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arXiv · 1912.08506

General Mixed State Quantum Data Compression with and without Entanglement Assistance

Zahra Baghali Khanian·Andreas Winter
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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.

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Zahra Baghali Khanian, Andreas Winter. 2019-12-18. General Mixed State Quantum Data Compression with and without Entanglement Assistance. https://doi.org/10.1109/tit.2022.3143846

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