A Classical Analog to Entanglement Reversibility

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 Gács-Körner Common Information.

References in corpus (3)

• Entanglement irreversibility from quantum discord and quantum deficit
• Bound entangled states with a private key and their classical counterpart
• Distributions Attaining Secret Key at a Rate of the Conditional Mutual Information

Cited by in corpus (7)

• Quantum Resource Theories
• Irreversibility of Asymptotic Entanglement Manipulation Under Quantum Operations Completely Preserving Positivity of Partial Transpose
• Dephasing-Covariant Operations Enable Asymptotic Reversibility of Quantum Resources
• Round Complexity in the Local Transformations of Quantum and Classical States
• Distributions Attaining Secret Key at a Rate of the Conditional Mutual Information
• Communication Cost for Non-Markovianity of Tripartite Quantum States: A Resource Theoretic Approach
• One-Shot Distributed Source Simulation: As Quantum as it Can Get