Hannover 2010 – scientific programme
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Q: Fachverband Quantenoptik und Photonik
Q 52: Quantum Information: Concepts and Methods IV / Photons and Nonclassical Light I
Q 52.9: Talk
Thursday, March 11, 2010, 16:00–16:15, E 214
Directly detecting negative Wigner functions — Andrea Mari1, •Konrad Kieling1, and Jens Eisert1,2 — 1Institut für Physik und Astronomie, Universität Potsdam, 14476 Potsdam-Golm — 2Institute for Advanced Study Berlin, 14193 Berlin
One of the most accepted signatures of non-classicality of a quantum state is the Wigner function – the phase space distribution becoming a probability distribution in the classical limit – being negative. To witness such a negative Wigner function is a valid test of having prepared a quantum state – in a mode of the light field, or even in an optomechanical system.
Yet, to reconstruct an entire Wigner function is a very difficult task, and requires a large series of highly accurate measurements. This is due to the fact that the usual way of achieving full tomographic knowledge and then reconstructing the state is highly ill-conditioned and hence prone to errors. It seems important and desirable, therefore, to find ways to directly measure signatures of Wigner function negativity, in a robust fashion, that make use of as little data as possible, which yet still give quantitative bounds.
We will introduce such certifiable bounds by bringing together phase space methods such as Bochner’s theorem and optimization tools such as semi-definite programming. Also, the multi-mode version of this scheme can be used to witness entanglement. By showing applications to sample data we demonstrate the reliable functioning of the method and that it is ready to use as a tool for quantum state characterisation.