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Thermodynamic Interpretation of the Quantum Error Correcting Criterion

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Abstract

Shannon's fundamental coding theorems relate classical information theory to thermodynamics. More recent theoretical work has been successful in relating quantum information theory to thermodynamics. For example, Schumacher proved a quantum version of Shannon's 1948 classical noiseless coding theorem. In this note, we extend the connection between quantum information theory and thermodynamics to include quantum error correction. There is a standard mechanism for describing errors that may occur during the transmission, storage, and manipulation of quantum information. One can formulate a criterion of necessary and sufficient conditions for the errors to be detectable and correctable. We show that this criterion has a thermodynamical interpretation.

PACS: 03.67; 05.30; 63.10

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Authors and Affiliations

  1. Yang Institute of Theoretical Physics, State University of New York, Stony Brook, New York, 11794-3840

    Vladimir Korepin

  2. Department of Mathematics, State University of New York, Stony Brook, New York, 11794-3651

    John Terilla

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  1. Vladimir Korepin
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  2. John Terilla
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Korepin, V., Terilla, J. Thermodynamic Interpretation of the Quantum Error Correcting Criterion. Quantum Information Processing 1, 225–242 (2002). https://doi.org/10.1023/A:1022135318321

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