{0.35cm}
	+
	\delta
	\alpha
	e^{-\iota\left(\varphi-\phi\right)/2}
	\sin\left(\theta/2\right)
	\ket{011}_{\text{ABC}}
	\\
	&\hspace{0.35cm}
	+
	\delta
	\beta
	e^{+\iota\left(\varphi+\phi\right)/2}
	\cos\left(\theta/2\right)
	\ket{102}_{\text{ABC}}
	\\
	&\hspace{0.35cm}
	-
	\delta
	\beta
	e^{+\iota\left(\varphi-\phi\right)/2}
	\sin\left(\theta/2\right)
	\ket{112}_{\text{ABC}},
\end{aligned}
\label{eq:psi 3}
\end{align}
where $\phi$, $\theta$, and $\varphi$ are the Euler angles of the unitary operator $\M{U}=\M{R}_\mathrm{z}\hspace{-0.05cm}\left(\phi\right)\M{R}_\mathrm{y}\hspace{-0.05cm}\left(\theta\right)\M{R}_\mathrm{z}\hspace{-0.05cm}\left(\varphi\right)$.
\begin{figure}[t!]
  \centering
\includegraphics[width=0.5\textwidth]{QZE.eps}
    \caption{
     A H(V)-\ac{QZ}$_N$ gate with $N$ cycles where H (V) stands for horizontal (vertical) polarization of the photon, OC for an optical circulator, SM for a switchable mirror, PR for a polarizing rotator, PBS for a polarizing beam splitter, MR for a mirror, and AO shows the state of an absorptive object.
      }
    \label{fig:QZE}
\end{figure}
Now, Alice and Bob apply two counterfactual controlled flipping operations $\M{Q}_1$ and $\M{Q}_2$,
which transform the composite state $\ket{\psi_3}_{\text{ABC}}$ as follows:
\begin{equation}
\begin{aligned}
\ket{\psi_4}_{\text{ABC}}
	&
	=
	\gamma
	\ket{\psi}_\mathrm{A}
	\ket{00}_\text{BC}
	\\
	&\hspace{0.35cm}
	+
	\delta
	\alpha
	e^{-\iota\left(\varphi+\phi\right)/2}
	\cos\left(\theta/2\right)
	\ket{011}_{\text{ABC}}
	\\
	&\hspace{0.35cm}
	+
	\delta
	\alpha
	e^{-\iota\left(\varphi-\phi\right)/2}
	\sin\left(\theta/2\right)
	\ket{111}_{\text{ABC}}
	\\
	&\hspace{0.35cm}
	+
	\delta
	\beta
	e^{+\iota\left(\varphi+\phi\right)/2}
	\cos\left(\theta/2\right)
	\ket{112}_{\text{ABC}}
	\\
	&\hspace{0.35cm}
	-
	\delta
	\beta
	e^{+\iota\left(\varphi-\phi\right)/2}
	\sin\left(\theta/2\right)
	\ket{012}_{\text{ABC}}.
\end{aligned}
\label{eq:psi 4}
\end{equation}
\begin{table*}[t!]
\centering
\setlength{\tabcolsep}{8pt}
\renewcommand{\arraystretch}{1.5}
\caption{H(V)-\ac{QZ}$_N$ and H(V)-\ac{CQZ}$_{M,N}$ gates.}\label{tab:I-QZE}
\vspace{0.2cm}
\begin{tabular}{P{1.2cm} |  P{1.2cm} | P{1.2cm} | P{1.4cm} | P{2.4cm} | P{1.2cm} | P{1.4cm} | P{2.4cm}}
\hline
\multirow{2}{*}{Input} & \multirow{2}{*}{Control} &  \multicolumn{3}{c|}{\ac{QZ} Gate} & \multicolumn{3}{c}{\ac{CQZ} Gate}  \\
 \cline{3-8}
 & &  Output & Probability & Counterfactuality & Output & Probability & Counterfactuality\\%[0.5ex]
\hline
\hline
\multirow{2}{*}{$\ket{\mathrm{H}\left(\mathrm{V}\right)}_{\mathrm{p}}$} & $\ket{0}_{\mathrm{AO}}$ &  $\ket{\mathrm{V}\left(\mathrm{H}\right)}_{\mathrm{p}}$ & 1 & No & $\ket{\mathrm{H}\left(\mathrm{V}\right)}_{\mathrm{p}}$ & $\lambda_0$ & Yes\\
& $\ket{1}_{\mathrm{AO}}$ &  $\ket{\mathrm{H}\left(\mathrm{V}\right)}_{\mathrm{p}}$ &  $\cos^{2N}\theta_N$ & Yes & $\ket{\mathrm{V}\left(\mathrm{H}\right)}_{\mathrm{p}}$ & $\lambda_1$ & Yes\\%[0.5ex]
\hline
\end{tabular}
\end{table*}
Bob's local operation $\M{V}_2$ followed by the Hadamard gate $\M{H}$ and the measurement on the ancillary qutrit in the computational basis collapses $\ket{\psi_4}_{\text{ABC}}$ to
\begin{align}
\label{eq:psi 5}
\ket{\psi_{5m}}_{\text{AB}}
	&
	=
	\gamma
	\ket{\psi}_\mathrm{A}
	\ket{0}_\text{B}\nonumber
	\\
	&\hspace{0.35cm}
	+
	\delta
	\alpha
	e^{-\iota\left(\varphi+\phi\right)/2}
	\cos\left(\theta/2\right)
	\ket{01}_{\text{AB}}\nonumber
	\\
	&\hspace{0.35cm}
	+
	\delta
	\alpha
	e^{-\iota\left(\varphi-\phi\right)/2}
	\sin\left(\theta/2\right)
	\ket{11}_{\text{AB}}
	\\
	&\hspace{0.35cm}
	+
	\left(-1\right)^{m}
	\delta
	\beta
	e^{+\iota\left(\varphi+\phi\right)/2}
	\cos\left(\theta/2\right)
	\ket{11}_{\text{AB}}\nonumber
	\\
	&\hspace{0.35cm}
	+
	\left(-1\right)^{1-m}
	\delta
	\beta
	e^{+\iota\left(\varphi-\phi\right)/2}
	\sin\left(\theta/2\right)
	\ket{01}_{\text{AB}},\nonumber
\end{align}
where $m\in\lbrace 0,1\rbrace$ is the measurement outcome. Finally, the counterfactual global operation $\M{Q}_3$ transforms $\ket{\psi_{5m}}_{\text{AB}}$ for the measurement outcome $m$ as follows:
\begin{align}
	\label{eq:psi 6}
\ket{\psi_{6m}}_{\text{AB}}
	&
	=
	\gamma
	\ket{\psi}_\mathrm{A}
	\ket{0}_\text{B}\nonumber
	\\
	&\hspace{0.35cm}
	+
	\delta
	\alpha
	e^{-\iota\left(\varphi+\phi\right)/2}
	\cos\left(\theta/2\right)
	\ket{01}_{\text{AB}}\nonumber
	\\
	&\hspace{0.35cm}
	+
	\left(-1\right)^{m}
	\delta
	\alpha
	e^{-\iota\left(\varphi-\phi\right)/2}
	\sin\left(\theta/2\right)
	\ket{11}_{\text{AB}}
	\\
	&\hspace{0.35cm}
	+
	\delta
	\beta
	e^{+\iota\left(\varphi+\phi\right)/2}
	\cos\left(\theta/2\right)
	\ket{11}_{\text{AB}}\nonumber
	\\
	&\hspace{0.35cm}
	+
	\left(-1\right)^{1-m}
	\delta
	\beta
	e^{+\iota\left(\varphi-\phi\right)/2}
	\sin\left(\theta/2\right)
	\ket{01}_{\text{AB}}, \nonumber
\end{align}
which can be written as (17) in the main text.
Note that the probability $\zeta_m$ that the CCT protocol fails in counterfactuality---called the \emph{abortion rate}---is given in \eqref{eq:FP}
when the global operations $\M{T},\M{Q}_1,\M{Q}_2$ and $\M{Q}_3$ are counterfactually implemented using the QZ and CQZ gates.

\subsection{\ac{QZ} Gates}

Fig.~\ref{fig:QZE} shows the Michelson version of the \ac{QZ} gate \cite{ZJS:19:SR} to perform \ac{IFM}. The \ac{QZ} gate is to ascertain the classical behavior of an absorptive object, i.e., to infer the absence state $\ket{0}_\mathrm{AO}$ or the presence state $\ket{1}_\mathrm{AO}$ of AO without interacting with it. The H(V)-\ac{QZ}$_N$ gate takes an H~(V) polarized photon as input. The switchable mirror SM$_N$ is initially turned off to allow passing the photon and is turned on for $N$ cycles once the photon is passed. After $N$ cycles, SM$_N$ is turned off again allowing the photon out.  The polarization rotator PR$_N^{\mathrm{H}\left(\mathrm{V}\right)}$ gives rotation to the input photon by an angle $\theta_N=\pi/\left(2N\right)$ as follows:
\begin{align}
\text{PR}_N^{\mathrm{H}\left(\mathrm{V}\right)}:
	\begin{cases}
	\ket{\mathrm{H}\left(\mathrm{V}\right)}_{\mathrm{p}}
		\rightarrow
		\cos\theta_N
		\ket{\mathrm{H}\left(\mathrm{V}\right)}_{\mathrm{p}}
		+
		\sin\theta_N
		\ket{\mathrm{V}\left(\mathrm{H}\right)}_{\mathrm{p}},\\
	\ket{\mathrm{V}\left(\mathrm{H}\right)}_{\mathrm{p}}
		\rightarrow
		\cos\theta_N
		\ket{\mathrm{V}\left(\mathrm{H}\right)}_{\mathrm{p}}
		-
		\sin\theta_N
		\ket{\mathrm{H}\left(\mathrm{V}\right)}_{\mathrm{p}}.
	\end{cases}
\end{align}
The photon state $\ket{\phi}$ after PR$_N^{\mathrm{H}\left(\mathrm{V}\right)}$ in the first cycle of the H(V)-\ac{QZ}$_N$ gate is given by
\begin{align}
\ket{\phi}=\cos\theta_N\ket{\mathrm{H}\left(\mathrm{V}\right)}_{\mathrm{p}}+\sin\theta_N\ket{\mathrm{V}\left(\mathrm{H}\right)}_{\mathrm{p}}. \label{eq:QZ pass}
\end{align}
Then, the polarizing beam splitter PBS separates the H and V components of the photon into two different optical paths: SM $\rightarrow$ MR$_1$ and SM $\rightarrow$ MR$_2$. The H~(V) component  goes towards MR$_1$ and the V~(H) component goes towards MR$_2$. The photon component in the second optical path only interacts with AO (control terminal).
\begin{itemize}
\item
$\text{AO}=\ket{0}_\mathrm{AO}$:
In the absence of the absorptive object, the V~(H) component of the photon is reflected by MR$_2$ and is returned back to PBS. Hence, the photon state remains unchanged. After $n \left(<N\right)$ cycles, the photon state is given by
\begin{align}	\label{eq:state:n}
\ket{\phi}
	=
	\cos\left(n\theta_N\right)
	\ket{\mathrm{H}\left(\mathrm{V}\right)}_{\mathrm{p}}
	+
	\sin\left(n\theta_N\right)
	\ket{\mathrm{V}\left(\mathrm{H}\right)}_{\mathrm{p}}.
\end{align}
The photon will end up in the state $\ket{\mathrm{V}\left(\mathrm{H}\right)}_{\mathrm{p}}$ with certainty by $\pi/2$ rotation after $N$ cycles.

