Optimal entanglement witnesses based on local orthogonal observables

Abstract

We show that the entanglement witnesses based on local orthogonal observables which are introduced in [S. Yu and N.-L. Liu, Phys. Rev. Lett. 95, 150504 (2005)] and [O. Gühne, M. Mechler, G. Tóth and P. Adam, Phys. Rev. A 74, 010301 (2006)] in linear and nonlinear forms can be optimized, respectively. As applications, we calculate the optimal nonlinear witnesses of pure bipartite states and show a lower bound on the I-concurrence of bipartite higher dimensional systems with our method.

6 pages, 1 figure; minor changes, references added

References in corpus (6)

• Detecting Genuine Multipartite Entanglement with Two Local Measurements
• Concurrence of arbitrary dimensional bipartite quantum states
• Lower bounds on concurrence and separability conditions
• Entanglement criteria based on local uncertainty relations are strictly stronger than the computable cross norm criterion
• Separability criteria and bounds for entanglement measures
• Experimental entanglement verification and quantification via uncertainty relations

Cited by in corpus (10)

• Entanglement detection
• Covariance matrices and the separability problem
• Unifying several separability conditions using the covariance matrix criterion
• Entanglement detection beyond the cross-norm or realignment criterion
• Further results on entanglement detection and quantification from the correlation matrix criterion
• A lower bound of concurrence for multipartite quantum states
• Local commutativity versus Bell inequality violation for entangled states and versus non-violation for separable states
• Bipartite quantum systems: on the realignment criterion and beyond
• Strengthened Bell inequalities for orthogonal spin directions
• Separability and Entanglement of Quantum States Based on Covariance Matrices