Stuttgart 2012 – scientific programme

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Q: Fachverband Quantenoptik und Photonik

Q 70: Quanteninformation: Konzepte und Methoden 6

Q 70.7: Talk

Friday, March 16, 2012, 15:30–15:45, V7.03

Optimizing the presence of states in phase space regions — •Christoph Tempel, Lev Plimak, Karl Vogel, and Wolfgang P. Schleich — Institute of Quantum Physics, Ulm University

The problem of maximizing the integral of the Wigner function of a quantum state over a region in phase space emerges in the context of quantum tomography [1]. For an elliptical region the optimal state is squeezed vacuum [2]. Furthermore, such an optimal state may be characterized [3] as an eigenstate of the so-called region operator in the conventional Hilbert space. We combine the results of [2] and [3], using the fact that the region operator of a disconnected region is a sum of region operators of the components, giving rise to an efficient numerical approach to the optimization problem. For regions consisting of two non-overlapping disks, we find the said integral to be larger than one, which is a purely quantum effect. We also demonstrate that in the limit of well separated disks one encounteres a coherent superposition of coherent states centered at the disks (the so-called “cat state”).

[1] U. Leonhardt, Measuring the Quantum State of Light, Cambrigde Univ. Press, 1997.

[2] P. Flandrin, ICASSP-88 4 2176, 1988.

[3] A. J. Bracken et. al., Acta Physica Hung. B 20 121, 2004.