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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Man’ko, M.A., Man’ko, V.I. & Vilela Mendes, R. A probabilistic operator symbol framework for quantum information. J Russ Laser Res 27, 507–532 (2006). https://doi.org/10.1007/s10946-006-0032-x
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DOI: https://doi.org/10.1007/s10946-006-0032-x