Inclusion relations among separability criteria

Separability Criteria from Uncertainty Relations

We explain several separability criteria which rely on uncertainty relations. For the derivation of these criteria uncertainty relations in terms of variances or entropies can be used. We investigate the strength of the separability conditions for the case of two qubits and show how they can improve entanglement witnesses.

ar X iv : q ua nt - p h / 03 07 16 7 v 1 2 3 Ju l 2 00 3 Inclusion relations among separability criteria

We revisit the application of different separability criteria by recourse to an exhaustive Monte Carlo exploration involving the pertinent state-space of pure and mixed states. The corresponding chain of implications of different criteria is in such a way numerically elucidated. We also quantify, for a bipartite system of arbitrary dimension, the proportion of states ρ that can be distilled acc...

Complete family of separability criteria

We introduce a family of separability criteria that are based on the existence of extensions of a bipartite quantum state r to a larger number of parties satisfying certain symmetry properties. It can be easily shown that all separable states have the required extensions, so the nonexistence of such an extension for a particular state implies that the state is entangled. One of the main advanta...

On independent permutation separability criteria

Recently P. Wocjan and M. Horodecki [quant-ph/0503129] gave a characterization of combinatorially independent permutation separability criteria. Combinatorial independence is a necessary condition for permutations to yield truly independent criteria meaning that that no criterion is strictly stronger that any other. In this paper we observe that some of these criteria are still dependent and an...

Rank Inclusion in Criteria