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No-signaling quantum key distribution: solution by linear programming

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Abstract

We outline a straightforward approach for obtaining a secret key rate using only no-signaling constraints and linear programming. Assuming an individual attack, we consider all possible joint probabilities. Initially, we study only the case where Eve has binary outcomes, and we impose constraints due to the no-signaling principle and given measurement outcomes. Within the remaining space of joint probabilities, by using linear programming, we get bound on the probability of Eve correctly guessing Bob’s bit. We then make use of an inequality that relates this guessing probability to the mutual information between Bob and a more general Eve, who is not binary-restricted. Putting our computed bound together with the Csiszár–Körner formula, we obtain a positive key generation rate. The optimal value of this rate agrees with known results, but was calculated in a more straightforward way, offering the potential of generalization to different scenarios.

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Acknowledgments

This study was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2010-0007208), and by National Research Foundation and Ministry of Education, Singapore, and the people programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme (FP7/2007-2013) under REA grant agreement N.609305. NK acknowledges the Ontario Graduate Scholarship program for support.

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Authors and Affiliations

  1. Department of Physics Education, Chonnam National University, Gwangju, 500-757, Republic of Korea

    Won-Young Hwang

  2. Department of Physics and Astronomy, Institute for Quantum Computing, University of Waterloo, Waterloo, N2L 3G1, Canada

    Won-Young Hwang & Nathan Killoran

  3. Centre for Quantum Technologies, National University of Singapore, Singapore, 117542, Singapore

    Joonwoo Bae

  4. Freiburg Institute for Advanced Studies (FRIAS), University of Freiburg, Albertstrasse 19, 79104, Freiburg, Germany

    Joonwoo Bae

  5. Institut für Theoretische Physik, Universität Ulm, Albert-Einstein-Allee 11, 89069, Ulm, Germany

    Nathan Killoran

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  1. Won-Young Hwang
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  2. Joonwoo Bae
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  3. Nathan Killoran
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Correspondence to Won-Young Hwang.

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Hwang, WY., Bae, J. & Killoran, N. No-signaling quantum key distribution: solution by linear programming. Quantum Inf Process 14, 687–696 (2015). https://doi.org/10.1007/s11128-014-0880-1

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  • DOI: https://doi.org/10.1007/s11128-014-0880-1

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