# Stuttgart 2012 – wissenschaftliches Programm

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# Q: Fachverband Quantenoptik und Photonik

## Q 70: Quanteninformation: Konzepte und Methoden 6

### Q 70.7: Vortrag

### Freitag, 16. März 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.