A Classical Analog to Entanglement Reversibility

TL;DR

This paper explores the conditions under which secret bits can be reversibly distilled and transformed from tripartite distributions, introducing the concept of secrecy reversibility as a classical analog to quantum entanglement reversibility.

Contribution

It characterizes the structure of distributions with reversible secrecy, especially when one party has a binary distribution, expanding understanding beyond classical analogs of quantum states.

Findings

Identifies conditions for classical secrecy reversibility.

Shows that reversible distributions may have a broader structure than previously known.

Uses Gács-Körner Common Information as a key analytical tool.

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.