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• W1990758844 abstract "We consider low rank density operators $varrho$ supported on a $Mtimes N$ Hilbert space for arbitrary $M$ and $N$ ($Mleq N$) and with a positive partial transpose (PPT) $varrho^{T_A}ge 0$. For rank $r(varrho) leq N$ we prove that having a PPT is necessary and sufficient for $varrho$ to be separable; in this case we also provide its minimal decomposition in terms of pure product states. It follows from this result that there is no rank 3 bound entangled states having a PPT. We also present a necessary and sufficient condition for the separability of generic density matrices for which the sum of the ranks of $varrho$ and $varrho^{T_A}$ satisfies $r(varrho)+r(varrho^{T_A}) le 2MN-M-N+2$. This separability condition has the form of a constructive check, providing thus also a pure product state decomposition for separable states, and it works in those cases where a system of couple polynomial equations has a finite number of solutions, as expected in most cases." @default.
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• W1990758844 date "2000-08-17" @default.
• W1990758844 modified "2023-10-18" @default.
• W1990758844 title "Operational criterion and constructive checks for the separability of low-rank density matrices" @default.
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• W1990758844 doi "https://doi.org/10.1103/physreva.62.032310" @default.
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