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\citation{Mills:1991,PTP,piester2008time,jiang2017bipm}
\citation{narula:17}
\citation{mizrahi2012game,ullmann2009delay,tsang2006security}
\citation{rabadi2017taming}
\citation{lee2019symmetrical,hou2018fiber,lamas2018secure}
\citation{lee2019symmetrical}
\citation{hou2018fiber}
\citation{yang2006simple}
\citation{wootters1982single}
\citation{Troupe:2018}
\citation{berry:87}
\citation{kwiat:91,strekalov:97,brendel:95,jha:08}
\citation{Troupe:2018}
\citation{Troupe:2018}
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\@writefile{toc}{\contentsline {title}{Asymmetric delay attack on an entanglement-based bidirectional clock synchronization protocol}{1}{section*.2}}
\@writefile{toc}{\contentsline {abstract}{Abstract}{1}{section*.1}}
\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces  Clock synchronization scheme. Alice and Bob each have a source of polarization-entangled photon pairs $|{\Psi ^-}\delimiter "526930B $, and avalanche photodetectors at D$_{\text  {A,B}}$. One photon of the pair is detected locally, while the other photon is sent through a fiber to be detected on the remote side. Arrival times for all detected photons are recorded at each side with respect to local clocks, each locked to a rubidium frequency reference. Grey region: asymmetric delay attack. An adversary (Eve) uses a pair of circulators to introduce a direction-dependent propagation delay: photons originating at Bob\IeC {\textquoteright }s site will always take the bottom path, while photons originating at Alice\IeC {\textquoteright }s side will take the top path. }}{1}{figure.1}}
\newlabel{fig:setup}{{1}{1}{Clock synchronization scheme. Alice and Bob each have a source of polarization-entangled photon pairs $\ket {\Psi ^-}$, and avalanche photodetectors at D$_{\text {A,B}}$. One photon of the pair is detected locally, while the other photon is sent through a fiber to be detected on the remote side. Arrival times for all detected photons are recorded at each side with respect to local clocks, each locked to a rubidium frequency reference. Grey region: asymmetric delay attack. An adversary (Eve) uses a pair of circulators to introduce a direction-dependent propagation delay: photons originating at Bob’s site will always take the bottom path, while photons originating at Alice’s side will take the top path}{figure.1}{}}
\citation{glauber1963quantum}
\citation{Troupe:2018}
\citation{Troupe:2018}
\citation{berry:87}
\citation{lee2019symmetrical}
\citation{Kwiat:1995ub}
\citation{ho2009clock}
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\citation{Kwiat:1995ub}
\citation{Kwiat:1995ub}
\citation{altepeter2005photonic}
\citation{altepeter2005photonic}
\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces  Time correlations of Alice and Bob's detection events normalized to background coincidences. The separation between peaks corresponds to the round-trip time\nobreakspace  {}$\Delta T$, and the midpoint is the offset between the clocks\nobreakspace  {}$\delta $. Symmetric delays with $L=L'$ show that the offset remains constant for both the (a) initial and (b) extended round-trip times. An asymmetric delay with (c) $L=L'+10$ results in an offset shift. $L_o/2$: minimum length of the fiber belonging to each circulator port. ${\delta _{\text  {o}}}$: the offset estimated in (a). }}{3}{figure.2}}
