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arXiv · 1502.04433

A Classical Analog to Entanglement Reversibility

Eric Chitambar·Ben Fortescue·Min-Hsiu Hsieh
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Abstract

In this letter we introduce the problem of secrecy reversibility. This asks when two honest parties can distill secret bits from some tripartite distribution $p_{XYZ}$ and transform secret bits back into $p_{XYZ}$ at equal rates using local operation and public communication (LOPC). This is the classical analog to the well-studied problem of reversibly concentrating and diluting entanglement in a quantum state. We identify the structure of distributions possessing reversible secrecy when one of the honest parties holds a binary distribution, and it is possible that all reversible distributions have this form. These distributions are more general than what is obtained by simply constructing a classical analog to the family of quantum states known to have reversible entanglement. An indispensable tool used in our analysis is a conditional form of the G\'{a}cs-K\"{o}rner Common Information.

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Eric Chitambar, Ben Fortescue, Min-Hsiu Hsieh. 2015-02-16. A Classical Analog to Entanglement Reversibility. https://doi.org/10.1103/physrevlett.115.090501

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