Quantum Information Processing

, Volume 14, Issue 2, pp 687–696 | Cite as

No-signaling quantum key distribution: solution by linear programming

  • Won-Young HwangEmail author
  • Joonwoo Bae
  • Nathan Killoran


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.


No-signaling principle Quantum key distribution Linear programming 



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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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Won-Young Hwang
    • 1
    • 2
    Email author
  • Joonwoo Bae
    • 3
    • 4
  • Nathan Killoran
    • 2
    • 5
  1. 1.Department of Physics EducationChonnam National UniversityGwangjuRepublic of Korea
  2. 2.Department of Physics and Astronomy, Institute for Quantum ComputingUniversity of WaterlooWaterlooCanada
  3. 3.Centre for Quantum TechnologiesNational University of SingaporeSingaporeSingapore
  4. 4.Freiburg Institute for Advanced Studies (FRIAS)University of FreiburgFreiburgGermany
  5. 5.Institut für Theoretische PhysikUniversität UlmUlmGermany

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