A probabilistic operator symbol framework for quantum information

M. A. Man'ko; V. I. Man'ko; R. Vilela Mendes

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A probabilistic operator symbol framework for quantum information

M. A. Man'ko·V. I. Man'ko·R. Vilela Mendes

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Abstract

Hilbert space operators may be mapped onto a space of ordinary functions (operator symbols) equipped with an associative (but noncommutative) star-product. A unified framework for such maps is reviewed. Because of its clear probabilistic interpretation, a particular class of operator symbols (tomograms) is proposed as a framework for quantum information problems. Qudit states are identified with maps of the unitary group into the simplex. The image of the unitary group on the simplex provides a geometrical characterization of the nature of the quantum states. Generalized measurements, typical quantum channels, entropies and entropy inequalities are discussed in this setting.

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M. A. Man'ko, V. I. Man'ko, R. Vilela Mendes. 2006-02-22. A probabilistic operator symbol framework for quantum information. https://arxiv.org/abs/quant-ph/0602189

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