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arXiv:quant-ph/0403105

A note on continuous ensemble expansions of quantum states

Romàn R. Zapatrin

Published Mar 15, 2004• 6 citations
arXivHTMLPDF

Abstract

Generalizing the notion of relative entropy, the difference between a priori and a posteriori relative entropy for quantum systems is drawn. The former, known as quantum relative entropy, is associated with quantum states recognition. The latter -- a posteriori relative quantum entropy is shown to be related with state reconstruction due to the following property: given a density operator $ρ$, ensembles of pure states with Gibbs distribution with respect to the defined distance are proved to represent the initial state $ρ$ up to an amount of white noise (completely mixed state) which can be made arbitrary small.

DOI
10.48550/arxiv.quant-ph/0403105

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•Jan 11, 2016•1 citation
Generalizing the notion of relative entropy, the difference between a priori and a posteriori relative entropy for quantum systems is drawn. The former, known as quantum relative entropy, is associated with quantum states recognition. The latter -- a posteriori relative quantum entropy is shown to be related with state reconstruction due to the following property: given a density operator ρρρ, ensembles of pure states with Gibbs distribution with respect to the defined distance are proved to represent the initial state ρρρ up to an amount of white noise (completely mixed state) which can be made arbitrary small.
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