990,351 research outputs found

    Realigning random states

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    We study how the realignment criterion (also called computable cross-norm criterion) succeeds asymptotically in detecting whether random states are separable or entangled. We consider random states on \C^d \otimes \C^d obtained by partial tracing a Haar-distributed random pure state on \C^d \otimes \C^d \otimes \C^s over an ancilla space \C^s. We show that, for large dd, the realignment criterion typically detects entanglement if and only if s≤(8/3π)2d2s \leq (8/3\pi)^2 d^2. In this sense, the realignment criterion is asymptotically weaker than the partial transposition criterion

    Generalized reduction criterion for separability of quantum states

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    A new necessary separability criterion that relates the structures of the total density matrix and its reductions is given. The method used is based on the realignment method [K. Chen and L.A. Wu, Quant. Inf. Comput. 3, 193 (2003)]. The new separability criterion naturally generalizes the reduction separability criterion introduced independently in previous work of [M. Horodecki and P. Horodecki, Phys. Rev. A 59, 4206 (1999)] and [N.J. Cerf, C. Adami and R.M. Gingrich, Phys. Rev. A 60, 898 (1999)]. In special cases, it recovers the previous reduction criterion and the recent generalized partial transposition criterion [K. Chen and L.A. Wu, Phys. Lett. A 306, 14 (2002)]. The criterion involves only simple matrix manipulations and can therefore be easily applied.Comment: 17 pages, 2 figure
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