Fully Quantum Source Compression with a Quantum Helper

TL;DR

This paper extends classical source compression with a quantum helper to the fully quantum setting, characterizing quantum resource requirements and deriving a single-letter achievable rate region with entanglement assistance.

Contribution

It introduces a novel quantum source compression framework involving a helper, combining quantum state merging and QRST protocols, and provides a single-letter rate region characterization.

Findings

Derived a single-letter rate region for quantum source compression with a helper.

Connected distributed source compression to the quantum reverse Shannon theorem.

Demonstrated the role of entanglement assistance in the quantum compression setting.

Abstract

We study source compression with a helper in the fully quantum regime, extending our earlier result on classical source compression with a quantum helper [arXiv:1501.04366, 2015]. We characterise the quantum resources involved in this problem, and derive a single-letter expression of the achievable rate region when entanglement assistance is available. The direct coding proof is based on a combination of two fundamental protocols, namely the quantum state merging protocol and the quantum reverse Shannon theorem (QRST). This result demonstrates an unexpected connection between distributed source compression with the QRST protocol, a quantum protocol that consumes noiseless resources to simulate a noisy quantum channel.