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Information Theories with Adversaries, Intrinsic Information, and Entanglement

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There are aspects of privacy theory that are analogous to quantum theory. In particular one can define distillable key and key cost in parallel to distillable entanglement and entanglement cost. We present here classical privacy theory as a particular case of information theory with adversaries, where similar general laws hold as in entanglement theory. We place the result of Renner and Wolf—that intrinsic information is lower bound for key cost—into this general formalism. Then we show that the question of whether intrinsic information is equal to key cost is equivalent to the question of whether Alice and Bob can create a distribution product with Eve using I M bits of secret key. We also propose a natural analogue of relative entropy of entanglement in privacy theory and show that it is equal to the intrinsic information. We also provide a formula analogous to the entanglement of formation for classical distributions.

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Authors and Affiliations

  1. Department of Mathematics, Physics and Computer Science, University of Gdańsk, Poland

    Karol Horodecki

  2. Institute of Theoretical Physics and Astrophysics, University of Gdańsk, 80-952, Gdańsk, Poland

    Michał Horodecki

  3. Faculty of Applied Physics and Mathematics, Technical University of Gdańsk, 80-952, Gdańsk, Poland

    Pawel Horodecki

  4. Dept. of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, UK

    Jonathan Oppenheim

Authors
  1. Karol Horodecki
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  2. Michał Horodecki
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  3. Pawel Horodecki
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  4. Jonathan Oppenheim
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Correspondence to Michał Horodecki.

Additional information

It is our pleasure to dedicate this paper to Asher Peres on the occasion of his seventieth birthday.

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Horodecki, K., Horodecki, M., Horodecki, P. et al. Information Theories with Adversaries, Intrinsic Information, and Entanglement. Found Phys 35, 2027–2040 (2005). https://doi.org/10.1007/s10701-005-8660-5

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  • DOI: https://doi.org/10.1007/s10701-005-8660-5

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