Frankfurt 2006 – scientific programme

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Q: Quantenoptik und Photonik

Q 9: Quanteninformation I

Q 9.6: Talk

Monday, March 13, 2006, 15:15–15:30, HI

Optimal entanglement witnesses for continuous-variable systems — •Philipp Hyllus and Jens Eisert — QOLS, Blackett Laboratory, and Institute of Mathematical Sciences, Imperial College London, SW7 London 2PE, United Kingdom.

We present work which is concerned with all tests for continuous-variable entanglement that arise from linear combinations of second moments or variances of canonical coordinates, as they are commonly used in experiments to detect entanglement. All such tests for bi-partite and multi-partite entanglement correspond to hyperplanes in the set of second moments. It is shown that all optimal tests, those that are most robust against imperfections with respect to some figure of merit for a given state, can be constructed from solutions to semi-definite optimization problems. Moreover, we show that for each entanglement witnesses, there is a one-to-one correspondence between the witness and a stronger product criterion, based on the same measurements. This generalizes the known product criteria. To provide a service to the community, we also present the documentation of two numerical routines, FULLYWIT and MULTIWIT, which have been made publicly available.