One-shot decoupling

TL;DR

This paper establishes a criterion for when a quantum system becomes nearly independent of its initial correlations after evolution, with applications in quantum information processing and state merging.

Contribution

It introduces a new decoupling criterion based on smooth entropies applicable in the one-shot quantum setting, and demonstrates its tightness and practical applications.

Findings

Decoupling criterion based on smooth entropies

Application to one-shot state merging protocol

Optimal entanglement consumption in the protocol

Abstract

If a quantum system A, which is initially correlated to another system, E, undergoes an evolution separated from E, then the correlation to E generally decreases. Here, we study the conditions under which the correlation disappears (almost) completely, resulting in a decoupling of A from E. We give a criterion for decoupling in terms of two smooth entropies, one quantifying the amount of initial correlation between A and E, and the other characterizing the mapping that describes the evolution of A. The criterion applies to arbitrary such mappings in the general one-shot setting. Furthermore, the criterion is tight for mappings that satisfy certain natural conditions. Decoupling has a number of applications both in physics and information theory, e.g., as a building block for quantum information processing protocols. As an example, we give a one-shot state merging protocol and show that it is essentially optimal in terms of its entanglement consumption/production.