\item
$\text{AO}=\ket{1}_\mathrm{AO}$:
In the presence of the absorptive object, the V~(H) component is absorbed by AO if it is found in the control terminal. In each cycle, the probability of this absorption event is equal to $\sin^2\theta_N$. Unless the photon is absorbed, the photon state collapses to the initial state $\ket{\mathrm{H}\left(\mathrm{V}\right)}_{\mathrm{p}}$.
After $N$ cycles, the photon is not absorbed and ends up in the state $\ket{\mathrm{H}\left(\mathrm{V}\right)}_{\mathrm{p}}$ with probability $\cos^{2N}\theta_N$ tending to one as $N\rightarrow\infty$.
\end{itemize}

Table~\ref{tab:I-QZE} shows the overall action of the \ac{QZ} gate. Note that the H(V)-\ac{QZ}$_N$ gate has the output $\ket{\mathrm{H}\left(\mathrm{V}\right)}_{\mathrm{p}}$ in the presence state $\ket{1}_\mathrm{AO}$  if the photon has not traveled over the control terminal (quantum channel). Hence, the \ac{QZ} gate is counterfactual only for this measurement outcome.

\begin{figure}[t!]
 \centering{
\includegraphics[width=0.35\textwidth]{MCQZ.eps}}
    \caption{
   A H(V)-\ac{CQZ}$_{M,N}$ gate with $M$ outer and $N$ inner cycles where D is a photon detector. Table~\ref{tab:I-QZE} shows the overall action of the H(V)-\ac{CQZ}$_{M,N}$ gate.
   }
    \label{fig:MCQZ}
\end{figure}

\begin{figure*}[t!]
    \centering
    \subfigure[~Type I]
    {
        \includegraphics[width=0.4\textwidth]{QAO-QZ.eps}
        \label{fig:QAO:1}
    }
    \subfigure[~Type II]
    {
        \includegraphics[width=0.4\textwidth]{QAO-CQZ.eps}
        \label{fig:QAO:2}
    }
\caption{A quantum absorptive object (electron) for (a) the \ac{QZ} gate (type I) and (b) the \ac{CQZ} gate (type II). The electron takes the superposition of two paths $\ket{\uparrow}_{\mathrm{e}}$ and $\ket{\downarrow}_{\mathrm{e}}$. In type~I, the electron states
$\ket{\uparrow}_\mathrm{e}$ and $\ket{\downarrow}_\mathrm{e}$ act as the presence (absence) state $\ket{1 \left(0\right)}_\mathrm{AO}$ and the absence (presence) state $\ket{0 \left(1\right)}_\mathrm{AO}$ of the absorptive object for the H(V)-\ac{QZ} gate, respectively. In type~II, the electron states simply act as $\ket{\uparrow}_\mathrm{e}=\ket{0}_\mathrm{AO}$ and $\ket{\downarrow}_\mathrm{e}=\ket{1}_\mathrm{AO}$ for the \ac{CQZ} gate. If the photon is absorbed by the electron, the electron state is in an erasure state orthogonal to $\ket{\uparrow}_{\mathrm{e}}$ and $\ket{\downarrow}_{\mathrm{e}}$.
}
\label{fig:QAO}
\end{figure*}

\subsection{\ac{CQZ} Gates}
Fig.~\ref{fig:MCQZ} shows the nested version of \ac{QZ} gates with $M$ outer and $N$ inner cycles \cite{ZJS:18:SR}. The \ac{CQZ} gate enables to ascertain the absence or presence of the absorptive object counterfactually for both the outcomes. The H(V)-\ac{CQZ}$_{M,N}$ gate also takes an H~(V) polarized photon as input. In each outer cycle, the V~(H) component of the photon enters the inner V(H)-\ac{QZ}$_N$ gate.

\begin{itemize}

\item
$\text{AO}=\ket{0}_\mathrm{AO}$:
In the absence of the absorptive object, the inner V(H)-\ac{QZ}$_N$ gate transforms the photon state $\ket{\mathrm{V}\left(\mathrm{H}\right)}_{\mathrm{p}}$ into $\ket{\mathrm{H}\left(\mathrm{V}\right)}_{\mathrm{p}}$ after $N$ cycles.
This component ends up at the detector D after PBS. Hence, the inner \ac{QZ} gate acts as an absorptive object for the outer \ac{QZ} gate in the absence state $\ket{0}_\mathrm{AO}$, where D serves to detect the event that the photon is found in the control terminal. In each outer cycle, unless the photon is discarded, the photon state collapses back to the initial state $\ket{\mathrm{H}\left(\mathrm{V}\right)}_{\mathrm{p}}$ with probability $\cos^2 \theta_M$. After $M$ outer cycles, the photon is not discarded at the detector D and ends up in the initial state $\ket{\mathrm{H}\left(\mathrm{V}\right)}_{\mathrm{p}}$ with probability
\begin{align}
\lambda_0
	=
	\cos^{2M} \theta_M.
\end{align}
tending to one as $M \rightarrow \infty$.

\item
$\text{AO}=\ket{1}_\mathrm{AO}$:
In case the absorptive object is present, the V~(H) component of the photon recombines with the H~(V) component and
the photon state remains unchanged for the next outer cycle, unless the photon is absorbed by AO.
Hence, the inner \ac{QZ} gate acts as a mirror for the outer \ac{QZ} gate in the presence state $\ket{1}_\mathrm{AO}$.
After $i \left(<M\right)$ outer cycles, unless the photon is absorbed, the photon state is given by \eqref{eq:state:n},
which is again not absorbed by AO for the next outer cycle with probability
\begin{align}
\left[
	1-
	\sin^2\left(i\theta_M\right)
	\sin^2\theta_N
\right]^{N}.
\end{align}
Hence, unless the photon is absorbed by AO, the H(V)-\ac{CQZ}$_{M,N}$ gate transforms the input state $\ket{\mathrm{H}\left(\mathrm{V}\right)}_{\mathrm{p}}$ into $\ket{\mathrm{V}\left(\mathrm{H}\right)}_{\mathrm{p}}$ with probability
\begin{align}	\label{eq:P1}
\lambda_1
	=
	\prod_{i=1}^M
	\left[
		1-
		\sin^2\left(i\theta_M\right)
		\sin^2\theta_N
	\right]^{N}
\end{align}
tending to one as $M, N \rightarrow \infty$.

\end{itemize}

Note that the \ac{CQZ} gate is counterfactual for both the outcomes and infers the absence or presence of the absorptive object (with probability $\lambda_0$ or $\lambda_1$) but no physical particle (photon) is found in the control terminal (see Table~\ref{tab:I-QZE}).

\begin{figure}[t!]
 \centering{
\includegraphics[width=0.445\textwidth]{HV-CEPI.eps}}
    \caption{
A H(V)-\ac{CEPI}$_N$ gate where the superposition state $\ket{\text{electron}}_\mathrm{e}=\alpha \ket{\uparrow}_{\mathrm{e}}+\beta\ket{\downarrow}_{\mathrm{e}}$ of the quantum absorptive object (electron) is collapsed to $\ket{\uparrow\left(\downarrow\right)}_\mathrm{e}$ using the H(V)-\ac{QZ}$_N$ gate unless the photon is absorbed by the electron. If the photon is found in the quantum channel, the pair of photon and electron is discarded in transforming $\ket{\eta_1}_\mathrm{ep}$ to $\ket{\eta_2}_\mathrm{ep}$ where the photon that has traveled over the channel is diverted again to the quantum absorptive object and absorbed by the electron. This electron-photon interaction is designed to output the photon and electron by using the presence state (blocking event) only. Hence, the protocol is fully counterfactual.
   }
    \label{fig:H(V)-CEPI}
\end{figure}

\section{\ac{CCT} implementation using \ac{QZ} and \ac{CQZ} gates}\label{sec: 2}

As shown in Fig.~\ref{fig:QAO}, an electron as a quantum absorptive object takes superposition of two paths $\ket{\uparrow}_{\mathrm{e}}$ and $\ket{\downarrow}_{\mathrm{e}}$ where the subscript $\mathrm{e}$ denotes the electron. In type~I (Fig.~S\ref{fig:QAO:1}), the electron state $\ket{\uparrow\left(\downarrow\right)}_\mathrm{e}$ or $\ket{\downarrow\left(\uparrow\right)}_\mathrm{e}$ acts as the presence state $\ket{1}_\mathrm{AO}$ or the absence state $\ket{0}_\mathrm{AO}$ of the absorptive object for the H(V)-\ac{QZ}$_N$ gate.  For the counterfactuality of the protocol, we setup four gates:
\begin{enumerate}[1)]
\item
\acf{CEPI} gates using the H(V)-\ac{QZ}$_N$ gate;

\item
\ac{DCEPI} gates using  the dual \ac{QZ} (DQZ) gate;

\item
\ac{DCFO} gates using the \ac{CEPI} gates;

\item
\ac{DDCFO} gates using the \ac{DCEPI} gates.
\end{enumerate}
From the above list of gates, the second (first) and forth (third) gates are used to devise the \ac{CCT} for general (Bell-type) input states.

\subsection{\ac{CEPI} Gates}\label{sec: 2-1}

Fig.~\ref{fig:H(V)-CEPI} shows the H(V)-\ac{CEPI}$_N$ gate  where the quantum absorptive object is in the superposition state
\begin{align}
\ket{\text{electron}}_\mathrm{e}
=
	\alpha
	\ket{\uparrow}_{\mathrm{e}}
	+
	\beta
	\ket{\downarrow}_{\mathrm{e}}
	\label{eq:electron}
\end{align}
with $|\alpha|^2+|\beta|^2=1$.
Unless the photon is absorbed by the electron, the H(V)-\ac{CEPI}$_N$ gate collapses this quantum state by entangling and disentangling the electron-photon pair
\begin{align}
\ket{\eta_0}_\mathrm{ep}
=
	\ket{\text{electron}}_\mathrm{e}
	\ket{\mathrm{H}\left(\mathrm{V}\right)}_{\mathrm{p}}
\end{align}
as follows:
\begin{align}	\label{eq:QHV:1}
\ket{\eta_0}_\mathrm{ep}
&\rightarrow
	\ket{\eta_1}_\mathrm{ep}
	=
	\alpha
	\ket{\uparrow\mathrm{H}}_{\mathrm{ep}}
	+
	\beta
	\ket{\downarrow\mathrm{V}}_{\mathrm{ep}} \\
&\rightarrow
	\ket{\eta_2}_\mathrm{ep}
	=
	\ket{\uparrow\left(\downarrow\right)}_\mathrm{e}
	\ket{\mathrm{H}\left(\mathrm{V}\right)}_{\mathrm{p}}
\end{align}
with probability
\begin{align}
\left(
	1-
	\nabla_0
	\sin^2\theta_N
\right)^N
\nabla_0,
\end{align}
where $\nabla_0=|\alpha|^2 \left(|\beta|^2\right)$ is the probability that the electron is in the presence state for the H(V)-\ac{QZ}$_N$ gate.

