One-shot lossy quantum data compression

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-s...

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Bibliographic Details
Published in:arXiv.org
Main Authors: Datta, Nilanjana, Renes, Joseph M, Renner, Renato, Wilde, Mark M
Format: Paper
Language:English
Published: Ithaca Cornell University Library, arXiv.org 17.09.2013
Subjects:
Data compression
Distortion
Quantum entanglement
Quantum phenomena
Quantum theory
Qubits (quantum computing)
Shannon theorem
Shot
ISSN:2331-8422
Online Access:Get full text
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Summary: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.
Bibliography:SourceType-Working Papers-1
ObjectType-Working Paper/Pre-Print-1
content type line 50
ISSN:2331-8422
DOI:10.48550/arxiv.1304.2336