Separability criterion and inseparable mixed states with positive partial transposition

Details Separability criterion and inseparable mixed states with positive partial transposition Separability criterion and inseparable mixed states with positive partial transposition

1997-03-04

arxiv.org/abs/quant-ph/9703004v2

Phys.Lett. A232 (1997) 333

Physics

Quantum Physics

It is improved and extended version of the former manuscript, in particular the theorem concerning finite decomposition of sep

Scientific paper

10.1016/S0375-9601(97)00416-7

It is shown that any separable state on Hilbert space ${\cal H}={\cal H}_1\otimes{\cal H}_2$, can be written as a convex combination of N pure product states with $N\leq (dim{\cal H})^2$. Then a new separability criterion for mixed states in terms of range of density matrix is obtained. It is used in construction of inseparable mixed states with positive partial transposition in the case of $3\times 3$ and $2\times 4$ systems. The states represent an entanglement which is hidden in a more subtle way than it has been known so far.

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