Quantum Computation and Information Seminar 

09/03/2007, 15:00 — 16:00 — Room P4.35, Mathematics Building
Vladimir Man’ko, Lebedev Physical Institute, Russian Academy of Sciences

A probabilistic operator symbol framework for quantum information

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. Joint work with M. ManŽko and R. Vilela Mendes.