Separability criterion for density matrices. (English) Zbl 0947.81003

Peres, Asher

Phys. Rev. Lett. 77, No. 8, 1413-1415 (1996).

Summary: A quantum system consisting of two subsystems is separable if its density matrix can be written as \(\rho=\sum_A w_A\rho'_A\otimes\rho"_A\), where \(\rho'_A\) and \(\rho"_A\) are density matrices for the two subsystems, and the positive weights \(w_A\) satisfy \(\sum w_A=1\). In this letter, we prove that a necessary condition for separability is that a matrix, obtained by partial transposition of \(\rho\), has only non-negative eigenvalues. Some examples show that this criterion is more sensitive than Bell’s inequality for detecting quantum inseparability.

MSC:

81P05	General and philosophical questions in quantum theory
82B10	Quantum equilibrium statistical mechanics (general)

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