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arXiv:quant-ph/0101111 · Physical Review A

Visible compression of commuting mixed states

Wolfgang Dür, Guifré Vidal, J. I. Cirac

Published Jul 12, 2001• 15 citations
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Abstract

We analyze the problem of quantum data compression of commuting density operators in the visible case. We show that the lower bound for the compression factor given by the Levitin-Holevo function is reached by providing an explicit protocol.
DOI
10.1103/physreva.64.022308

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We consider visible compression for discrete memoryless sources of mixed quantum states when only classical information can be sent from Alice to Bob. We assume that Bob knows the source statistics, and that Alice and Bob have identical random number generators. We put in an information theoretic framework some recent results on visible compression for sources of states with commuting density operators, and remove the commutativity requirement. We derive a general achievable compression rate, which is for the noncommutative case still higher than the known lower bound. We also present several related problems of classical information theory, and show how they can be used to answer some questions of the mixed state compression problem.
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