Optimal decomposable witnesses without the spanning property

Details Optimal decomposable witnesses without the spanning property Optimal decomposable witnesses without the spanning property

2011-07-03

arxiv.org/abs/1107.0505v3

Physical Review A 84, 052323 (2011)

Physics

Quantum Physics

11 pages, published version, title modified, some references added, other minor improvements

Scientific paper

10.1103/PhysRevA.84.052323

One of the unsolved problems in the characterization of the optimal entanglement witnesses is the existence of optimal witnesses acting on bipartite Hilbert spaces H_{m,n}=C^m\otimes C^n such that the product vectors obeying =0 do not span H_{m,n}. So far, the only known examples of such witnesses were found among indecomposable witnesses, one of them being the witness corresponding to the Choi map. However, it remains an open question whether decomposable witnesses exist without the property of spanning. Here we answer this question affirmatively, providing systematic examples of such witnesses. Then, we generalize some of the recently obtained results on the characterization of 2\otimes n optimal decomposable witnesses [R. Augusiak et al., J. Phys. A 44, 212001 (2011)] to finite-dimensional Hilbert spaces H_{m,n} with m,n\geq 3.

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