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 (27)

• Entanglement of Formation of an Arbitrary State of Two Qubits
• Separability Criterion for Density Matrices
• Separability of Mixed States: Necessary and Sufficient Conditions
• Universal state inversion and concurrence in arbitrary dimensions
• Bell Inequalities and the Separability Criterion
• Unextendible Product Bases and Bound Entanglement
• Optimization of entanglement witnesses
• Characterizing Entanglement
• Fidelity and Concurrence of conjugated states
• Violation of local uncertainty relations as a signature of entanglement
• Detecting Genuine Multipartite Entanglement with Two Local Measurements
• Concurrence of arbitrary dimensional bipartite quantum states
• Bell inequality, Bell states and maximally entangled states for n qubits
• Concurrence of mixed bipartite quantum states in arbitrary dimensions
• Characterization of separable states and entanglement witnesses
• Quantum dynamics as a physical resource
• Direct measurement of non-linear properties of bipartite quantum states
• Lower bounds on concurrence and separability conditions
• Nonlinear entanglement witnesses
• Entanglement criteria based on local uncertainty relations are strictly stronger than the computable cross norm criterion
• Entanglement Detection by Local Orthogonal Observables
• Separability criteria and bounds for entanglement measures
• Separability criteria based on the Bloch representation of density matrices
• Bound entangled states violate a non-symmetric local uncertainty relation
• Bell states diagonal entanglement witnesses
• Entanglement quantification through local observable correlations
• Experimental entanglement verification and quantification via uncertainty relations

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