%!TEX root = qlight-poster2017.tex
\begin{center}
  {\bf \Large \textsf{Many-pairs non-locality}}\\[.2cm]
collaborators:~Jean-Daniel~Bancal$^1$,~Yu~Cai,~Nicolas~Sangouard$^1$,~and~Valerio~Scarani.\\[-.2cm]
\end{center}
We consider the many-pairs scenario, when~$n$ identical entangled pairs are produced and measured collectively, and show experimentally that a Bell inequality can be violated in this scenario considering two binning strategy: majority vote and parity.
The maximal number of pairs for which a violation can be observed quantifies the high quality of the pair source. In our experiment we report a violation up to~$41$ pairs in the presence of majority voting and up to~$12$ pairs in the presence of parity binning~[1].

\begin{figurehere}
\begin{minipage}[c]{0.45\linewidth}
     \centering
         \includegraphics[width=.7\columnwidth]{manypairs/figure1.eps}\\[1cm]
         \includegraphics[width=.85\columnwidth]{manypairs/compression_setup.eps}
\end{minipage}
\begin{minipage}[c]{0.55\linewidth}
    \includegraphics[width=\columnwidth]{manypairs/majority_versus_separation_angle.eps}\\
    \includegraphics[width=\columnwidth]{manypairs/parity_versus_separation_angle.eps}
\end{minipage}
\figcaption{Top left: Many-pairs scenario.
  Bottom left: experimental setup: high purity non-collinear SPDC source of near-IR polarization entangles photon pairs.
  Right: CHSH parameter $S$ as function of the separation angle between measurement basis for majority voting (top) and parity binning (bottom).}
\end{figurehere}

% We assume each party is not able to observe the entire string of outcomes, but only their sum.
% We return to a two-input and two-output scenario using local binnings:
% \begin{align}\label{manyboxdef}
%   a_{xy}=\sum_{i=1}^n a_{xy}^i\rightarrow a'_{xy}&,\;\; b_{xy}=\sum_{i=1}^n b_{xy}^i \rightarrow b'_{xy}\quad\textrm{with}\quad a'_{xy},b'_{xy}\in\{+1,-1\}
% \end{align}
% We consider two such local binnings, majority vote and parity
% \begin{align*}
% &\textrm{Majority vote:}\quad a_{xy}' = \text{sign}\left(a_{xy}-\frac{n}{2}\right)
% &\textrm{Parity binning:}\quad a'_{xy}=(-1)^{a_{xy}},
% \end{align*}
% and the CHSH inequality~[5]
% \begin{equation}\label{eq:CHSH_ineq}
%     S_n = E_{11}^{(n)} + E_{12}^{(n)} + E_{21}^{(n)} - E_{22}^{(n)}\leq 2\,,
% \end{equation}
% where
% $E_{xy}^{(n)}=\textrm{Prob}(a'_{xy}=b'_{xy})-\textrm{Prob}(a'_{xy}\neq b'_{xy})$
% for a family of measurements indexed by a single angle~$\beta$:
% $A_1 = \sigma_z$,
% $A_2 = \cos(2\beta)\sigma_z + \sin(2\beta)\sigma_x$,
% $B_1 = \cos\beta\ \sigma_z + \sin\beta\ \sigma_x$,
% and $B_2 = \cos\beta\ \sigma_z - \sin\beta\ \sigma_x$.
% \begin{figurehere}
% \begin{minipage}{0.5\linewidth}
%     \includegraphics[width=\columnwidth]{./manypairs/figure4.eps}
%   \end{minipage}
%   \begin{minipage}{0.5\linewidth}
%     \includegraphics[width=\columnwidth]{./manypairs/figure5.eps}
%   \end{minipage}
%   \figcaption{Majority (left) and Parity (right) processing for different~$n$ applied to the data.
%     The continuous lines are
%     numerical simulations using as input the Werner state
%     \mbox{$\rho=V\ket{\psi^-}\bra{\psi^-}+(1-V){\mathbf I}/4$},
%     corresponding to a worst-case scenario,
%     % obtained numerically
%     with~$V=0.9892$ for majority and~$V=0.9871$ for parity.
%     }
% \end{figurehere}