Optimal decomposable witnesses without the spanning property
- ICFO-Institut de Ciencies Fotoniques, E-08860 Castelldefels (Barcelona) (Spain)
- Insitute of Physics, Nicolaus Copernicus University, Grudzicdzka 5, PL-87-100 Torun (Poland)
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{sub m,n}=C{sup m} x C{sup n} such that the product vectors obeying =0 do not span H{sub 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 x n optimal decomposable witnesses [R. Augusiak et al., J. Phys. A 44, 212001 (2011)] to finite-dimensional Hilbert spaces H{sub m,n} with m,n{>=}3.
- OSTI ID:
- 22093492
- Journal Information:
- Physical Review. A, Vol. 84, Issue 5; Other Information: (c) 2011 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 1050-2947
- Country of Publication:
- United States
- Language:
- English
Similar Records
Geometry of entanglement witnesses and local detection of entanglement
One-parameter family of indecomposable optimal entanglement witnesses arising from generalized Choi maps