Unifying several separability conditions using the covariance matrix criterion

Details Unifying several separability conditions using the covariance matrix criterion Unifying several separability conditions using the covariance matrix criterion

2008-03-06

arxiv.org/abs/0803.0757v3

Phys. Rev. A 78, 052319 (2008)

Physics

Quantum Physics

19 pages, 2 figures

Scientific paper

10.1103/PhysRevA.78.052319

We present a framework for deciding whether a quantum state is separable or entangled using covariance matrices of locally measurable observables. This leads to the covariance matrix criterion as a general separability criterion. We demonstrate that this criterion allows to detect many states where the familiar criterion of the positivity of the partial transpose fails. It turns out that a large number of criteria which have been proposed to complement the positive partial transpose criterion - the computable cross norm or realignment criterion, the criterion based on local uncertainty relations, criteria derived from extensions of the realignment map, and others - are in fact a corollary of the covariance matrix criterion.

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