Distinguishing separable and entangled states

Details Distinguishing separable and entangled states Distinguishing separable and entangled states

2001-12-01

arxiv.org/abs/quant-ph/0112007v3

Physical Review Letters, Vol. 88, No. 18, 187904, 2002.

Physics

Quantum Physics

4 pages, Latex2e. Expanded discussion of numerical procedures. Accepted for publication in Physical Review Letters

Scientific paper

10.1103/PhysRevLett.88.187904

We show how to design families of operational criteria that distinguish entangled from separable quantum states. The simplest of these tests corresponds to the well-known Peres-Horodecki positive partial transpose (PPT) criterion, and the more complicated tests are strictly stronger. The new criteria are tractable due to powerful computational and theoretical methods for the class of convex optimization problems known as semidefinite programs. We successfully applied the results to many low-dimensional states from the literature where the PPT test fails. As a byproduct of the criteria, we provide an explicit construction of the corresponding entanglement witnesses.

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