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 (24)

• Entanglement detection
• Entanglement monogamy relations of qubit systems
• Evaluation of convex roof entanglement measures
• 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
• Tighter entanglement monogamy relations of qubit systems
• A lower bound of concurrence for multipartite quantum states
• Observable estimation of entanglement for arbitrary finite-dimensional mixed states
• Estimating entanglement monotones with a generalization of the Wootters formula
• Lower bounds on entanglement measures from incomplete information
• Quantum Entanglement: Separability, Measure, Fidelity of Teleportation and Distillation
• Improved Separability Criteria Based on Bloch Representation of Density Matrices
• General Monogamy Relations of Quantum Entanglement for Multiqubit W-class States
• Inequalities Detecting Quantum Entanglement for $2\otimes d$ Systems
• Lower Bound of Concurrence Based on Positive Maps
• Separability and Entanglement of Quantum States Based on Covariance Matrices
• Improved lower and upper bounds for entanglement of formation
• A lower bound of concurrence for multipartite quantum systems
• Lower Bound of Multipartite Concurrence Based on Sub-quantum State Decomposition
• Monogamy relations of concurrence for any dimensional quantum systems
• A Note on Quantum Entanglement and PPT
• Computable constraints on entanglement-sharing of multipartite quantum states