\begin{frame}{Asymmetric Delay Attack}
  % \begin{block}{We have assumed that delays were symmetric:}
  % \begin{center}
  % % \vfill
  % \vspace*{-15pt}
  % \def\svgwidth{0.8\textwidth}
  % \hspace*{45pt}\import{images/offset_schematic/}{offset_concept.pdf_tex}
  % \fbox{$\delta$ = midpoint between two coincidence peaks}
  % \end{center}
  % \end{block}
  % \begin{block}{}
  \begin{center}
    \includegraphics[width=\textwidth]{images/asymmetric_delay_expt_setup/clocksyncsetup_assymetric.pdf}
  \end{center}
  % \end{block}

  % \begin{block}{}
  \begin{center}
  \def\svgwidth{0.7\textwidth}
  \hspace*{45pt}\import{images/offset_schematic/}{offset_concept_assymetric.pdf_tex}
  \bigbreak
  \fbox{$\delta\neq$ midpoint between two coincidence peaks}
  \end{center}
  % \end{block}
% \footnotetext[1]{Detecting Circulators using Geometric Phases (arXiv:1808.09019)}
  \note{
    The security of the protocol to an asymetric delay attack remains an open question.

    So far, we have assumed that the delay between Alice and Bob is the same in both directions.
    % We histogram t and t' and assume that the midpoint between the peaks is the clock error.
    However, this may not be necessarily true.
    For example, two circulators can use to introduce different propagation delays, L and L', depending on the propagation direction of the photons.
    In this case, the true offset delta is no longer at the mid pt between the peaks and cannot be determined independently of L and L'.
    Using polarization-independent circulators also means that this attack cannot be directly detected with a Bell measurement. 
    Separately, we have published work on the arXiv describing how the circulators change the geometric phase of the photons, but we have yet to figure out an experiment capable of extracting the GP from the overall phase change imposed by the circulators.
  }
\end{frame}

\begin{frame}{Estimated Offset Shift}
  \begin{center}
    \includegraphics[width=\textwidth]{images/asymmetric_delay_g2/g2.eps}
  \end{center}
  \note{
  }
\end{frame}

\begin{frame}{State Tomography with Circulators}
  \begin{center}
    \includegraphics[width=0.9\textwidth]{images/tomography/tomography_setup.pdf}
  \end{center}
    \centering
  % \vspace{-0.5cm}
    \fbox{$n\times180^\text{o}$ rotation: \quad 
    $\ket{\psi}_B\rightarrow\pm\ket{\psi}_B$ \quad 
    $\ket{\Psi^-} \rightarrow \pm\ket{\Psi^-}$}
    % \\$\ket{\Psi^-} \rightarrow = \frac{1}{\sqrt{2}}\left(\redpmket{H}\ket{V} - \redpmket{V}\ket{H}\right) 
    % = \pm\ket{\Psi^-}$}
    % \fbox{$180^\text{o}\times n$\quad rotation:\\ 
    % $\ket{\Psi^-} = 
    % \frac{1}{\sqrt{2}}\left(\ket{H}\ket{V} - \ket{V}\ket{H}\right)
    % \rightarrow
    % \frac{1}{\sqrt{2}}\left(\redpmket{H}\ket{V} - \redpmket{V}\ket{H}\right) = \pm\ket{\Psi^-}$}
    % \fbox{$180^\text{o}\times n$\quad rotation:\\ 
    % $\ket{\Psi^-} = 
    % \frac{1}{\sqrt{2}}\left(\ket{H}\ket{V} - \ket{V}\ket{H}\right)
    % \rightarrow
    % \frac{1}{\sqrt{2}}\left(\redpmket{H}\ket{V} - \redpmket{V}\ket{H}\right) = \pm\ket{\Psi^-}$}
  \begin{center}
    \includegraphics[width=0.5\textwidth]{images/tomography/rho_before_real.pdf}
  % \end{center}
  % \begin{center}
    \includegraphics[width=0.5\textwidth]{images/tomography/rho_after_real.pdf}
  \end{center}
  \vfill
  \note{
  }
\end{frame}