Separability criteria and bounds for entanglement measures

Abstract

Employing a recently proposed separability criterion we develop analytical lower bounds for the concurrence and for the entanglement of formation of bipartite quantum systems. The separability criterion is based on a nondecomposable positive map which operates on state spaces with even dimension N >= 4, and leads to a class of nondecomposable optimal entanglement witnesses. It is shown that the bounds derived here complement and improve the existing bounds obtained from the criterion of positive partial transposition and from the realignment criterion.

8 pages, 2 figures

References in corpus (23)

• Entanglement of Formation of an Arbitrary State of Two Qubits
• Mixed State Entanglement and Quantum Error Correction
• Separability Criterion for Density Matrices
• Separability of Mixed States: Necessary and Sufficient Conditions
• Scaling of Entanglement close to a Quantum Phase Transitions
• Entanglement in a simple quantum phase transition
• Universal state inversion and concurrence in arbitrary dimensions
• Bell Inequalities and the Separability Criterion
• Entanglement monotones
• Optimization of entanglement witnesses
• Quantum Phase Transitions and Bipartite Entanglement
• Concurrence of arbitrary dimensional bipartite quantum states
• The Entanglement of Formation for Isotropic States
• Some Properties of the Computable Cross Norm Criterion for Separability
• I-concurrence and tangle for isotropic states
• Optimal entanglement criterion for mixed quantum states
• Characterization of separable states and entanglement witnesses
• Long-distance entanglement in spin systems
• Entanglement of Formation of Bipartite Quantum States
• Entanglement in SO(3)-invariant bipartite quantum systems
• Entanglement in SU(2)-invariant quantum systems: The positive partial transpose criterion and others
• State space structure and entanglement of rotationally invariant spin systems
• R Function Related to Entanglement of Formation

Cited by in corpus (65)

• Quantum entanglement
• Entanglement detection
• Quantitative entanglement witnesses
• Entanglement witnesses: construction, analysis and classification
• Quantifying entanglement resources
• Entanglement monogamy relations of qubit systems
• Lower bounds on concurrence and separability conditions
• 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
• Concurrence and a proper monogamy inequality for arbitrary quantum states
• Further results on entanglement detection and quantification from the correlation matrix criterion
• Tighter monogamy relations in multipartite systems
• 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
• Generalized Monogamy Relations of Concurrence for N-qubit Systems
• Entanglement detection via tighter local uncertainty relations
• Superactivation of monogamy relations for nonadditive quantum correlation measures
• Monogamy relation of multi-qubit systems for squared Tsallis-\emph{q} entanglement
• Quantifying entanglement of a two-qubit system via measurable and invariant moments of its partially transposed density matrix
• Experimental Determination of Entanglement for Arbitrary Pure States
• Quantum Entanglement: Separability, Measure, Fidelity of Teleportation and Distillation
• Upper bound of the fully entangled fraction
• General Monogamy Relations of Quantum Entanglement for Multiqubit W-class States
• Finer Distribution of Quantum Correlations among Multiqubit Systems
• Inequalities Detecting Quantum Entanglement for $2\otimes d$ Systems
• Estimating multipartite entanglement measures
• Lower Bound of Concurrence and Distillation for Arbitrary Dimensional Bipartite Quantum States
• Lower Bound of Concurrence for Qubit Systems
• Lower Bound of Concurrence Based on Positive Maps
• Tighter monogamy relations of quantum entanglement for multiqubit W-class states
• Analytical Expression of Quantum Discord for Rank-2 Two-qubit States
• Entanglement of Multipartite Schmidt-correlated States
• Improved monogamy relations with concurrence of assistance and negativity of assistance for multiqubit W-class states
• Constrained bounds on measures of entanglement
• An Upper Bound of Fully Entangled Fraction of Mixed States
• Beyond the standard entropic inequalities: stronger scalar separability criteria and their applications
• Lower Bound of Multipartite Concurrence Based on Sub-quantum State Decomposition
• Generating and detecting bound entanglement in two-qutrits using a family of indecomposable positive maps
• Extremal extensions of entanglement witnesses and their connection with UPB
• Estimating Concurrence via Entanglement Witnesses
• Tighter constraints of multiqubit entanglement in terms of Rényi-$\alpha$ entropy
• Generalized Entanglement Monogamy and Polygamy Relations for N -Qubit Systems
• Triangle inequalities in coherence measures and entanglement concurrence
• A new bound of concurrence
• Monogamy relations of concurrence for any dimensional quantum systems
• Tighter constraints of multiqubit entanglement in terms of unified entropy
• Lower bound on concurrence for arbitrary-dimensional tripartite quantum systems
• Generalising Wigner's theorem
• Tighter monogamy and polygamy relations of quantum entanglement in multi-qubit systems
• Polygamy relations of multipartite systems
• General Monogamy and polygamy properties of quantum systems
• Long range entanglement in quantum dot systems under the Fermi-Hubbard approach
• A Note on Quantum Entanglement and PPT
• Tighter constraints of multiqubit entanglement for negativity
• Polygamy relations of multipartite entanglement beyond qubits
• Tighter generalized monogamy and polygamy relations for multiqubit systems
• Tetrahedron genuine entanglement measure of four-qubit systems
• Polygamy relation of quantum correlations with equality
• Lower bound of multipartite concurrence based on sub-multipartite quantum systems
• Generalized product-form monogamy relations in multi-qubit systems
• $k$-Positive Maps: New Characterizations and a Generation Method
• Universal Bound on the Eigenvalues of 2-Positive Trace-Preserving Maps
• Monogamy and polygamy for multi-qudit generalized $W$-class states based on concurrence of assistance and Tsallis-$q$ entanglement of assistance