Concurrence of arbitrary dimensional bipartite quantum states

Abstract

We derive an analytical lower bound for the concurrence of a bipartite quantum state in arbitrary dimension. A functional relation is established relating concurrence, the Peres-Horodecki criterion and the realignment criterion. We demonstrate that our bound is exact for some mixed quantum states. The significance of our method is illustrated by giving a quantitative evaluation of entanglement for many bound entangled states, some of which fail to be identified by the usual concurrence estimation method.

4 pages, published version

References in corpus (1)

• Quantum Phase Transitions and Bipartite Entanglement

Cited by in corpus (88)

• Entanglement detection
• Monogamy Inequality in terms of Negativity for Three-Qubit States
• Optimal entanglement criterion for mixed quantum states
• Entanglement monogamy relations of qubit systems
• Lower bounds on concurrence and separability conditions
• Optimal entanglement witnesses based on local orthogonal observables
• Evaluation of convex roof entanglement measures
• Unifying several separability conditions using the covariance matrix criterion
• Entanglement detection beyond the cross-norm or realignment criterion
• Separability criteria and bounds for entanglement measures
• Concurrence and a proper monogamy inequality for arbitrary quantum states
• 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
• Lower Bounds of Concurrence for Tripartite Quantum Systems
• Estimating entanglement monotones with a generalization of the Wootters formula
• Lower bounds on entanglement measures from incomplete information
• Hierarchical monogamy relations for the squared entanglement of formation in multipartite systems
• Geometric mean of bipartite concurrences as a genuine multipartite entanglement measure
• An Introduction to Quantum Entanglement: a Geometric Approach
• Bounds on Negativity of Superpositions
• A Note on Fully Entangled Fraction
• Measure and detection of genuine multipartite entanglement for tripartite systems
• Entanglement dynamics of three-qubit states in noisy channels
• Concurrence via entanglement witnesses
• Local Unitary Equivalence of Arbitrary Dimensional Bipartite Mixed Quantum States
• Superactivation of monogamy relations for nonadditive quantum correlation measures
• Quantum Entanglement: Separability, Measure, Fidelity of Teleportation and Distillation
• Novel Schemes for Directly Measuring Entanglement of General States
• Partial transpose as a direct link between concurrence and negativity
• A Class of Bound Entangled States
• Classification of multipartite entanglement containing infinitely many kinds of states
• Upper bound of the fully entangled fraction
• General Monogamy Relations of Quantum Entanglement for Multiqubit W-class States
• Inequalities Detecting Quantum Entanglement for $2\otimes d$ Systems
• A Note on Equivalence of Bipartite States under Local Unitary Transformations
• Evolution equation of entanglement for multi-qubit systems
• Boundary effects to the entanglement entropy and two-site entanglement of the spin-1 valence-bond solid
• Lower Bound of Concurrence Based on Positive Maps
• Separability and Entanglement of Quantum States Based on Covariance Matrices
• A lower bound of concurrence for multipartite quantum systems
• Improved lower and upper bounds for entanglement of formation
• Entanglement of Multipartite Schmidt-correlated States
• Constrained bounds on measures of entanglement
• Lower Bound of Multipartite Concurrence Based on Sub-quantum State Decomposition
• Quantitative bound entanglement in two-qutrit states
• Monogamy relations of concurrence for any dimensional quantum systems
• Pairwise quantum correlations in four-level quantum dot systems
• Tighter constraints of multiqubit entanglement in terms of Rényi-$\alpha$ entropy
• Symmetric measurement-induced lower bounds of concurrence
• Local Equivalence of Rank-Two Quantum Mixed States
• Tighter monogamy and polygamy relations of quantum entanglement in multi-qubit systems
• Polygamy relations of multipartite systems
• Tighter constraints of multiqubit entanglement in terms of unified entropy
• General Monogamy and polygamy properties of quantum systems
• A Family of Bipartite Separability Criteria Based on Bloch Representation of Density Matrices
• A Note on Quantum Entanglement and PPT
• Lower bounds on concurrence and negativity from a trace inequality
• Estimating the Schmidt numbers of quantum states via symmetric measurements
• Tighter constraints of multiqubit entanglement for negativity
• Measurement-induced nonlocality in arbitrary dimensions in terms of the inverse approximate joint diagonalization
• A new entanglement measure based on the total concurrence
• Mapping generalized Jaynes-Cummings interaction into correlated finite-sized systems
• Polygamy relation of quantum correlations with equality
• Analytically Computable Symmetric Quantum Correlations
• Separability and Entanglement of Identical Bosonic Systems
• Local unitary equivalence of arbitrary-dimensional multipartite quantum states
• Entanglement in general two-mode continuous-variable states: local approach and mapping to a two-qubit system
• Verifying Quantum Memory in the Dynamics of Spin Boson Models
• Representation Class and Geometrical Invariants of Quantum States under Local Unitary Transformations
• A note on quantum Bell nonlocality and quantum entanglement for high dimensional quantum systems
• Local entanglement of multidimensional continuous-variable systems
• Nonviolation of the CHSH inequality under local spin-1 measurements on two spin qutrits
• A note on lower bounds of concurrence for arbitrary dimensional bipartite quantum states
• Generalized product-form monogamy relations in multi-qubit systems
• Superior monogamy and polygamy relations and estimates of concurrence
• Entanglement - A Queer In The World Of Quantum : Some Perspectives
• Measuring Hamming Distance between Boolean Functions via Entanglement Measure
• Computable constraints on entanglement-sharing of multipartite quantum states
• Identifying local unitary equivalence based on reduction of quantum states
• Monogamy inequalities of entanglement of assistance in $2\otimes 2\otimes d$ systems
• Unified monogamy and polygamy relations for multipartite systems
• Maximum residual strong monogamy inequality for multiqubit entanglement
• Monogamy and polygamy for multi-qudit generalized $W$-class states based on concurrence of assistance and Tsallis-$q$ entanglement of assistance
• Tighter bounds for generalized monogamy and polygamy relations
• Enhanced separability criteria based on symmetric measurements
• Detection of genuine multipartite entanglement based on local sum uncertainty relations