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Quantum Rate-Distortion Coding of Relevant Information

Research output: Contribution to journalArticle

Original languageEnglish
Article number8513885
Pages (from-to)2603-2613
Number of pages11
JournalIEEE Transactions on Information Theory
Volume65
Issue number4
Early online date29 Oct 2018
DOIs
DateAccepted/In press - 23 Oct 2018
DateE-pub ahead of print - 29 Oct 2018
DatePublished (current) - 1 Apr 2019

Abstract

Rate-distortion theory provides bounds for compressing data produced by an information source to a specified encoding rate that is strictly less than the source's entropy. This necessarily entails some loss, or distortion, between the original source data and the best approximation after decompression. The so-called Information Bottleneck Method is designed to compress only 'relevant' information. Which information is relevant is determined by the correlation between the data being compressed and a variable of interest, so-called side information. In this paper, an Information Bottleneck Method is introduced for the compression of quantum data. The channel communication picture is used for compression and decompression. The rate of compression is derived using an entanglement-assisted protocol with classical communication, and under an unproved conjecture that the rate function is convex in the distortion parameter. The optimum channel achieving this rate for a given input state is characterized. The conceptual difficulties arising due to differences in the mathematical formalism between quantum and classical probability theory are discussed and solutions are presented.

    Research areas

  • quantum Information Bottleneck Method, Quantum rate-distortion theory, quantum reverse Shannon theorem

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    Rights statement: This is the submitted manuscript. This is also available via arXiv at https://arxiv.org/abs/1704.02903

    Submitted manuscript, 536 KB, PDF document

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