\newlabel{fig:g2}{{2}{3}{Time correlations of Alice and Bob's detection events normalized to background coincidences. The separation between peaks corresponds to the round-trip time~$\Delta T$, and the midpoint is the offset between the clocks~$\delta $. Symmetric delays with $L=L'$ show that the offset remains constant for both the (a) initial and (b) extended round-trip times. An asymmetric delay with (c) $L=L'+10$ results in an offset shift. $L_o/2$: minimum length of the fiber belonging to each circulator port. ${\delta _{\text {o}}}$: the offset estimated in (a)}{figure.2}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces  (a) Measured offset $\delta $ between two clocks, both locked on the same frequency reference. Each value of $\delta $ was evaluated from measuring photon pair timing correlations from a block of photodetection times recorded by Alice and Bob. Each block is 40\tmspace  +\thinmuskip {.1667em}s long. (b) The round-trip time $\Delta T$. Block 6 to 7: increasing the symmetric delay ($L=L'$) does not change $\delta $. Block 15 to 16: introducing an asymmetric delay ($L\not =L'$) creates an offset error. The delay was created by redistributing the additional delays in Blocks 7 to 15, so that $\Delta T$ remains the same. $\delta _{\text  {o}}$: offset measured in the first block. }}{3}{figure.3}}
\newlabel{fig:asymmetric_attack_results}{{3}{3}{(a) Measured offset $\delta $ between two clocks, both locked on the same frequency reference. Each value of $\delta $ was evaluated from measuring photon pair timing correlations from a block of photodetection times recorded by Alice and Bob. Each block is 40\,s long. (b) The round-trip time $\Delta T$. Block 6 to 7: increasing the symmetric delay ($L=L'$) does not change $\delta $. Block 15 to 16: introducing an asymmetric delay ($L\neq L'$) creates an offset error. The delay was created by redistributing the additional delays in Blocks 7 to 15, so that $\Delta T$ remains the same. $\delta _{\text {o}}$: offset measured in the first block}{figure.3}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {4}{\ignorespaces  Setup for quantum state tomography on a polarization-entangled photon pair state, with one photon passing through a pair of circulators. Dashed box: optical setup of our polarization-entangled photon source\nobreakspace  {}\cite  {Kwiat:1995ub}. LD: laser diode, BBO: $\beta $-Barium\nobreakspace  {}Borate, CC: compensation crystals, FPC: fiber polarization controller, SMF: single mode fiber, $\lambda $/4: quarter-wave plate, $\lambda $/2: half-wave plate, PBS: polarizing beam splitter, APD: avalanche photodiode. }}{3}{figure.4}}
\newlabel{fig:tomography_setup}{{4}{3}{Setup for quantum state tomography on a polarization-entangled photon pair state, with one photon passing through a pair of circulators. Dashed box: optical setup of our polarization-entangled photon source~\cite {Kwiat:1995ub}. LD: laser diode, BBO: $\beta $-Barium~Borate, CC: compensation crystals, FPC: fiber polarization controller, SMF: single mode fiber, $\lambda $/4: quarter-wave plate, $\lambda $/2: half-wave plate, PBS: polarizing beam splitter, APD: avalanche photodiode}{figure.4}{}}
\citation{narula:17}
\citation{jalas2014optical,dmitriev2013possible,dmitriev2013compact,bi2011chip,yu2009complete}
\citation{lamas2018secure}
\citation{Troupe:2018}
\citation{Troupe:2018}
\bibcite{Mills:1991}{{1}{1991}{{Mills}}{{}}}
\bibcite{PTP}{{2}{2009}{{PTP}}{{}}}
\bibcite{piester2008time}{{3}{2008}{{Piester\ \emph  {et~al.}}}{{Piester, Bauch, Breakiron, Matsakis, Blanzano,\ and\ Koudelka}}}
\bibcite{jiang2017bipm}{{4}{2017}{{Jiang\ \emph  {et~al.}}}{{Jiang, Huan, Zhang,\ and\ Dirk}}}
\bibcite{narula:17}{{5}{2018}{{Narula\ and\ Humphreys}}{{}}}
\bibcite{mizrahi2012game}{{6}{2012}{{Mizrahi}}{{}}}
\bibcite{ullmann2009delay}{{7}{2009}{{Ullmann\ and\ V{\"o}geler}}{{}}}
