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:IEEE transactions on information theory Vol. 59; no. 12; pp. 8057 - 8076
Main Authors: Datta, Nilanjana, Renes, Joseph M., Renner, Renato, Wilde, Mark M.
Format: Journal Article
Language:English
Published: New York, NY IEEE 01.12.2013
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Applied sciences
Asymptotic methods
Classical and quantum physics: mechanics and fields
Codes
Coding, codes
Data compression
Distortion measurement
Entanglement assistance
Entropy
Exact sciences and technology
hypothesis testing
Information theory
Information, signal and communications theory
lossy quantum data compression
max-information
min- and max-entropy
Physics
Probability distribution
Quantum entanglement
Quantum information
quantum rate distortion
Rate distortion theory
Rate-distortion
relative entropy
Signal and communications theory
Telecommunications and information theory
Lossy compression
hypothesis testing
Entanglement assistance
Data compression
quantum rate distortion
Information quantity
Rate distortion theory
Entropy
Hypothesis test
lossy quantum data compression
max-information
Information source
Coding
Minimax method
relative entropy
min- and max-entropy
Quantum information
Memoryless source
ISSN:0018-9448, 1557-9654
Online Access:Get full text
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Description
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 symbolwise distortion constraint.
Bibliography:SourceType-Scholarly Journals-1
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ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2013.2283723