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One-Shot Lossy Quantum Data Compression

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4 Author(s)
Nilanjana Datta ; Stat. Lab., Univ. of Cambridge, Cambridge, UK ; Joseph M. Renes ; Renato Renner ; Mark M. Wilde

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 symbolwise distortion constraint.

Published in:

IEEE Transactions on Information Theory  (Volume:59 ,  Issue: 12 )