Relation between entanglement measures and Bell inequalities for three qubits
Abstract
For two qubits in a pure state there exists a onetoone relation between the entanglement measure (the concurrence C ) and the maximal violation M of a Bell inequality. No such relation exists for the threequbit analog of C (the tangle τ ), but we have found that numerical data is consistent with a simple set of upper and lower bounds for τ given M . The bounds on τ become tighter with increasing M , so they are of practical use. The Svetlichny form of the Bell inequality gives tighter bounds than the Mermin form. We show that the bounds can be tightened further if the tangle is replaced by an entanglement monotone that can identify both the W state and the GreenbergerHorneZeilinger state.
 Publication:

Physical Review A
 Pub Date:
 March 2004
 DOI:
 10.1103/PhysRevA.69.032317
 arXiv:
 arXiv:quantph/0311105
 Bibcode:
 2004PhRvA..69c2317E
 Keywords:

 03.67.Mn;
 03.65.Ud;
 Entanglement production characterization and manipulation;
 Entanglement and quantum nonlocality;
 Quantum Physics
 EPrint:
 3 pages, 2 figures