Quantum rate distortion coding with auxiliary resources

TL;DR

This paper advances quantum rate distortion theory by incorporating auxiliary resources like classical side channels and quantum side information, deriving new bounds and theorems for lossy quantum data compression.

Contribution

It introduces the first quantum rate distortion bounds with classical side channels and quantum side information, extending existing theories and proving a quantum reverse Shannon theorem with QSI.

Findings

Regularized entanglement of formation characterizes quantum rate distortion with classical side channel.

Derived the best known bounds for isotropic qubit sources.

Proved a quantum reverse Shannon theorem with quantum side information.

Abstract

We extend quantum rate distortion theory by considering auxiliary resources that might be available to a sender and receiver performing lossy quantum data compression. The first setting we consider is that of quantum rate distortion coding with the help of a classical side channel. Our result here is that the regularized entanglement of formation characterizes the quantum rate distortion function, extending earlier work of Devetak and Berger. We also combine this bound with the entanglement-assisted bound from our prior work to obtain the best known bounds on the quantum rate distortion function for an isotropic qubit source. The second setting we consider is that of quantum rate distortion coding with quantum side information (QSI) available to the receiver. In order to prove results in this setting, we first state and prove a quantum reverse Shannon theorem with QSI (for tensor-power states), which extends the known tensor-power quantum reverse Shannon theorem. The achievability part of this theorem relies on the quantum state redistribution protocol, while the converse relies on the fact that the protocol can cause only a negligible disturbance to the joint state of the reference and the receiver's QSI. This quantum reverse Shannon theorem with QSI naturally leads to quantum rate-distortion theorems with QSI, with or without entanglement assistance.