\begin{figure}[t!]
 \centering{
\includegraphics[width=0.475\textwidth]{D-CEPI.eps}}
    \caption{
A \ac{DCEPI}$_N$ gate where the quantum absorptive object (electron) gets entangled with the existing photon (unless absorbed by the electron) using the DQZ$_N$ gate. Initially, the photon is in the superposition state $\ket{\text{photon}}_\mathrm{p}=\gamma\ket{0}_{\mathrm{p}}+\delta\ket{1}_{\mathrm{p}}$, which is entangled with the ancillary path state by PBS$^\mathrm{H}$ as $\ket{\text{photon}}_\mathrm{pa} = \gamma\ket{\mathrm{H0}}_{\mathrm{pa}} + \delta\ket{\mathrm{V1}}_{\mathrm{pa}}$ to start the \ac{DCEPI}. Similar to the H(V)-\ac{CEPI}$_N$ gate in Fig.~\ref{fig:H(V)-CEPI}, the \ac{DCEPI}$_N$ gate then transforms the electron-photon pair $\ket{\eta_0}_{\mathrm{epa}}$ to $\ket{\eta_2}_{\mathrm{epa}}=\gamma\ket{\uparrow\mathrm{H}0}_{\mathrm{epa}}+\delta\ket{\downarrow\mathrm{V}1}_{\mathrm{epa}}$ by using the blocking event only (unless the photon is absorbed by the electron).
}
    \label{fig:D-CEPI}
\end{figure}

The second (first) term of $\ket{\eta_1}_\mathrm{ep}$ is the outcome corresponding to the electron in the absence state for the H(V)-\ac{QZ}$_N$ gate. Since this outcome is not counterfactual, it is discarded (absorbed) by the electron using the PBS$^{\mathrm{H}\left(\mathrm{V}\right)}$ and the $\M{X}$ operator. To discard the factual (non-counterfactual) outcome $\ket{\mathrm{V}\left(\mathrm{H}\right)}_{\mathrm{p}}$ of the H(V)-\ac{QZ}$_N$ gate, PBS$^{\mathrm{H}\left(\mathrm{V}\right)}$ redirects this photon component to the quantum absorptive object (followed by the $\M{X}$ operator) to be absorbed by the electron. Hence, whenever the photon is found in the quantum channel, the electron absorbs it and becomes in an erasure state, leading the  H(V)-\ac{CEPI}$_N$ gate to output no photon and electron (e.g., particles in the erasure state).  This enables the protocol to abort nonlocally by discarding both the photon and the electron whenever its counterfactuality is broken.

\begin{figure*}[t!]
 \centering{
\includegraphics[width=0.85\textwidth]{HV-DCFO.eps}}
    \caption{
A H(V)-\ac{DCFO}$_{K,N}$ gate for Bell-type states of 1(0)-class.  Here $\M{\mathcal{A}}=\M{R}_\mathrm{y}\hspace{-0.05cm}\left(2\theta_K\right)$ is a rotation operation with rotation angle $\theta_K=\pi/\left(2K\right)$ and $\M{\mathcal{B}}=\M{X}^\ell$ for $\ell$-class states where $K$ is the number of \ac{CEPI} gates and $\M{R}_\mathrm{y}\hspace{-0.05cm}\left(2\theta_K\right)$ is the rotation around  $y$-axis.
}
    \label{fig:H(V)-DCFO}
\end{figure*}

\subsection{\ac{DCEPI} Gates}
Fig.~\ref{fig:D-CEPI} shows the dual form of the H(V)-\ac{CEPI}$_N$ gate in Fig.~\ref{fig:H(V)-CEPI}. For counterfacuality, this \ac{DCEPI}$_N$ gate works similarly to the H(V)-\ac{CEPI}$_N$ gate. The only difference is that the superposition polarization state
\begin{align}
\ket{\text{photon}}_\mathrm{p}=\gamma\ket{\mathrm{H}}_{\mathrm{p}}+\delta\ket{\mathrm{V}}_{\mathrm{p}}\label{eq:photon}
\end{align}
of the input photon is entangled with the ancillary path state in the DQZ$_N$ gate as follows:
\begin{align}
\ket{\text{photon}}_\mathrm{pa}
=
	\gamma\ket{\mathrm{H0}}_{\mathrm{pa}}
	+
	\delta\ket{\mathrm{V1}}_{\mathrm{pa}},
\end{align}
where the ancilla states $\ket{0}_\mathrm{a}$ and $\ket{1}_\mathrm{a}$ show the paths for the H- and V-\ac{QZ} gates, respectively. Unless the photon is absorbed by the electron, the \ac{DCEPI}$_N$ gate transforms the electron-photon pair
\begin{align}
\ket{\eta_0}_\mathrm{epa}
=
	\ket{\text{electron}}_\mathrm{e}
	\ket{\text{photon}}_\mathrm{pa}
\end{align}
as follows:
\begin{align}
&\begin{aligned}
\ket{\eta_0}_\mathrm{epa}
\rightarrow
	\ket{\eta_1}_\mathrm{epa}
	&=
	\alpha
	\gamma
	\ket{\uparrow\mathrm{H}0}_{\mathrm{epa}}
	+
	\beta
	\gamma
	\ket{\downarrow\mathrm{V}0}_{\mathrm{epa}}
	\\
	&\hspace{0.35cm}+
	\alpha
	\delta
	\ket{\uparrow\mathrm{H}1}_{\mathrm{epa}
	+
	\beta
	\delta
	\ket{\downarrow\mathrm{V}1}_{\mathrm{epa}}
\end{aligned}\\
&~~~~~~~~~\rightarrow
	\ket{\eta_2}_\mathrm{epa}
	=
	\gamma
	\ket{\uparrow\mathrm{H}0}_{\mathrm{epa}}
	+
	\delta
	\ket{\downarrow\mathrm{V}1}_{\mathrm{epa}}
\end{align}
with probability
\begin{align}
\left(
	1-
	\nabla_1
	\sin^2\theta_N
\right)^N
\nabla_1,
\end{align}
where
$\nabla_1
	=
	\vert
	\alpha
	\gamma
	\vert^2
	+
	\vert
	\beta
	\delta
	\vert^2
$
is the probability that the electron is in the presence state for \ac{QZ} gates in both paths.

\subsection{\ac{DCFO} Gates}
To devise the \ac{DCFO} gate, $K$ H(V)-\ac{CEPI}$_N$ gates are concatenated serially where Alice has the quantum absorptive object (electron) and Bob equips the \ac{QZ} gates (see Fig.~\ref{fig:H(V)-DCFO}). To explain the operation of the \ac{DCFO}$_{K,N}$ gate, consider  the Bell-type state of electron-photon pair
\begin{align}
\ket{\eta_0}_\text{ep}:
	\begin{cases}
		\ket{\eta^\pm_{00}}_\text{ep}
			=
			\alpha\ket{\uparrow\mathrm{H}}_\text{ep}
			\pm
			\beta\ket{\downarrow\mathrm{V}}_\text{ep},\\
		\ket{\eta^\pm_{01}}_\text{ep}
			=
			\gamma\ket{\uparrow\mathrm{V}}_\text{ep}
			\pm
			\delta\ket{\downarrow\mathrm{H}}_\text{ep},\\
	\end{cases}\label{eq:H(V)-DCFO input}
\end{align}
where $\ket{\eta^\pm_{00}}_\text{ep}$ and $\ket{\eta^\pm_{01}}_\text{ep}$ are $0$- and $1$-class states, respectively. The H(V)-\ac{DCFO}$_{K,N}$ protocol for Bell-type states of 1(0)-class
takes the following steps.

\begin{figure*}[t!]
 \centering{
\includegraphics[width=0.95\textwidth]{D-DCFO.eps}}
    \caption{
A dual version of the H(V)-\ac{DCFO}$_{K,N}$ gate.
}
    \label{fig:D-DCFO}
\end{figure*}

\begin{enumerate}
\item
Bob starts the H(V)-\ac{DCFO}$_{K,N}$ protocol by throwing his photon towards PBS$^{\mathrm{V}}$, which allows the V component to pass and detour the H component to be recombined after $K$ successive H(V)-\ac{CEPI}$_N$ operations. Bob performs the $\M{\mathcal{B}}$ operator on the V photon component  where $\M{\mathcal{B}}=\M{X}^\ell$ for $\ell$-class states.

\item
Alice performs $\M{R}_\mathrm{y}\hspace{-0.05cm}\left(2\theta_K\right)$
on her qubit (electron) where $\theta_K=\pi/\left(2K\right)$. The rotation gate $\M{R}_\mathrm{y}\hspace{-0.05cm}\left(2\theta_K\right)$ transforms $\ket{\uparrow}_{\mathrm{e}}$ and $\ket{\downarrow}_{\mathrm{e}}$ as follows:
\begin{align}
\ket{\uparrow}_{\mathrm{e}}
	&
	\rightarrow
	\cos\theta_K
	\ket{\uparrow}_{\mathrm{e}}
	+
	\sin\theta_K
	\ket{\downarrow}_{\mathrm{e}},
	\\
\ket{\downarrow}_{\mathrm{e}}
	&
	\rightarrow
	\cos\theta_K
	\ket{\downarrow}_{\mathrm{e}}
	-
	\sin\theta_K
	\ket{\uparrow}_{\mathrm{e}}.
\end{align}

\item
Bob inputs the H~(V) component to the H(V)-\ac{CEPI}$_N$ gate.
Unless the photon is absorbed by the electron, the first H(V)-\ac{CEPI}$_N$ gate transforms the $\ket{\eta_0}_\text{ep}$ as follows:
\begin{widetext}
\begin{align}
\ket{\eta_1}_\text{epa}:
	\begin{cases}
	\ket{\eta^\pm_{10}}_\text{epa}
	=
	\alpha
	\bigl(
		\cos\theta_K
		\ket{\uparrow\mathrm{H}0}_\mathrm{epa}
		+
		\sin\theta_K
		\ket{\downarrow\mathrm{H}0}_\mathrm{epa}
	\bigr)
	\pm
	\beta
	\ket{\downarrow\mathrm{V}1}_\mathrm{epa},\\
	\ket{\eta^\pm_{11}}_\text{epa}
	=
	\gamma
	\ket{\uparrow\mathrm{H}1}_\mathrm{epa}
	\pm
	\delta
	\bigl(
		\cos\theta_K
		\ket{\downarrow\mathrm{H}0}_\mathrm{epa}
		-
		\sin\theta_K
		\ket{\uparrow\mathrm{H}0}_\mathrm{epa}
	\bigr)
	\end{cases}
\end{align}
\end{widetext}
with probability
\begin{align}
\begin{aligned}
\nabla_2
	&=
	\left(
		1-
		\nabla
		\cos^2\theta_K
		\sin^2\theta_{N}
	\right)^{N}
	\\
	&\hspace{0.425cm}
	\left(
		1-
		\nabla
		\sin^2\theta_K
	\right),\label{eq:nabla 2}
\end{aligned}
\end{align}
where $\nabla=\vert\gamma\vert^2\left(\vert\beta\vert^2\right)$. Whenever the photon is found in the transmission channel between Alice and Bob, the electron absorbs it and the protocol declares an erasure.

