Journal
IEEE TRANSACTIONS ON INFORMATION THEORY
Volume 59, Issue 12, Pages 8057-8076Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TIT.2013.2283723
Keywords
Entanglement assistance; hypothesis testing; relative entropy; lossy quantum data compression; max-information; min- and max-entropy; quantum rate distortion
Funding
- Swiss National Science Foundation through the National Centre of Competence in Research Quantum Science and Technology [200020-135048]
- European Research Council [258932]
- Centre de Recherches Mathematiques
- Statistical Laboratory at the University of Cambridge
- Pauli Center for Theoretical Studies (ETH Zurich)
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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.
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