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A note on continuous ensemble expansions of quantum states

Roman R. Zapatrin
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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.

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Roman R. Zapatrin. 2004-03-15. A note on continuous ensemble expansions of quantum states. https://arxiv.org/abs/quant-ph/0403105

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