\item
Alice and Bob repeat the second and third steps for subsequent H(V)-\ac{CEPI}$_N$ gates. After $K$ H(V)-\ac{CEPI}$_N$ gates, unless the photon is absorbed by the electron,
Bob performs the $\M{\mathcal{B}}$ operator again on the output photon to recombine the H and V components of the photon and the composite state of electron-photon pair transforms to:
\begin{align}
\ket{\eta_2}_\text{ep}:
	\begin{cases}
		\ket{\eta^\pm_{20}}_\text{ep}
			=
			\alpha\ket{\downarrow\mathrm{H}}_\text{ep}
			\pm
			\beta\ket{\downarrow\mathrm{V}}_\text{ep},\\
		\ket{\eta^\pm_{21}}_\text{ep}
			=
			\gamma\ket{\uparrow\mathrm{V}}_\text{ep}
			\mp
			\delta\ket{\uparrow\mathrm{H}}_\text{ep}\\
	\end{cases}\label{eq:H(V)-DCFO output}
\end{align}
with probability
\begin{align} \label{eq:zeta}
\nabla_3
=
	\nabla_2^K.
\end{align}

\end{enumerate}

\begin{figure*}[t!]
 \centering{
\includegraphics[width=0.87\textwidth]{QZ-CQZ-BNCU.eps}}
    \caption{
A \ac{CCT} protocol for general input states using \ac{QZ} and \ac{CQZ} gates.  Here $\M{\mathcal{B}}_1=\M{R}_\mathrm{z}\hspace{-0.05cm}\left(\varphi\right)\M{X}$ and $\M{\mathcal{B}}_2=\M{R}_\mathrm{z}\hspace{-0.05cm}\left(\phi\right)\M{R}_\mathrm{y}\hspace{-0.05cm}\left(\theta\right)$  where $\M{R}_\mathrm{z}\hspace{-0.05cm}\left(\varphi\right)$ denotes the rotation around $z$-axis.
}
    \label{fig:QZ-CQZ-BNCU}
\end{figure*}

\subsection{\ac{DDCFO} Gates}\label{sec: 2-4}
Similar to the H(V)-\ac{DCFO}$_{K,N}$ gate, $K$ \ac{DCEPI}$_N$ gates are concatenated serially to devise the \ac{DDCFO} gate where Alice has quantum absorptive object (electron) and Bob equips \ac{QZ}$_N$ gates, as shown in Fig.~\ref{fig:D-DCFO}. To explain the operation of the \ac{DDCFO}$_{K,N}$ gate, consider the initial state of electron-photon pair
\begin{align}
\begin{aligned}
\ket{\eta_0}_\text{epa}
	&=
	\frac{1}{\sqrt{2}}
	\bigl(
		\alpha
		\ket{\downarrow\mathrm{H}}_\mathrm{ep}
		+
		\beta
		\ket{\uparrow\mathrm{V}}_\mathrm{ep}
	\bigr)
	\ket{0}_\mathrm{a}\\
	&\hspace{0.5cm}
	\frac{1}{\sqrt{2}}
	\bigl(
		\gamma
		\ket{\uparrow\mathrm{H}}_\mathrm{ep}
		+
		\delta
		\ket{\downarrow\mathrm{V}}_\mathrm{ep}
	\bigr)
	\ket{1}_\mathrm{a}.
\end{aligned}\label{eq:D-DCFO input}
\end{align}
The \ac{DDCFO}$_{K,N}$ gate takes the following steps.
\begin{enumerate}
\item
Bob starts the \ac{DDCFO} by applying PBS$^{\mathrm{V}}$ in each path of the photon and recombines the respective components of the photon after $K$ successive \ac{DCEPI}$_N$ operations. Bob applies the $\M{X}$ operator on the photon component in path state $\ket{0}_\mathrm{a}$.

\item
Now, Alice performs $\M{R}_\mathrm{y}\hspace{-0.05cm}\left(2\theta_K\right)$ on her qubit and Bob inputs the photon components in path states $\ket{0}_\mathrm{a}$ and $\ket{1}_\mathrm{a}$ to the \ac{DCEPI}$_N$ gate. Unless the photon is absorbed by the electron, the first \ac{DCEPI}$_N$ gate transforms the $\ket{\eta_0}_\text{epa}$ as
\begin{align}
\begin{aligned}
\ket{\eta_1}_\text{epa}
	&=
	\frac{1}{\sqrt{2}}
	\big(
		\beta
		\ket{\uparrow\mathrm{H}0}_\mathrm{epa}
		+
		\delta
		\ket{\downarrow\mathrm{V}1}_\mathrm{epa}
		\big.
		\\
		&\big.\hspace{0.55cm}
		+~\alpha
		\cos\theta_K
		\ket{\downarrow\mathrm{H}2}_\mathrm{epa}
		\big.
		\\
		&\big.\hspace{0.55cm}
		-~
		\alpha
		\sin\theta_K
		\ket{\uparrow\mathrm{H}2}_\mathrm{epa}
		\big.
		\\
		&\big.\hspace{0.55cm}
		+~
		\gamma
		\cos\theta_K
		\ket{\uparrow\mathrm{H}3}_\mathrm{epa}
		\big.
		\\
		&\big.\hspace{0.55cm}
		+~
		\gamma
		\sin\theta_K
		\ket{\downarrow\mathrm{H}3}_\mathrm{epa}
	\big)
\end{aligned}
\end{align}
with probability
\begin{align}
\begin{aligned}
\nabla_5
	&=
	\left(
		1-
		\nabla_4
		\cos^2\theta_K
		\sin^2\theta_{N}
	\right)^{N}
	\\
	&\hspace{0.425cm}
	\left(
		1-
		\nabla_4
		\sin^2\theta_K
	\right),
\end{aligned}
\end{align}
where $\nabla_4=\vert\beta\vert^2+\vert\delta\vert^2$.

\item
Alice and Bob repeat the second step for subsequent \ac{DCEPI}$_N$ gates. After $K$ \ac{DCEPI}$_N$ gates, unless the photon is absorbed by the electron,
Bob performs the $\M{X}$ operator on the photon component in path state $\ket{0}_\mathrm{a}$ and recombines the respective photon components. Then, the composite state of electron-photon pair transforms to
\begin{align}
\begin{aligned}
\ket{\eta_2}_\text{epa}
	=&
	\frac{1}{\sqrt{2}}
	\bigl(
		-\alpha
		\ket{\uparrow\mathrm{H}}_\mathrm{ep}
		+
		\beta
		\ket{\uparrow\mathrm{V}}_\mathrm{ep}
	\bigr)
	\ket{0}_\mathrm{a}\\
	&
	\frac{1}{\sqrt{2}}
	\bigl(
		\gamma
		\ket{\downarrow\mathrm{H}}_\mathrm{ep}
		+
		\delta
		\ket{\downarrow\mathrm{V}}_\mathrm{ep}
	\bigr)
	\ket{1}_\mathrm{a}
\end{aligned}\label{eq:D-DCFO output}
\end{align}
with probability
\begin{align}
\nabla_6
=
	\nabla_5^K.
\end{align}

\end{enumerate}

\subsection{\ac{CCT} for General Input States}\label{sec: 2-5}
For the \ac{CCT} with general input states, Alice and Bob prepare the target and control qubits in electron and photon: $\ket{\psi}_\text{A}=\ket{\text{electron}}_\mathrm{e}$ and  $\ket{\psi}_\text{B}=\ket{\text{photon}}_\mathrm{p}$ where
\begin{align}
\begin{aligned}
\ket{0}_{\mathrm{A}}
	&=
	\ket{\uparrow}_{\mathrm{e}},
	\\
\ket{1}_{\mathrm{A}}
	&=
	\ket{\downarrow}_{\mathrm{e}}, \\
\ket{0}_{\mathrm{B}}
	&=
	\ket{\mathrm{H}}_{\mathrm{p}},\\
\ket{1}_{\mathrm{B}}
	&=
	\ket{\mathrm{V}}_{\mathrm{p}}.
	\label{eq:B:1}
\end{aligned}
\end{align}
To devise the \ac{CCT}, Alice and Bob takes the following steps (see Fig.~\ref{fig:QZ-CQZ-BNCU}).
\begin{enumerate}
\item
Bob starts the protocol by throwing his photon towards PBS$^\mathrm{H}$ to entangle the polarization (control qubit) state $\ket{\psi}_\mathrm{B}$ with path state $\ket{0}_\mathrm{C}$. Then Alice and Bob have the composite state $\ket{\psi_1}_\mathrm{ABC}$ in \eqref{eq:psi 1}.

\item
Bob detours the H component of the photon to recombine it at the end of the protocol and inputs the V component of the photon to the V-\ac{CQZ}$_{M,N}$ gate. Unless the photon is absorbed by the electron or discarded at the detector in V-\ac{CQZ}$_{M,N}$ gate, it transforms $\ket{\psi_1}_\mathrm{ABC}$ to $\ket{\psi_2}_\mathrm{ABC}$ in \eqref{eq:psi 2} with probability
\begin{align}
\begin{aligned}
\lambda_2
	&=
	\left(
		1-
		\vert
			\alpha
			\delta
		\vert^2
		\sin^2\theta_M
	\right)^M
	\\
	&\hspace{0.425cm}
	\prod_{i=1}^M
	\left[
		1-
		\vert
			\beta
			\delta
		\vert^2
		\sin^2\left(i\theta_M\right)
		\sin^2\theta_N
	\right]^N
\end{aligned}
\end{align}
tending to one as $M,N\rightarrow\infty$.

\item
Bob applies the $\M{\mathcal{B}}_1=\M{R}_\mathrm{z}\hspace{-0.05cm}\left(\varphi\right)\M{X}$ operation followed by PBS$^\mathrm{H}$ on the component of the photon in path state $\ket{1}_\mathrm{C}$.

\item
Bob applies $\M{\mathcal{B}}_2=\M{R}_\mathrm{z}\hspace{-0.05cm}\left(\phi\right)\M{R}_\mathrm{y}\hspace{-0.05cm}\left(\theta\right)$ and $\M{X}\M{\mathcal{B}}_2$ operators on the photon components in the path states $\ket{1}_\mathrm{C}$ and $\ket{2}_\mathrm{C}$, respectively.
Then, the composite state of Alice and Bob transforms to $\ket{\psi_3}_\text{ABC}$ in \eqref{eq:psi 3}.

\item
Bob inputs the photon components in path states $\ket{1}_\mathrm{C}$ and $\ket{2}_\mathrm{C}$ to the D-DCFO$_{K,N}$ gate. From \eqref{eq:D-DCFO input}--\eqref{eq:D-DCFO output}, unless the photon is absorbed by the electron in the \ac{DDCFO}$_{K,N}$ gate, it transforms $\ket{\psi_3}_\mathrm{ABC}$ as follows:
\begin{equation}
\begin{aligned}
\ket{\psi'_3}_{\text{ABC}}
	&=
	\gamma
	\ket{\psi}_\mathrm{A}
	\ket{00}_\text{BC}
	\\
	&\hspace{0.35cm}+
	\delta
	\alpha
	e^{-\iota\left(\varphi+\phi\right)/2}
	\cos\left(\theta/2\right)
	\ket{101}_{\text{ABC}}
	\\
	&\hspace{0.35cm}+
	\delta
	\alpha
	e^{-\iota\left(\varphi-\phi\right)/2}
	\sin\left(\theta/2\right)
	\ket{011}_{\text{ABC}}
	\\
	&\hspace{0.35cm}-
	\delta
	\beta
	e^{\iota\left(\varphi+\phi\right)/2}
	\cos\left(\theta/2\right)
	\ket{002}_{\text{ABC}}
	\\
	&\hspace{0.35cm}-
	\delta
	\beta
	e^{\iota\left(\varphi-\phi\right)/2}
	\sin\left(\theta/2\right)
	\ket{112}_{\text{ABC}}
\end{aligned}
\end{equation}
with probability
\begin{align}
\begin{aligned}
\lambda_3
	&=
	\left(
		1-
		\vert\delta\vert^2
		\sin^2\left(\theta/2\right)
		\cos^2\theta_K
		\sin^2\theta_N
	\right)^{KN}
	\\
	&\hspace{0.425cm}
	\left(
		1-
		\vert\delta\vert^2
		\sin^2\left(\theta/2\right)
		\sin^2\theta_K
	\right)^K.
\end{aligned}
\end{align}

\item
Alice applies the $\M{X}$ followed by the $\M{Z}$ on her qubit and Bob performs $\M{X}\M{Z}\M{X}$ operation on the path state    $\ket{2}_\mathrm{C}$, respectively.

