Mathematics Department Técnico Técnico

Quantum Computation and Information Seminar   RSS

30/04/2018, 14:00 — 15:00 — Seminar room (2.8.3), Physics Building
, Université Libre de Bruxelles

On Shannon entropy in quantum phase space : from entropic uncertainty relations to continuous majorization relations

Shannon differential entropy is a na tural uncertainty measure when considering a continuous-spectrum observable, such as a quadrature component of a mode of the electromagnetic field. I will show that it makes a very useful — though not yet fully explored — tool for the phase-space description of light. After a short survey on the entropic uncertainty relations generalizing the Heisenberg principle with differential entropies instead of variances, I will emphasize the notion of entropy power in this context and formulate new entropic uncertainty relations expressing the balance between multimode Gaussian projective measurements. This will lead me to discuss the differential entropy of a Wigner function, which, for states with non-negative such functions, yields a perfect uncertainty measure that is invariant under all Gaussian unitaries (symplectic transformations and displacements) and is saturated by all Gaussian pure states. I will then consider entropy-power inequalities for a beam splitter and finally discuss some conjectured continuous-variable majorization relations in phase space.

Supported by: Phys-Info (IT), SQIG (IT), CeFEMA and CAMGSD, with funding from FCT, FEDER and EU FP7, specifically through the Doctoral Programme in the Physics and Mathematics of Information (DP-PMI), FCT strategic projects PEst-OE/EEI/LA0008/2013 and UID/EEA/50008/2013, IT project QuSim, project CRUP-CPU CQVibes, the FP7 Coordination Action QUTE-EUROPE (600788), and the FP7 projects Landauer (GA 318287) and PAPETS (323901).


Instituto de TelecomunicaçõesCAMGSDFCT7th Framework Programme