We consider the problem of the optimal compression rate in the case of a source producing mixed signal states within the visible scheme (where Alice, who is to compress the signal, can know the identities of the produced states). We show that a simple strategy based on replacing the signal states with their extensions gives optimal compression. As a result we obtain a considerable simplification of the formula for an optimal compression rate within a visible scheme.

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Visible compression of commuting mixed states

Wolfgang Dür, Guifré Vidal, J. I. Cirac

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.

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arXiv:quant-ph/0110130

Compressing Mixed-State Sources by Sending Classical Information

Emina Soljanin

Published Oct 23, 2001• 1 citation

arXiv HTML PDF

Abstract

DOI: 10.48550/arxiv.quant-ph/0110130

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Compressing quantum mixed-state sources by sending classical information

Emina Soljanin

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 access to the same source of random numbers. We put in an information-theoretic framework some previous 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.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 access to the same source of random numbers. We put in an information-theoretic framework some previous 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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arXiv:quant-ph/0101111Physical Review AJul 12, 200115 citations

Inblindcompression of quantum states, a sender Alice is given a specimen of a quantum state$\rho

drawn from a known ensemble (but without knowing what

\rho

is), and she transmits sufficient quantum data to a receiver Bob so that he can decode a near perfect specimen of

\rho $. For many such states drawn iid from the ensemble, the asymptotically achievable rate is the number of qubits required to be transmitted per state. The Holevo information is a lower bound for the achievable rate, and is attained for pure state ensembles, or in the related scenario of entanglement-assistedvisiblecompression of mixed states wherein Alice knows what state is drawn. In this paper, we prove a general and robust lower bound on the achievable rate for ensembles of classical states, which holds even in the least demanding setting when Alice and Bob share free entanglement and a constant per-copy error is allowed. We apply the bound to aspecificensemble of only two states and prove a near-maximal separation (saturating the dimension bound in leading order) between the best achievable rate and the Holevo information for constant error. This also implies that the ensemble is incompressible – compression does not reduce the communication cost by much. Since the states areclassical, the observed incompressibility is not fundamentally quantum mechanical. We lower bound the difference between the achievable rate and the Holevo information in terms of quantitative limitations to clone the specimen or to distinguish the two classical states.