\item
Bob inputs the component of the photon in path state $\ket{1}_\mathrm{C}$ to the H-\ac{CQZ}$_{M,N}$ gate and $\ket{2}_\mathrm{C}$ to the V-\ac{CQZ}$_{M,N}$ gate, respectively. Unless the photon is discarded in the \ac{CQZ}$_{M,N}$ gates, Bob applies $\M{X}$ operator on the component of photon in path state $\ket{1}_\mathrm{C}$ and the composite of Alice and Bob transforms to $\ket{\psi_4}_\mathrm{ABC}$ in \eqref{eq:psi 4} \footnote{In the presence of the absorptive object, the H(V)-\ac{CQZ}$_{M,N}$ gate transforms $\ket{\mathrm{V}\left(\mathrm{H}\right)}_{\mathrm{p}}$ to $-\ket{\mathrm{H}\left(\mathrm{V}\right)}_{\mathrm{p}}$.}
with probability
\begin{align}
\begin{aligned}
\lambda_4
	&=
	\left(
		1-
		\nabla_7
		\sin^2\theta_M
	\right)^M
	\\
	&\hspace{0.425cm}
	\prod_{i=1}^M
	\left[
		1-
		\nabla_8
		\sin^2\left(i\theta_M\right)
		\sin^2\theta_N
	\right]^N,
\end{aligned}
\end{align}
where $\nabla_7$ and $\nabla_8$ are defined as:
\begin{align}
\nabla_7
	&=
	\vert
		\delta
		\alpha
	\vert^2
	\cos^2\left(\theta/2\right)
	+
	\vert
		\delta
		\beta
	\vert^2
	\sin^2\left(\theta/2\right),
	\\
\nabla_8
	&=
	\vert
		\delta
		\beta
	\vert^2
	\cos^2\left(\theta/2\right)
	+
	\vert
		\delta
		\alpha
	\vert^2
	\sin^2\left(\theta/2\right).
\end{align}

\item
To disentangle the ancillary qutrit, Bob applies the local operation $\M{V}_2$ followed by the Hadamard gate $\M{H}$ on the ancilla and performs the measurement on the ancilla in the computational basis. It collapses the composite state $\ket{\psi_4}_{\text{ABC}}$ to $\ket{\psi_{5m}}_\mathrm{AB}$ in \eqref{eq:psi 5}.

\begin{figure}[t!]
 \centering{
\includegraphics[width=0.35\textwidth]{CCZ.eps}}
    \caption{
   A counterfactual controlled-$\M{Z}$ operator.
   }
    \label{fig:CCZ}
\end{figure}

\item
Alice and Bob apply the global unitary operation $\M{Q}_3$ depending on
Bob's announcement of the measurement result $m$ with classical communication. For $m=0$, $\M{Q}_3=\M{I}$. For $m=1$, Alice applies the $\M{Z}$ operator on her qubit and Bob applies $\M{X}$. Bob throws his photon towards PBS$^{\mathrm{H}}$ again and inputs the V components of the photon to the V-\ac{CQZ}$_{2M,N}$ gate with $2M$ outer cycles to apply the controlled-$\M{Z}$ operator counterfactually as shown in Fig.~\ref{fig:CCZ}.
Unless the photon is discarded in the \ac{CQZ} gate,
Bob recombines the H and V components of the photon with probability
\begin{align}
\begin{aligned}
\lambda_5
	&=
	\left(
		1-
		\vert
			\alpha
			\gamma
		\vert^2
		\sin^2\theta_M
	\right)^{2M}
	\\
	&\hspace{0.35cm}
	\prod_{i=1}^{2M}
	\left[
		1-
		\vert
			\beta
			\gamma
		\vert^2
		\sin^2\left(i\theta_M\right)
		\sin^2\theta_N
	\right]^N,
\end{aligned}
\end{align}
followed by applying the $\M{X}$ operator on his qubit.
Unless the photon is discarded, the composite state $\ket{\psi_{5m}}_\mathrm{AB}$ transforms to $\ket{\psi_{6m}}_\mathrm{AB}$ in \eqref{eq:psi 6} with probability $\lambda_5^m$.

\end{enumerate}
In the CCT protocol for general input states, there exists the nonzero probability (abortion rate) $\zeta_m$ that the photon is traveled over the quantum channel and the protocol fails in counterfactuality where
\begin{align}
\label{eq:FP}
\zeta_m
	=
	1-
	\lambda_2
	\lambda_3
	\lambda_4
	\lambda_5^m,
\end{align}
which tends to zero as $M,N,K\rightarrow\infty$.

\begin{figure*}[t!]
 \centering{
\includegraphics[width=0.63\textwidth]{QZ-CQZ-BTS-BNCU.eps}}
    \caption{
A \ac{CCT} protocol using the H(V) DCFO$_{K,N}$ gate for Bell-type states of 1(0)-class. Here $\M{\mathcal{C}}_1=\M{X}^{1-\ell}\M{U}\M{X}^\ell$, $\M{\mathcal{C}}_2=\M{X}\M{Z}^{1-\ell}\M{X}^{1-\ell}$ for $\ell$-class states and $\ket{\psi_0}_\mathrm{ABC}=\ket{\psi_0}_\mathrm{AB}\otimes\ket{0}_\mathrm{C}$.
}
    \label{fig:QZ-CQZ-BTS-BNCU}
\end{figure*}

\subsection{\ac{CCT} for Bell-Type Input States}\label{sec: 2-6}
To demonstrate the implementation of \ac{CCT} for Bell-type states, consider that the composite input state of Alice and Bob is $\ket{\psi_0}_\mathrm{AB}=\ket{\psi^\pm_{0\ell}}_\text{AB}$,  $\ell=0,1$, in (19) of the main text.
Similar to the general setup, Bob starts the protocol by entangling his qubit with the ancillary qubit $\ket{0}_\mathrm{C}$ by throwing his photon towards PBS$^\mathrm{H}$ as shown in Fig.~\ref{fig:QZ-CQZ-BTS-BNCU}. The \ac{CCT} protocol for Bell-type states of 1(0)-class takes the following steps.

\begin{enumerate}
\item
Bob applies $\M{\mathcal{C}}_1$ on the component of the photon in path state $\ket{1}_\mathrm{C}$ where $\M{\mathcal{C}}_1=\M{X}^{1-\ell}\M{U}\M{X}^\ell$ for $\ell$-class states.

\item
Bob inputs the photon component in path state $\ket{1}_\mathrm{C}$ to the H(V)-\ac{DCFO}$_{K,N}$ gate. From \eqref{eq:H(V)-DCFO input}--\eqref{eq:H(V)-DCFO output}, unless the photon is absorbed by the electron, the H(V)-\ac{DCFO}$_{K,N}$ gate transforms the composite of Alice and Bob as follows:
\begin{widetext}
\begin{align}
\ket{\psi'_{0}}_\text{ABC}:
	\begin{cases}
	\ket{\psi'^{\pm}_{00}}_\text{ABC}
	=
	\alpha
	\ket{100}_\mathrm{ABC}
	\pm
	\beta
	\left(
			-e^{\iota\left(\varphi+\phi\right)/2}
			\cos\left(\theta/2\right)
			\ket{001}_\mathrm{ABC}
			-
			e^{\iota\left(\varphi-\phi\right)/2}
			\sin\left(\theta/2\right)
			\ket{111}_\mathrm{ABC}
	\right),
	\\
	\ket{\psi'^{\pm}_{01}}_\text{ABC}
	=
	\gamma
	\left(
			e^{\iota\left(\varphi+\phi\right)/2}
			\cos\left(\theta/2\right)
			\ket{101}_\mathrm{ABC}
			+
			e^{\iota\left(\varphi-\phi\right)/2}
			\sin\left(\theta/2\right)
			\ket{011}_\mathrm{ABC}
	\right)
	\mp
	\delta
	\ket{000}_\mathrm{ABC}
	\end{cases}
\end{align}
\end{widetext}
with probability
\begin{align}
\begin{aligned}
\lambda_6
	&=
	\left(
		1-
		\nabla
		\sin^2\left(\theta/2\right)
		\cos^2\theta_K
		\sin^2\theta_N
	\right)^{KN}
	\\
	&\hspace{0.425cm}
	\left(
		1-
		\nabla
		\sin^2\left(\theta/2\right)
		\sin^2\theta_K
	\right)^K.
\end{aligned}
\end{align}

\item
Alice applies the $\M{X}$ followed by the $\M{Z}$ on her qubit and Bob performs $\M{\mathcal{C}}_2=\M{X}\M{Z}^{1-\ell}\M{X}^{1-\ell}$ for $\ell$-class states on the photon component in path state $\ket{1}_\mathrm{C}$, respectively.
\item
Bob inputs the photon component in path state $\ket{1}_\mathrm{C}$ to the V-\ac{CQZ}$_{M,N}$ gate and recombines the photon component in path state $\ket{0}_\mathrm{C}$ and $\ket{1}_\mathrm{C}$ after the V-\ac{CQZ}$_{M,N}$ gate. At the end of the protocol, unless the photon is discarded in the V-\ac{CQZ}$_{M,N}$ gate,  Bob recombines the H and V components of the photon and the composite state $\ket{\psi'_{0}}_\text{ABC}$ transforms to $\ket{\psi}_\mathrm{ABC}$ in (23) of the main text with probability
\begin{align}
\begin{aligned}
\lambda_7
	&=
	\left(
		1-
		\nabla_{9\left(10\right)}
		\sin^2\theta_M
	\right)^M
	\\
	&\hspace{0.35cm}
	\prod_{i=1}^{M}
	\left[
		1-
		\nabla_{10\left(9\right)}
		\sin^2\left(i\theta_M\right)
		\sin^2\theta_N
	\right]^N
\end{aligned}
\end{align}
for $1\left(0\right)$-class states where
\begin{align}
\nabla_{9}
&=\nabla\cos^{2}\left(\theta/2\right),
\\
\nabla_{10}
&=\nabla\sin^{2}\left(\theta/2\right).
\end{align}

\end{enumerate}
For the CCT protocol with Bell-type states, the probability (abortion rate) that the protocol fails to ensure the counterfactuality is given by
\begin{align}
\zeta
	=
	1
	-
	\lambda_6
	\lambda_7
\end{align}
tending again to zero as $M,N,K\rightarrow\infty$.

