One-shot quantum state redistribution and quantum Markov chains

Abstract

We revisit the task of quantum state redistribution in the one-shot setting, and design a protocol for this task with communication cost in terms of a measure of distance from quantum Markov chains. More precisely, the distance is defined in terms of quantum max-relative entropy and quantum hypothesis testing entropy. Our result is the first to operationally connect quantum state redistribution and quantum Markov chains, and can be interpreted as an operational interpretation for a possible one-shot analogue of quantum conditional mutual information. The communication cost of our protocol is lower than all previously known ones and asymptotically achieves the well-known rate of quantum conditional mutual information. Thus, our work takes a step towards the important open question of near-optimal characterization of the one-shot quantum state redistribution.

v2: Exposition improved, references added, typos corrected. 32 pages, 2 figures. v1: 26 pages, 2 figures

References in corpus (5)

• Coding Theorem and Strong Converse for Quantum Channels
• Structure of states which satisfy strong subadditivity of quantum entropy with equality
• Renyi generalizations of the conditional quantum mutual information
• Sine distance for quantum states
• Quantum state discrimination bounds for finite sample size

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