Covariance matrices and the separability problem

Details Covariance matrices and the separability problem Covariance matrices and the separability problem

2006-11-29

arxiv.org/abs/quant-ph/0611282v3

Phys. Rev. Lett. 99, 130504 (2007)

Physics

Quantum Physics

4 pages, no figures; v3: final version to appear in PRL

Scientific paper

10.1103/PhysRevLett.99.130504

We propose a unifying approach to the separability problem using covariance matrices of locally measurable observables. From a practical point of view, our approach leads to strong entanglement criteria that allow to detect the entanglement of many bound entangled states in higher dimensions and which are at the same time necessary and sufficient for two qubits. From a fundamental perspective, our approach leads to insights into the relations between several known entanglement criteria -- such as the computable cross norm and local uncertainty criteria -- as well as their limitations.

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