This work was supported in part by the the National Research Foundation of Korea under Grant  2019R1A2C2007037 and in part by the Office of Naval Research under Grant  N00014-19-1-2724.

redpajama_set_name: RedPajamaArXiv


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Software is critical to everything we do in the modern world and is behind our most critical systems. As such, it is imperative that it be secure by design. Software security is therefore as much a business decision as it is about avoiding security risks.
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text:
American Journal of Energy Engineering
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Home / Journals / Earth, Energy & Environment / American Journal of Energy Engineering / Article
Natural Antioxidant Changes in Fresh and Dried celery (Apium graveolens)
Volume 3, Issue 2-1, March 2015, Pages: 12-16
Received: Feb. 7, 2015; Accepted: Feb. 8, 2015; Published: Feb. 27, 2015
Views 3069 Downloads 140
Manal A. Sorour, Food Engineering and Packaging Dept., Food Technology Research Institute, Agric. Research Center, Giza, Egypt
Naglaa H. M. Hassanen, Special Food and Nutrition Dept., Food Technology Research Institute, Agric. Research Center, Giza, Egypt
Mona H. M. Ahmed, Special Food and Nutrition Dept., Food Technology Research Institute, Agric. Research Center, Giza, Egypt
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The effect of temperature on natural antioxidant changes in fresh and dried celery was studied. Celery herbs were dried at 50 and 90ᵒC using a laboratory scale hot air dryer. Fifteen phenolic components (gallic acid, protocatechuic acid, catechol , chlorogenic acid, syringic acid, caffeine , p-coumaric acid, ferulic acid, salycilic acid, cinnamic acid, chrysin, pyrogallol, ellagic acid , catechin and caffeic acid), five flavonoids components were identified in celery herbs (apignen, hesperitin, luteolin, quercetrin and rosmarinic) and three isoflavones components were identified in celery herbs (daidzein, genistein and isorhamnetin) were identified in celery herbs at 50 and 90ᵒC. The chemical constituents of apium graveolens volatile oil were determined, the results observed that eleven components were isolated from apium graveolens essential oil and classified into five chemical categories namely, monocyclic terpenes (78.24%), bicyclic terpenes (14.88%), aliphatic hydrocarbons (1.79%), ketones (0.19) and sesquiterpene (2.89%). These identified compounds accounted for 97.99 % of the composition of apium graveolens essential oil. Organoleptic evaluation of Apium graveolens represented the mean scores and their statistical analysis indication for color, aroma, taste, texture and overall acceptability for biscuit treatments mixed with different concentrations of dried Apium graveolens at 50°C and 90°C.
Drying of Celery, Phenolic Compounds, Flavor, Application of Dried Celery, Flavones
To cite this article
Manal A. Sorour, Naglaa H. M. Hassanen, Mona H. M. Ahmed, Natural Antioxidant Changes in Fresh and Dried celery (Apium graveolens), American Journal of Energy Engineering. Special Issue: Energy Conservation in Food Industry. Vol. 3, No. 2-1, 2015, pp. 12-16. doi: 10.11648/j.ajee.s.2015030201.13
M. Keinänen and R. Julkunen-Tiitto, Effect of sample preparation method on birch (Betula pendula Roth leaf phenolics, Journal of Agricultural and Food Chemistry, 44: 2724–2727, 1996.
J. Pokorny, Addition of antioxidants for food stabilization to control oxidative rancidity, Czech Journal of Food Sciences, 4: 299–307, 1986.
D.O. Kim, S.W. Jeong and C. Y. Lee, Food Chem. 81:321–326, doi:10.1016/S0308-8146(02)00423-5, 2003
G. Giuseppe, B. Davide, G. Claudia, Ugo Leuzzi and C. Corrado: Flavonoid Composition of Citrus Juices. Molecules, 12, 1641-1673, 2007
S. S. Fazal and R. K. Singla, Review on the Pharmacognostical & Pharmacological Characterization of Apium Graveolens Linn. Indo Global, Journal of Pharmaceutical Sciences, 2(1): 36-42, 2012.
A. Schieber, P. Keller, R. Carle, Determination of phenolic acids and flavonoids of apple and pear by high performance liquid chromatography system, J. of Chromatography A, 910:265-273, 2001.
D. Mantovani, L. C. Filho, L. C. Santos, V.L.F. de Souza and C.S. Watanabe, The use of HPLC identification and quantification of isoflavones content in samples obtained in pharmacies. Acta Scientiarum. Biological Sciences. Maringá, v. 33, n. 1, pp. 7-10, 2011.
M. Guenther, The essential oils, Vol. III, IV, 4th Ed. D. Van Nostrand Company, Inc. Princeton, New Jersy. Tornto, New York, London, 1961.
Naglaa H.M. Hassanen and Gehad, F.A.Fath El-bab. Anti-microbial activities of Matricaria chamomilla L. flower. Egypt. J. Biomed. Sci., 37: 189-211, 2011.
M. A. Amerine, R. M. Panglorn, and Roessler, E. B. (): Principals of sensory evaluation of food"Academic Press, New York, 1965.
G.W. Snedecor and W.G. Cochran, Statistical methods.7th Ed., p. 420. Iowa Stat. Univ. Press, Ames, Iowa, USA, 1980.
A. Crozier, B. J. Indu and N. Michael, Dietary phenolics: chemistry, bioavailability and effects on health. Nat. Prod. Rep., 26, 1001–1043, 2009.
M. S. M. Manal and S. A. Sahar, The Effects of Purslane and Celery on Hypercholesterolemic Mice, World Journal of Dairy & Food Sciences, 7 (2): 212-221, 2012.
Liga Priecina and Daina Karklina, Natural Antioxidant Changes in Fresh and Dried Spices and Vegetables, International Journal of Biological, Veterinary, Agricultural and Food Engineering Vol. 8, No. 5, 480-484, 2014.
N. Balasundram, K. Sundram and S. Samman, Phenolic compounds in plants and agri-industrial by-products: Antioxidant activity, occurrence, and potential uses, Food Chemistry, 99, 191- 203, 2006.
A. Wach, K. Pyrzyn´ska and Magdalena Biesaga, Quercetin content in some food and herbal samples. Food Chemistry 100 :699–704, 2007.
Misic Dusan, Irena Zizovic, Marko Stameni, Ruzica Asanin, Mihailo Risti, Slobodan Petrovi and Dejan Skala, Antimicrobial activity of celery fruit isolates and SFE process modeling Biochemical Engineering Journal, 42, 148–152, 2008.
O. O. Okoh, A. P. Sadimenko, O. T. Asekun and A. J. Afolayan, The effects of drying on the chemical components of essential oils of Calendula officinalis L. African Journal of Biotechnology Vol. 7 (10), pp. 1500-1502, 2008.
Lawiess and Julia, The Encyclopaedia of essential oils.Published in Great Britain in 1992 by Element Books Limited Longmead, Shaftesbury, Dorset, pp.81-84 and 103-105, 1992.
Van Wassenhove, F., Dirinck, P., Vulsteke, G. and Schamp, N., Aromatic volatile composition of celery and celeriac cultivars. Hort. Sci., 25, 556-559, 1990
Fazal, S. S., Ansari, M. M., Singla, R. K., Khan, S., Isolation of 3-n-Butyl Phthalide & Sedanenolide from Apium graveolens Linn. Indo Global Journal of Pharmaceutical Sciences, 2(3): 258-261, 2012.


text:
Aarghthropology
Oct10 by Faemon
I'd been curious about Dreamtime just for the word. It wasn't something I could learn about from osmosis. The most culture-altering thing I learned from going to an Australian school was that it's a "rubbish bin" not a "trash can". So, to start with the first ethnography I could get my hands on isn't the recommended beginning. Definitely, it gave me a lot more to consider about one's relationship to the land than the usual sentiment to just have that relationship and figure out how to keep it up from there.
But there was barely any connection to the hallucinations people get during sleep.
I finally figured out why. Lucien Levy-Bruhl was a French scholar who wrote Primitive Mythology: The Mythic World of the Australian and Papuan Natives, among other titles. Many of his observations influenced ideological lineages that I adopt heavily, such as Jungian psychology.
This work also influenced the translations of one William Edward Hanley Stanner, an anachronistically conscientious journalist, soldier, and political advisor. He was one of the first to speak out against a "naive search for uncontaminated cultures" and posited that anthropologists had a responsibility to see to the welfare of contacted and colonized peoples. Stanner counseled against racist policies in Australian law of his time.
For all those good things, Stanner glossed alcheringa as Dreaming and then Dreamtime. This was a mistranslation, or a misinterpretation. It got popular. So, Dreaming continues to be the gloss of wingara, mungai, poaradju, and everything in all the Aborigines languages that might be something sort of maybe like alcheringa. None of these, evidently, can be accurately Romanized because half the sounds in Arrernte are absent in English. Other Aboriginal languages might be very slightly more compatible.
There may have never been any such thing as Dreamtime.
So…does that mean I can use the word for Poesy stuff? Nah, I don't think so. I'm a little bit reminded of a short story collection, The Toughest Indian in the World by Sherman Alexie, where one character snarks to another, "You might be Native American, but you're not Indian." The connotations being that Indian is more authentic a descriptor of…now I don't know how to say it…surviving descendants of pre-colonial Americans? And Native American, to the speaker, was a politically-correct term that was a band aid to a broken bone, deserving of contempt for trying to help but not really helping, because it was just a couple of words.
Except that I live right beside actual South Asian India, and there will almost always be someone from South Asian India sharing the public space with me, and being demographic, and generating public holidays, and making food and fashion better in this town so part of me was about to give the same outraged, "Heeey…incorrect…" that I'd been giving the colonial ignoramuses who decided that Americans were Indians in the first place.
But, sometimes this happens. Words mean things, but something else than one thinks.
Earlier this week I attended a lecture on Ibn Khaldun, "the father of Islamic anthropology". The speaker was a Muslim woman, a classmate of Cecilia's. Khaldun had characterized the stages of civilizations on the rise and fall, articulated a way to be critical without being reductionist, criticized discrepancies in historical texts caused by "partisanship, overconfidence in the sources, the inability to read for intention, and the ignorance of laws that govern a culture" (the last one apparently not really being in existence until he wrote his observations on the laws that govern a culture), among other fascinatingly lucid concepts.
The Q & A portion from the rest of the class, fortunately or unfortunately, were more like requests for the basics of Islam, especially framed as a comparison to Christianity. The class would have needed to know more than they did about Islam before being able to delve into questions of anthropology from an Islamic perspective…which took more time than had been given. Cecilia said later that she would have liked it if the questions were more on the anthropology of the thing, because having a non-Western anthropologist from more than six hundred years ago still have a voice in this discipline was so refreshing. I learned more about Islam than I had from osmosis, at least, especially the history of it that even a short explanation contained some serious political complexities.
The follow-up to that was a talk on the work of Clifford Geertz, who analyzed cultures as a text in the way of literature. That talk was far more vague and conceptual, but one line quoted from Geertz caught my interest, which is that "culture is public because meaning is". The anthropological studies of appropriation might observe a different dynamic, but as far as Geertz's purpose went, to impart meaning to any act or symbol, there is nothing else to work with but the world.
My question to the second speaker then was about a comparison between the patterns of Javanese and Balinese batik. (Geertz specialized in the anthropological study of Indonesia. And Morocco, for some reason.) Abstract patterns characterize Javanese batik due to religious restrictions against portraying living things, considered an attempt at competition with the creator-god. Balinese batik patterns include flowers and Garuda birds with no such problem: rather than an act of hubris, I think the art becomes a platform from which to disseminate the mythos and generate reminders of it. The act of creating batik cloth is the same in both islands, waxing and dying. What creates those dynamics of meaning?
The speaker answered that it was up to the people who actually made the patterns, that what practitioners said it was, as "insiders" to the purpose and structure and social context of the act, would be the dynamics of meaning defined. Understanding a culture, Geertz said, would normalize it. This is not necessarily a process of removing the particularities of a culture, only contextualizing them.
This entry was posted in history, sidereal, sidereal fetch, studies.
← Contributions to Otherfaith Mythology
On Poetics →


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(December 17, 2010) T2p.tv - the online network providing On Demand sailing coverage - was in Miami for the ORACLE RC 44 Cup Miami. This was the American debut for the RC44 class, which has grown a season championship of events in Europe and the Middle East.
A significant feature of the class is the travel logistics, where the movement of each team's equipment and boats is organized by the class management. This class moves as a pack, and the Miami event saw a star studded fleet at the highest grand prix level the sport can offer.


text:
Q: Can we pass vue data object in command attribute in element-ui dropdown? HTML

<el-dropdown @command="handleCommand">

    Dropdown List

  <el-dropdown-menu slot="dropdown">
    <el-dropdown-item command="a">{{fields}} 1</el-dropdown-item>
    <el-dropdown-item command="b">Action 2</el-dropdown-item>
    <el-dropdown-item command="c">Action 3</el-dropdown-item>
    <el-dropdown-item command="d" disabled>Action 4</el-dropdown-item>
    <el-dropdown-item command="e" divided>Action 5</el-dropdown-item>
  </el-dropdown-menu>
</el-dropdown>

JS File
var Main = {
    methods: {
      handleCommand(command) {
        this.$message('click on item ' + command);
      }
    },
  data() {
        return {
            fields: 'test'
        }
  }
  }
var Ctor = Vue.extend(Main)
new Ctor().$mount('#app')

The example above is from https://element.eleme.io/#/en-US/component/dropdown#dropdown
here is a codepen for this https://codepen.io/pen/?&editable=true=https%3A%2F%2Felement.eleme.io%2F
So, I am trying to pass "field" data from js file to command attribute in {{fields}} 1 instead of "a". My assumption was to pass using the two curly brackets, but i think command attribute only takes a string. Any idea? Thanks.

