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arXiv · 1304.2336

One-shot lossy quantum data compression

Nilanjana Datta·Joseph M. Renes·Renato Renner·Mark M. Wilde
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Abstract

We provide a framework for one-shot quantum rate distortion coding, in which the goal is to determine the minimum number of qubits required to compress quantum information as a function of the probability that the distortion incurred upon decompression exceeds some specified level. We obtain a one-shot characterization of the minimum qubit compression size for an entanglement-assisted quantum rate-distortion code in terms of the smooth max-information, a quantity previously employed in the one-shot quantum reverse Shannon theorem. Next, we show how this characterization converges to the known expression for the entanglement-assisted quantum rate distortion function for asymptotically many copies of a memoryless quantum information source. Finally, we give a tight, finite blocklength characterization for the entanglement-assisted minimum qubit compression size of a memoryless isotropic qubit source subject to an average symbol-wise distortion constraint.

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Nilanjana Datta, Joseph M. Renes, Renato Renner, Mark M. Wilde. 2013-09-17. One-shot lossy quantum data compression. https://doi.org/10.1109/tit.2013.2283723

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