General Mixed State Quantum Data Compression with and without Entanglement Assistance

TL;DR

This paper establishes the optimal quantum data compression rates for general mixed states with and without entanglement assistance, based on the Koashi-Imoto decomposition, unifying various source coding scenarios.

Contribution

It provides a comprehensive formula for the minimal qubit rate for compressing general quantum sources, including entanglement-assisted cases, using the Koashi-Imoto decomposition.

Findings

Optimal compression rate expressed via Koashi-Imoto decomposition.

Determination of the full feasible qubit-ebit rate region.

Unification of pure and mixed state quantum source coding.

Abstract

We consider the most general (finite-dimensional) quantum mechanical information source, which is given by a quantum system $A$ that is correlated with a reference system $R$. The task is to compress $A$ in such a way as to reproduce the joint source state $\rho^{AR}$ at the decoder with asymptotically high fidelity. This includes Schumacher's original quantum source coding problem of a pure state ensemble and that of a single pure entangled state, as well as general mixed state ensembles. Here, we determine the optimal compression rate (in qubits per source system) in terms of the Koashi-Imoto decomposition of the source into a classical, a quantum, and a redundant part. The same decomposition yields the optimal rate in the presence of unlimited entanglement between compressor and decoder, and indeed the full region of feasible qubit-ebit rate pairs.