\@writefile{lof}{\contentsline {figure}{\numberline {5}{\ignorespaces  Real and imaginary part of the reconstructed density matrix for the target Bell state $|{\Psi ^-}\delimiter "526930B $ originating from Alice's source. Bob receives one photon of the pair through the synchronization channel. The density matrices obtained (a) without and (b) with polarization-insensitive circulators in the line (Figure\nobreakspace  {}\ref  {fig:tomography_setup}) do not deviate significantly from $|{\Psi ^-}\delimiter "526930B $. }}{4}{figure.5}}
\newlabel{fig:rho}{{5}{4}{Real and imaginary part of the reconstructed density matrix for the target Bell state $\ket {\Psi ^-}$ originating from Alice's source. Bob receives one photon of the pair through the synchronization channel. The density matrices obtained (a) without and (b) with polarization-insensitive circulators in the line (Figure~\ref {fig:tomography_setup}) do not deviate significantly from $\ket {\Psi ^-}$}{figure.5}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {6}{\ignorespaces  Fidelity distribution comparing the Bell state originating from Alice's source before and after introducing the circulators. The distribution is generated by numerically propagating errors due to counting statistics. A high mean fidelity suggests that the state remains unchanged and cannot be used to detect the attack. Error bars: Poissonian standard deviation. }}{4}{figure.6}}
\newlabel{fig:fidelity_distribution}{{6}{4}{Fidelity distribution comparing the Bell state originating from Alice's source before and after introducing the circulators. The distribution is generated by numerically propagating errors due to counting statistics. A high mean fidelity suggests that the state remains unchanged and cannot be used to detect the attack. Error bars: Poissonian standard deviation}{figure.6}{}}
\bibcite{tsang2006security}{{8}{2006}{{Tsang\ and\ Beznosov}}{{}}}
\bibcite{rabadi2017taming}{{9}{2017}{{Rabadi\ \emph  {et~al.}}}{{Rabadi, Tan, Yau,\ and\ Viswanathan}}}
\bibcite{lee2019symmetrical}{{10}{2019}{{Lee\ \emph  {et~al.}}}{{Lee, Shen, Cer{\`e}, Troupe, Lamas-Linares,\ and\ Kurtsiefer}}}
\bibcite{hou2018fiber}{{11}{2019}{{Hou\ \emph  {et~al.}}}{{Hou, Quan, Dong, Xiang, Li, Liu, Yang, Li, You, Wang,\ and\ Zhang}}}
\bibcite{lamas2018secure}{{12}{2018}{{Lamas-Linares\ and\ Troupe}}{{}}}
\bibcite{yang2006simple}{{13}{2006}{{Yang}}{{}}}
\bibcite{wootters1982single}{{14}{1982}{{Wootters\ and\ Zurek}}{{}}}
\bibcite{Troupe:2018}{{15}{2018}{{Troupe\ and\ Lamas-Linares}}{{}}}
\bibcite{berry:87}{{16}{1987}{{Berry}}{{}}}
\bibcite{kwiat:91}{{17}{1991}{{Kwiat\ and\ Chiao}}{{}}}
\bibcite{strekalov:97}{{18}{1997}{{Strekalov\ and\ Shih}}{{}}}
\bibcite{brendel:95}{{19}{1995}{{Brendel\ \emph  {et~al.}}}{{Brendel, Dultz,\ and\ Martinessen}}}
\bibcite{jha:08}{{20}{2009}{{Jha\ \emph  {et~al.}}}{{Jha, Malik,\ and\ Boyd}}}
\bibcite{glauber1963quantum}{{21}{1963}{{Glauber}}{{}}}
\bibcite{Kwiat:1995ub}{{22}{1995}{{Kwiat\ \emph  {et~al.}}}{{Kwiat, Mattle, Weinfurter, Zeilinger, Sergienko,\ and\ Shih}}}
\bibcite{ho2009clock}{{23}{2009}{{Ho\ \emph  {et~al.}}}{{Ho, Lamas-Linares,\ and\ Kurtsiefer}}}
\bibcite{altepeter2005photonic}{{24}{2005}{{Altepeter\ \emph  {et~al.}}}{{Altepeter, Jeffrey,\ and\ Kwiat}}}
\bibcite{jalas2014optical}{{25}{2014}{{Jalas\ \emph  {et~al.}}}{{Jalas, Petrov,\ and\ Eich}}}
\bibcite{dmitriev2013possible}{{26}{2013{}}{{Dmitriev\ \emph  {et~al.}}}{{Dmitriev, Portela,\ and\ Zimmer}}}
\bibcite{dmitriev2013compact}{{27}{2013{}}{{Dmitriev\ \emph  {et~al.}}}{{Dmitriev, Kawakatsu,\ and\ Portela}}}
\bibcite{bi2011chip}{{28}{2011}{{Bi\ \emph  {et~al.}}}{{Bi, Hu, Jiang, Kim, Dionne, Kimerling,\ and\ Ross}}}
\bibcite{yu2009complete}{{29}{2009}{{Yu\ and\ Fan}}{{}}}
\bibcite{anandan1992geometric}{{30}{1992}{{Anandan}}{{}}}
\bibcite{zak1991geometric}{{31}{1991}{{Zak}}{{}}}
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