Lower Bound on Expected Communication Cost of Quantum Huffman Coding
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Lower bound.pdf
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564.38 KB
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Author(s)
Anshu, Anurag
Garg, Ankit
Yao, Penghui
Harrow, Aram W
Alternative Title
Lower Bound on Expected Communication Cost of Quantum Huffman Coding
Date Issued
September 2016
Journal
Leibniz International Proceedings in Informatics (LIPIcs)
Publisher
Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik
Citation
Anshu, Anurag, Ankit Garg, Aram W. Harrow, and Penghui Yao. "Lower Bound on Expected Communication Cost of Quantum Huffman Coding." 11th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2016)
Version
Final published version
Abstract
Data compression is a fundamental problem in quantum and classical information theory. A typical version of the problem is that the sender Alice receives a (classical or quantum) state from some known ensemble and needs to transmit them to the receiver Bob with average error below some specified bound. We consider the case in which the message can have a variable length and the goal is to minimize its expected length. For classical messages this problem has a well-known solution given by Huffman coding. In this scheme, the expected length of the message is equal to the Shannon entropy of the source (with a constant additive factor) and the scheme succeeds with zero error. This is a single-shot result which implies the asymptotic result, viz. Shannon's source coding theorem, by encoding each state sequentially. For the quantum case, the asymptotic compression rate is given by the von-Neumann entropy. However, we show that there is no one-shot scheme which is able to match this rate, even if interactive communication is allowed. This is a relatively rare case in quantum information theory when the cost of a quantum task is significantly different than the classical analogue. Our result has implications for direct sum theorems in quantum communication complexity and one-shot formulations of Quantum Reverse Shannon theorem.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Massachusetts Institute of Technology. Department of Physics
Massachusetts Institute of Technology. Research Laboratory of Electronics
Terms of Use
Creative Commons Attribution 4.0 International License
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.4230/LIPIcs.TQC.2016.3