A: You can pass an object to the command option, but you have to add colon before command
<el-dropdown @command="handleCommand">

    Dropdown List

  <el-dropdown-menu slot="dropdown">
    <el-dropdown-item :command="{action: 'a', fields: fields}">{{fields}} 1</el-dropdown-item>
  </el-dropdown-menu>
</el-dropdown>

JS
methods: {
      handleCommand(command) {
        this.$message('click on item ' + command.a + 'command.fields');
      }
    },

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Many people report sleeping with either one or both arms draped over the facial area. There have been numerous suggestions and theories put forward to explain this, including anxiety, feelings of shame, lack of self esteem and fear of moths.
However, a more thorough investigation by Swedish psychologists found that in order to correctly study sleeping people, most researchers placed their subjects in well lit rooms. By switching off the lights, the Swedish experts think that not one of the people they studied adopted this position.
They cannot be certain however as they could not see what was happening.


text:
Local businesses urged to register for 'Eat Out to Help Out' scheme
Local Economy, My Work in Bridgend & Porthcawl, News, Press Releases
BRIDGEND MP Jamie Wallis is urging restaurants and pubs in the borough to register under the Eat Out to Help Out scheme brought in by the UK Government.
The scheme applies on Mondays, Tuesdays and Wednesdays throughout August. Pubs, restaurants and cafes are allowed to open up indoors in Wales from August 3 but the scheme also applies to those serving food outdoors but not take-aways.
Under the scheme, all participating businesses need to register online at Gov.UK
Jamie, who is a Welsh Conservative, said: "It has been set up to be as easy as possible for both businesses and patrons. People do not need vouchers – they can just go along to any participating business and the discount of up to £10 per person is taken off the bill. Businesses reclaim the money through an online portal supported by HMRC and can be made weekly with money being paid into their bank accounts within five working days.
"I really hope people will take advantage of this and boost businesses in Porthcawl and Bridgend by supporting them. The hospitality industry has been very hard hit by this pandemic and this is the UK Government's way of giving them extra support when they re-open.
"I see no reason why any business should fail to register as it's so easy. And it will undoubtedly encourage people to eat out especially if the whole family goes when the cost could be quite high."


First row sports is listing 1 soccer links in this category. Updated at 01:56:10 Coordinated Universal Time, 69 sec. ago. Use firstrowsports clock to set the time zone for displayed links.
Are you a true soccer fan? Don't forget to visit main pages of european football or the biggest soccer league in the USA to get the latest news.


text:
A Little Game
Posted in: No Huddle by Brent Lorentson on February 4th, 2015
No Huddle Reviews
I have to admit, seeing Ralph Macchio in any role other than in The Karate Kid is a bit jarring for me. Growing up in the 80's, it's hard to see Macchio and not hope for him to randomly balance on one leg and do a crane kick, but alas, decades have passed and Macchio has come a long way. Now we get to see Macchio all grown up step into the role of dad in his new film A Little Game. While Macchio may share the headlines of this all-star cast that includes F. Murray Abraham, Janeane Garofalo, and Olympia Dukakis, the real star of the film is a name many would be unfamiliar with, Makenna Ballard. You may not know her name now, but after this debut performance I'm willing to bet this is only the first step in a bigger and promising career.
Max (Ballard) goes through the unfortunate hurdle of being removed from her school where she was once surrounded by her friends to being thrust into a new school so she can get a "better" education. Though the school may look good on transcripts when applying for ivy league schools, right now Max is simply a 10-year-old girl who simply wants to be accepted by her classmates and have fun like any other 10-year-old girl would. Unfortunately being the new girl at school attracts the attention of a rival classmate who sees Max as nothing more than competition.
As Max's parents (Macchio and Garofalo) work overtime to help pay for Max's education, Max also has to struggle with the loss of her grandmother Yaya (Dukakis). It's no surprise that in her walks home from school, Max starts up a friendship with the crotchety Norman (Abraham) whom she sees sitting alone while others around him are playing chess. When Max propositions Norman to teach her the game of chess, little does she realize that he will eventually teach her many life lessons along the way as she learns to play the game.
A Little Game isn't just simply about a young girl learning to play chess, but obviously a coming-of-age story for young girls. The issue that I have with this film is really what holds this film back is that it tries so hard to force the jokes and get laughs that are just not deserved. Whether they are depending on sound or music cues to emphasize the joke, or dealing with exaggerated expression shots, either way it distracts from the story which actually works on its own merit. Speaking of forced moments, when a character dies there is an exterior shot that gives us nothing but people filing into a church; this is an insert shot that simply never should have made it into the final cut and simply detracts from the performances.
When we get to see Max under the tutelage of Norman the film comes alive, and it's a shame these lessons don't last longer, because the chemistry between these two is a beautiful thing that I haven't seen in a while with this kind of film. As the film builds steadily towards Max competing in a chess match with her school rival you would hope for perhaps more conflict, something to raise the stakes, but we don't get that, and instead we get what feels like a rushed ending that just feels too tidy and neat.
I understand the filmmakers were not setting out to do the female version of Bobby Fischer, but there were some missed opportunities to at least attempt to make these chess sequences seem more dramatic. Even when Max sets the stakes, you can't help but say to yourself, "She's ten, what makes her think this is even an option?" I won't say anything more about it, but it's a distracting moment that simply pulled me out of the film.
Going into the film without any big expectations, I can say I enjoyed the film more than I expected, and that is largely in part to some great casting choices. Though the actual chess sequences between Ballard and Abraham are too few in my opinion, it is in these sequences where you get to see some excellent acting and filmmaking.
Brent Lorentson
Brent Lorentson is a horror writer and film critic based out of Tampa, Florida. With a BA in Digital Film, he co-wrote and co-directed Scavenger Hunt. His short stories have appeared in various horror anthologies. In 2019 his short script Fertile Blood will be a part of the anthology horror film Slumber Party. He is currently working on his first novel A Dark and Secret Place set to be released in late 2019. Favorite Films: Taxi Driver, Fight Club, I Saw the Devil, The Wild Bunch, Dawn of the Dead, A Clockwork Orange, Pulp Fiction, Heathers, The Monster Squad, and High Fidelity.
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America's beverage companies take seriously their sustainability goals. Just this summer, PepsiCo and the Recycling Partnership announced a new initiative to significantly increase the amount of plastic containers recycled from curbside collections. PepsiCo has pledged $10 million over a five-year period to support the new "All In On Recycling" challenge, which aims to attract $100 million for curbside recycling programs.
But recycling shouldn't just take place at home; it should be accessible everywhere we go! That's why Keurig Dr Pepper teamed up with Keep America Beautiful (KAB) as a part of KAB's Park Recycling Bin Grant Program, funding 34 grants. That equals 936 new recycling bins in public parks across the country, making recycling more accessible for Americans enjoying the outdoors.
Not only are we helping to make it easier than ever to recycle our containers, we're also implementing even more sustainability practices into our business models. Earlier this year, The Coca-Cola Company announced that it is pursuing an ambitious new goal, which is part of a holistic plan called "World Without Waste." Coca-Cola's goal is an industry-first - to collect and recycle the equivalent of every bottle or can it sells globally by 2030.
Recycling is more than a core element in America's beverage companies' history of innovation. It's something we'll never stop working to improve. Click here to read more about how America's beverage companies are Innovating, Naturally.


Jessica was only in her 30s when her family's history of diabetes became her own reality. Now she is determined to take control of her disease so she can watch her seven nieces and nephews grow up.
During American Diabetes Month® we're sharing the stories of people affected by diabetes, just like Jessica. What do YOU want the world to know about this disease?
If you or someone you know is living with diabetes, share your story during November using #ThisIsDiabetes. And learn more at http://diabetes.org/adm.
This entry was posted in About Us, Advocacy, American Diabetes Month, Family, High-Risk Populations, Life with Diabetes, Prediabetes, Stop Diabetes, This Is Diabetes and tagged Advocacy, American Diabetes Association, diabetes, diabetes prevention, family, Prediabetes, Stop Diabetes, type 2 diabetes. Bookmark the permalink.
Today I went to the doctor he said I was pre-diabetes this is my which really scared me ,about 6 weeks ago I stopped smoking after 38 yrs. I think when I stopped smoking then I started eating more in just a few I gained 8 lbs.lwondering what's worsed dieing of cancer or slowly losing parts of your body ? Ian 63 years old and I am taking care of my mother who suffers from dementia, the stress is another thing ..Today I went to the senior center and asked what I can do for both of us before we both drop dead . There going to help me first I have to lose about 35 lbs no more starchy foods . This is the first time in my life I can say I am scared . I lost most of my friends I grew up with ,I just wish I had someone to talk to about these problems, a friend someone I can trust. Well that's my story I hoping I did not bore anyone.Thank You and God Bless You.


