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Nicolas J. Cerf

Universitè Libre de Bruxelles

On Hudson's Theorem: from Pure to Mixed Quantum States

November 20, 2008 - 8:30-8:55am

RLE Conference Center - 36-428

In this talk I will present an attempt towards the extension of Hudson's celebrated theorem, which states that for a continuous-variable system, the Wigner function of a pure state has no negative values if and only if the state is Gaussian. Turning to mixed states, I will derive upper and lower bounds on the allowed degree of non-Gaussianity of states with non-negative Wigner functions. These bounds are expressed in the form of parametric functions relating the degree of non-Gaussianity of a state, its purity, and the purity of the Gaussian state characterized by the same covariance matrix.  Although the bounds are not tight, they permit a better visualization of the set of states with non-negative Wigner functions. It is hoped that such bounds may serve as a guide in the recent experimental generation on non-Gaussian states of light, in order to probe the non-classicality of the generated states. As a side result, I also find a bound on the lowest purity of states with a non-negative Wigner function and a given covariance matrix. Surprisingly, Gaussian states turn out not to be the maximally mixed states in this scenario, making an exception to their extremality property. (Joint work with A. Mandilara and E. Karpov)

Nicolas J. Cerf received an Engineering Degree (1987), a M.Sc. in Physics (1988), and a Ph.D. in Physics (1993) from the Universite Libre de Bruxelles (ULB),  Belgium. He was then a Marie Curie postdoctoral fellow of the European Union, working at the Division of Theoretical Physics in Orsay (France) for two years. His research mainly concerned quantum many-body systems and quantum Monte Carlo methods, but also extended to the statistical physics of combinatorial problems. In 1995, he joined the research faculty of the California Institute of Technology to work on quantum computation and information theory, which then became his main research interest. In 1998, he was appointed as an associate professor at ULB, and kept since then occasional visiting appointments at Caltech and JPL/NASA. He was promoted to professor in 2006, and currently heads the Centre for Quantum Information and Communication (QuIC). He earned the Caltech President's Fund award in 1997,  the Alcatel-Bell prize awarded by the Belgian National Fund for Scientific Research in 1999, and a Marie Curie Excellence Award in 2006.