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

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• Tighter entanglement monogamy relations of qubit systems
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• Experimental Determination of Entanglement for Arbitrary Pure States
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• Probing the geometry of correlation matrices with randomized measurements
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• Finer Distribution of Quantum Correlations among Multiqubit Systems
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• Inequalities Detecting Quantum Entanglement for $2\otimes d$ Systems
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• Lower Bound of Concurrence and Distillation for Arbitrary Dimensional Bipartite Quantum States
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• Lower Bound of Concurrence Based on Positive Maps
• Tighter monogamy relations of quantum entanglement for multiqubit W-class states
• Separability and Entanglement of Quantum States Based on Covariance Matrices
• Improved lower and upper bounds for entanglement of formation
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• Monogamy properties of qubit systems
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• Entanglement criterion via general symmetric informationally complete measurement
• Estimating Concurrence via Entanglement Witnesses
• Generalized Entanglement Monogamy and Polygamy Relations for N -Qubit Systems
• Triangle inequalities in coherence measures and entanglement concurrence
• A new bound of concurrence
• Rényi formulation of entanglement criteria for continuous variables
• Lower and upper bounds for entanglement of Rényi-$\alpha$ entropy
• Monogamy relations of concurrence for any dimensional quantum systems
• Lower bound on concurrence for arbitrary-dimensional tripartite quantum systems
• Bounds for multipartite concurrence
• D-concurrence bounds for pair coherent states
• Polygamy relations of multipartite systems
• Tighter monogamy and polygamy relations of quantum entanglement in multi-qubit systems
• Symmetric measurement-induced lower bounds of concurrence
• A Family of Bipartite Separability Criteria Based on Bloch Representation of Density Matrices
• General Monogamy and polygamy properties of quantum systems
• Tighter generalized monogamy and polygamy relations for multiqubit systems
• A Note on Quantum Entanglement and PPT
• Tighter constraints of multiqubit entanglement for negativity
• Polygamy relations of multipartite entanglement beyond qubits
• Long range entanglement in quantum dot systems under the Fermi-Hubbard approach
• Mutual Uncertainty, Conditional Uncertainty and Strong Sub-Additivity
• Polygamy relation of quantum correlations with equality
• Tetrahedron genuine entanglement measure of four-qubit systems
• Polygamy Inequalities for Qubit Systems
• Uncertainty relations between quantum Fisher information and entanglement monotones
• Rényi and Tsallis formulations of separability conditions in finite dimensions
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• Generalized product-form monogamy relations in multi-qubit systems
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• Monogamy and polygamy for multi-qudit generalized $W$-class states based on concurrence of assistance and Tsallis-$q$ entanglement of assistance
• Detection of genuine multipartite entanglement based on local sum uncertainty relations
• Comparative analysis of robust entanglement generation in engineered XX spin chains
• Enhanced separability criteria based on symmetric measurements
• Monogamy inequalities of entanglement of assistance in $2\otimes 2\otimes d$ systems
• Computable constraints on entanglement-sharing of multipartite quantum states