A probabilistic operator symbol framework for quantum information (Englisch)

In: Journal of Russian Laser Research   ;  27 ,  6  ;  507-532  ;  2006

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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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