Bell inequalities and the separability criterion

Terhal, Barbara M.

doi:10.1016/S0375-9601(00)00401-1

Bell inequalities and the separability criterion

Barbara M. Terhal

Jul 6, 2000

8 pages

Published in:

Phys.Lett.A 271 (2000) 5-6, 319-326

Published: Jul 6, 2000

DOI:

10.1016/S0375-9601(00)00401-1 (publication)

reference search244 citations

Citations per year

Abstract: (Elsevier B.V.)

We analyze and compare the mathematical formulations of the criterion for separability for bipartite density matrices and the Bell inequalities. We show that a violation of a Bell inequality can formally be expressed as a witness for entanglement. We also show how the criterion for separability and the existence of a description of the state by a local hidden variable theory, become equivalent when we restrict the set of local hidden variable theories to the domain of quantum mechanics. This analysis sheds light on the essential difference between the two criteria.

03.65.Bz
03.67.-a
Bell inequalities
Quantum entanglement
Quantum information theory

References(23)

Figures(0)

[1]

Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels

Charles H. Bennett
(
- IBM Watson Res. Ctr.
)
,
Gilles Brassard
(
- Montreal U.
)
,
Claude Crepeau
(
- Montreal U. and
- Ecole Normale Supérieure, Paris
)
,
Richard Jozsa
(
- Montreal U.
)
,
Asher Peres
(
- Technion
)

et al.

- Phys.Rev.Lett. 70 (1993) 1895-1899
•
DOI:
- 10.1103/PhysRevLett.70.1895

[2]

H. Buhrman, R. Cleve, A. Wigderson, Quantum versus classical communication and computation, in: Proc. of 30th STOC, 1998, pp. 63–68, quant-ph/9802040

[3]

Separability criterion and inseparable mixed states with positive partial transposition

Pawel Horodecki
(
- Gdansk Tech. U.
)

- Phys.Lett.A 232 (1997) 333
•
e-Print:
- quant-ph/9703004
•
DOI:
- 10.1016/S0375-9601(97)00416-7

[4]

Unextendible product bases and bound entanglement

C.H. Bennett
,
David P. DiVincenzo
(
- IBM Watson Res. Ctr.
)
,
Tal Mor
(
- Montreal U. and
- UCLA
)
,
Peter W. Shor
(
- AT-T Res., Florham Park
)
,
John A. Smolin
(
- IBM Watson Res. Ctr.
)

et al.

- Phys.Rev.Lett. 82 (1999) 5385
•
e-Print:
- quant-ph/9808030
•
DOI:
- 10.1103/PhysRevLett.82.5385

[5]

D.P. DiVincenzo, T. Mor, P.W. Shor, J.A. Smolin, B.M. Terhal, Unextendible product bases, uncompletable product bases and bound entanglement, submitted to Comm. Math. Phys., quant-ph/9908070

[6]

D.P. DiVincenzo, P.W. Shor, J.A. Smolin, B.M. Terhal, A.V. Thapliyal, Evidence for bound entangled states with negative partial transpose, submitted to Phys. Rev. A, quant-ph/9910026

[7]

W. Duer, J.I. Cirac, M. Lewenstein, D. Bruss, Distillability and partial transposition in bipartite systems, quant-ph/9910022

[8]