Separability in 2xN composite quantum systems

Details Separability in 2xN composite quantum systems Separability in 2xN composite quantum systems

1999-12-02

arxiv.org/abs/quant-ph/9912010v1

Phys.Rev.A 61, 062302 (2000)

Physics

Quantum Physics

Extended version of quant-ph/9903012 with new results. 11 pages

Scientific paper

10.1103/PhysRevA.61.062302

We analyze the separability properties of density operators supported on $\C^2\otimes \C^N$ whose partial transposes are positive operators. We show that if the rank of $\rho$ equals N then it is separable, and that bound entangled states have rank larger than N. We also give a separability criterion for a generic density operator such that the sum of its rank and the one of its partial transpose does not exceed 3N. If it exceeds this number we show that one can subtract product vectors until decreasing it to 3N, while keeping the positivity of $\rho$ and its partial transpose. This automatically gives us a sufficient criterion for separability for general density operators. We also prove that all density operators that remain invariant after partial transposition with respect to the first system are separable.

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