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OP here. When I think about shidduchim for my kids I think they can marry almost anyone but NO ADD cause atleast then they have a fighting chance on not having all ADD kids. BH my kids have many good qualities but they are ALOT of work. The good news is my ADHD one is sooo polite and hardworking and has the best middos. My inattentive one is the sweetest mushiest love muffin and my youngest also a disorganized mess but the kindest sole you could ever meet.
Another Pink, sad to post this but I dreamed of a large family but really feel that having such chaos in my home has made me unable to parent more kids. Hoping to feel different soon but it's been 8 years since my last child and as of now this is how I feel.
Edited to correct autocorrect! Meant unable not unstable!
Same here....I have 4 kids, and right now I'm just done. And I only have one kid on meds!! My house is super chaotic, and I'm seriously struggling sometimes.
I feel my adhd gives me an advantage in having a large family. And I stopped taking meds when I got married. I do flylady for the house and empowered wife to work on my marriage.
I'm able to function on very little sleep.
I get more organized the more kids I have. As I'm forced to.
I'm able to handle a lot of chaos and mess.
My kids will all be diagnosed with some form of adhd at some point... I don't sweat it. It's just a brain style.
Ectomorph, that's cause your the mom with ADD I am speaking about having multiple kids with it. If I did have it I am sure I would have more energy for them. As it is I am more of a laid back low energy type so it's a hard combo! I see how it could work in your advantage for sure!!
I have adhd too, unofficially doagnosed and desperately in need of meds....like I said above, my house is chaotic. Each person is different, and each person deals and copes differently. Also, having it yourself, and mothering multiple kids with it is very different. Do you have any kids with adhd, diagnoses or not?
OP, more than medication, I think that your work with them (and possibly a therapist's, as well) will be to teach them organization strategies. The more they learn in childhood, the better they will cope with increased pressure as an adult.
I have ADD-like traits, and I grew up in a house that was a disorganized mess. That definitely makes me appear more ADD than I would if I had grown up and learn organizational strategies. My brain is actually hardwired to be pretty compartmentalized, but my nurture superseded my nature.
All four of us have been diagnosed although one's asd is the prevailing dx for him. We have found the incredible gift of how ketosis clears our heads, lowers anxiety and even makes asd son's tics go away. Daughter in challenging university programme took it on after seeing effects in us. She is normal weight.
Bully for you. Both me and dh have ADHD as do all our kids, and it's meant we cannot have as large a family as we'd like. I actually loved school and was a perfect straight A student all the way through graduate school, and if I could get paid to keep going to school, that's what I'd do for a living (dh was the more stereotypical brilliant-but-poor-student).
Household management is just completely beyond me. Flylady was useless to me. More kids has not forced me to be more organized, it's just meant more chaos that dh and I struggle to stay on top of. I cannot function on little sleep. That's another reason I have to space my kids, the newborn sleep deprivation kills me. And since so far they all have ADHD, they all have various therapies, medicines, and accommodations at school, which has to be managed on top of the typical things that have to managed, and it all has to be done by two ADHD parents who already struggle with exactly these things. So no, ADHD has not made us into better parents. I don't think we're bad parents, we do all right, and obviously we haven't let it stop us from having kids (and we aren't yet ready to declare ourselves done, we would like to have more, if Hashem grants us the mental strength to do so), but it is probably the biggest reason why the 8+ kid family we've always dreamed of is just never going to happen.
My kids will all be diagnosed w adhd - they have precursors. I just do a lot of reminding and it does help a lot that I understand them and dont get overwhelmed by chaos.
I'm sure you're a wonderful parent. Not judging anyone. Just providing an alternative view.
Adhd differs between people and its not necessarily a tragedy.
Me too! I am practically the opposite of an ADHD personality - organized, methodical, laid-back. My husband definitely has undiagnosed ADHD with a strong genetic component (at least two of his sisters and his father most likely have it too), and I always say that G-d knew what He was doing when He gave me IF. I don't think I can handle much more than the blessings that I already have (still have some embryos in the freezer and will iy"H try for one more).
My oldest is a difficult child who's on meds (we're currently tweaking), my second is an angel in school so far b"H but very high-energy and an incessant talker (not going to bother having her diagnosed at this point because it only seems to affect her positively b"H), and even the baby is high-energy!
As a mom who relishes order and quiet, it's very challenging for me to parent this bunch, but it's definitely taught me to be more flexible, to let more things slide, and to find the upside to ADHD on a daily basis. Parenting them is so hard, but it's also so rewarding. And I have to give a shout-out to all the moms on here who have given me priceless perspective on ADHD threads - singling out imasinger here!
Are you me? Except I didn't deal with IF. I chose to have less kids because of the difficulty raising them and practically by myself because dh doesn't do that much. My oldest is really difficult because it's not just ADHD, it's also OCD that manifests a lot of like ADHD because it's in thoughts. So he doesn't pay attention because he's so hyperfocused on the thought that he has.
Thank you, I needed to hear that. Not feeling like such a wonderful parent today, but yeah, like I said, I know we're actually decent parents. I've been feeling a bit down lately, because we very much want to start TTC for another one, but we know we don't have enough of a handle on our existing kids at the moment for that to be doable. And no, we can't rely on having 9 months' warning to shape up, we've gone down that road before and it wasn't good.
Soul sisters My DH is out of the house for long hours, he commutes and also travels about once a month, so I'm on my own when it comes to appointments and therapy and everything, and it's really hard to do with the other kids around too. I don't know how people with full-time jobs and lots of kids do it. I have a flex-time job from home and my baby is home with me, and I find it really challenging to stay on top of my oldest's needs.
Right now we're in the process of finding a new psychiatrist who will evaluate DS properly to see if we need to treat anxiety or ADHD more, the more therapists we go through the more I think it's anxiety that manifests as ADHD (or it's both) and we need some clarity for meds. He's a brilliant kid and doing much better in school now on low-dose stimulant, but his appetite is poor and the after-school hours are really rough on our whole family.
Omg same! My oldest started meds and his appetite is so poor and it's still really hard at home with him. Also brilliant Bh!
ruby- hugs but it sounds like you are making the right decision.
As I mentioned before I have multiple siblings with adhd.
Me being very organized and having a very consistent stable home schedule that I worked out over time is great for the kids.
It is hard. But oh so rewarding.
I sometimes feel like I'm at the end of my rope. But then I start again. And I try again.
I find the hardest to deal with the teachers. I feel like instead of making my child grow, they are squashing her because she doesn't fit into any box. She is learning to read and write but her spirit is being crushed. And then I have to deal with the afteraffects.
I am at the point where I'm not sure keeping her in her class is best. Even if she has to make new friends.
When the going gets really tough I think about my sisters kids. They are sweet kids. But it's by far not as "fun" raising them as mine are.
Her young toddler loves watching her cook and bake. Mine loved having ME watch THEM cook and bake .
Life is a chaotic and fun around here!
So nice to have someone in the same boat The poor kid has had a rough time in school ever since he was three years old, and now that he's in 5th grade he's finally starting to make progress. Academically he was always fine until last year when the work got harder (and his teacher was a moron), but socially he has always struggled. This year, he's finally getting calls from friends, we're not getting calls from the principal, and we had the first-ever positive parent-teacher conference for him.
My DD, on the other hand, is every teacher's favorite because she's enthusiastic and highly sociable and just all-around adorable, and it's hard on my DS to see that. I'm hoping that this light at the end of the tunnel means we're almost out of the tunnel!
Also, I think he may have a hint of ASD... these kids are so hard to pin down.


text:
Richard L. Latterell (born  March 14, 1928) is an American environmental activist, He was a Biology professor at Shepherd University from 1968 to 1992. He founded the Jefferson County Watersheds Coalition, has led an annual cleanup of the Potomac River near Shepherdstown, West Virginia, and has conducted spring and fall counts of macroinvertebrate species in streams in Jefferson County, West Virginia. The presence and diversity of species have shown poor water quality in most streams, because of sediment from construction sites and inadequately treated sewer plant effluent.

Legal Action

Latterell was one of the plaintiffs in the landmark case, decided in 2003, on rules concerning degradation of West Virginia waters, OVEC v. EPA 3:02-0059 US District Court for Southern District of West Virginia, Huntington Division. The case won stricter rules protecting water quality.

Latterell was also one of the plaintiffs in the first successful case stopping a subdivision at the Jefferson County Board of Zoning Appeals, the Thorn Hill case in 2000. Later he and others appealed other variations of the Thorn Hill subdivision, and his initial win in West Virginia Circuit Court was ultimately overturned by later decisions in Circuit Court. From 2004 to 2007 he and other citizens were the targets of a SLAPP suit by the Thorn Hill developers for two million dollars in damages alleged based on their opposition to Thorn Hill. The judge decided for the citizens and against the developers.

Latterell also participated in cases on pollution at the West Virginia Public Service Commission and Environmental Quality Board.

He and his wife, Frances Meehan Latterell, took soil samples at a former apple orchard proposed for the Huntfield subdivision, and found high levels of lead and arsenic, from the lead arsenate formerly used as an insecticide. The developer, who had not reported test results for lead and arsenic, committed to stripping the polluted soil and encapsulating it in berms.

Other activities

Dr. Richard Lewis Latterell is a scientist in plant genetics.    He completed his PhD study on the plant genus nicotina in 1958 at Cornell University.   Dr. Latterell also studied the interaction of bees and red clover plant species utilization, while at the  University of Pennsylvania.  Later in his career was a pioneer exobiologist on the Mars Simulator II (MSII), which simulated both the day/night cycle and the nitrogen & carbon dioxide environment of Mars in the Tarrytown, NY laboratory.    Over 250 different seed types were tested for germination in the Mars Simulator II model, where over 50 plant species germinated without oxygen, including corn and rye.   Studies found that an African succulent plant (cereus cactus) and a Peruvian cactus variety survived the longest in these Martian atmospheres.  While working under these NASA contracts the 1960s for Union Carbide Laboratory in Tarrytown, New York, Dr. Latterell published studies in a variety of Academic Journals on seed germinations from these simulated Martian environments (MSII).

Nitrogen- and helium-induced anoxia – different lethal effects on rye seeds, Science  v.153 (July 1) p. 69-70 (1966)
Behavior of plants under extraterrestrial conditions – seed germination in atmospheres containing nitrogen oxides, Proceedings of the National Academy of Sciences, v.52 (July) p. 11-13 (1964
Changes in Sensitivity of Maize chromosomes to X Rays during Seed Germination,  American Journal of Botany, v49, n5 (May-Jun., 1962): 472-478
The oxygen effect and its relation to changes in radiosensitivity during seed germination, Mutation Research  v.4 (2) p. 191-200 (1967)
Nitrogen- and helium-induced anoxia – different lethal effects on rye seeds, v.153 (July 1) p. 69-70 (1966)
S.M. Siegel & Latterell, Richard.  Elements of SPACE BIOLOGY – An experimental approach to the basic biology of Stress. Contract NASA CR-75437
LATTERELL, R. Lo, and SIEGEL, S, M.  Differential losses of seed viability condition by chemically inert gases. Am. J. Bot. NASA #N67-25642  52(6, Pt. 2) ~622-623. (Abstr.) July 1965.
From 2000 to 2005, the Latterells helped write Vision 2020, a plan for Shepherdstown, West Virginia, and its area.
In 2005 the Latterells put their farm under a perpetual conservation easement with the Jefferson County Farmland Protection Board and the Land Trust of the Eastern Panhandle.

References

Description of farm and easement

Court opinion in OVEC v. EPA Annotated copy of the same opinion

Court opinion in Thornhill v. Latterell

WV Public Service Commission decision

1928 births
Shepherd University faculty
Living people
Activists from West Virginia
American atheists
American environmentalists
Educators from West Virginia
People from Jefferson County, West Virginia
21st-century American biologists

redpajama_set_name: RedPajamaWikipedia


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Unlike most yogurt and cereals, egg consists of only one ingredient - "eggs" itself. It is the cheapest source of high-quality protein. An average size egg contains 6 grams of high-quality protein which helps in sustaining mental and physical energy throughout the day. Egg yolk contains a substance, Choline which helps to promote normal cell activity, liver function and the transportation of nutrients throughout the body. It is also vital in the infant's memory functions development. Egg contains zero carbs and sugar, which mean you can eat a well-rounded breakfast during the week without feeling round yourself. This book consists of over 60 healthy, delicious egg-as-ingredient recipes, easy-to-find ingredients, easy-to-follow cooking steps, covering breakfast, lunch as well as dinner. Don't miss it !!! Grab one book and read. Should you have any comment on the book, please feel free to provide your review. Your review is important to me as it allows me to rectify my shortfall and provide you with much better reading experience in future.


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