Quantum-to-classical rate distortion coding

TL;DR

This paper develops a theory for quantum-to-classical rate distortion coding, deriving formulas for the minimal classical communication rate needed to transmit measurement-based information about a quantum source with controlled distortion.

Contribution

It introduces a single-letter formula for the minimum rate of classical communication in quantum-to-classical rate distortion coding, including scenarios with quantum side information.

Findings

Optimal strategies involve collective measurements on the quantum source.

Derived a single-letter formula for the minimal communication rate.

Quantum side information can reduce the required rate.

Abstract

We establish a theory of quantum-to-classical rate distortion coding. In this setting, a sender Alice has many copies of a quantum information source. Her goal is to transmit classical information about the source, obtained by performing a measurement on it, to a receiver Bob, up to some specified level of distortion. We derive a single-letter formula for the minimum rate of classical communication needed for this task. We also evaluate this rate in the case in which Bob has some quantum side information about the source. Our results imply that, in general, Alice's best strategy is a non-classical one, in which she performs a collective measurement on successive outputs of the source.