General Mixed State Quantum Data Compression with and without Entanglement Assistance

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.

References in corpus (4)

• Structure of states which satisfy strong subadditivity of quantum entropy with equality
• A Sharp Fannes-type Inequality for the von Neumann Entropy
• Tight informationally complete quantum measurements
• Entanglement-Assisted Quantum Data Compression

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• On the distinguishability of geometrically uniform quantum states
• Exact and local compression of quantum bipartite states