Lower bounds on concurrence and separability conditions

Abstract

We obtain analytical lower bounds on the concurrence of bipartite quantum systems in arbitrary dimensions related to the violation of separability conditions based on local uncertainty relations and on the Bloch representation of density matrices. We also illustrate how these results complement and improve those recently derived [K. Chen, S. Albeverio, and S.-M. Fei, Phys. Rev. Lett. 95, 040504 (2005)] by considering the Peres-Horodecki and the computable cross norm or realignment criteria.

5 pages, 1 figure; minor changes, references added; final version: minor correction in proof of lemma 1, scope of theorem 2 clarified, to appear in PRA; mistake in proof of lemma 1 of published version corrected, results unchanged

References in corpus (5)

• Concurrence of arbitrary dimensional bipartite quantum states
• Optimal entanglement criterion for mixed quantum states
• Estimating entanglement measures in experiments
• Entanglement criteria based on local uncertainty relations are strictly stronger than the computable cross norm criterion
• Separability criteria and bounds for entanglement measures

Cited by in corpus (10)

• Entanglement detection
• Optimal entanglement witnesses based on local orthogonal observables
• 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
• Observable estimation of entanglement for arbitrary finite-dimensional mixed states
• Lower bounds on entanglement measures from incomplete information
• Separability and Entanglement of Quantum States Based on Covariance Matrices
• A Note on Quantum Entanglement and PPT