Further results on entanglement detection and quantification from the correlation matrix criterion

Abstract

The correlation matrix (CM) criterion is a recently derived powerful sufficient condition for the presence of entanglement in bipartite quantum states of arbitrary dimensions. It has been shown that it can be stronger than the positive partial transpose (PPT) criterion, as well as the computable cross norm or realignment (CCNR) criterion in different situations. However, it remained as an open question whether there existed sets of states for which the CM criterion could be stronger than both criteria simultaneously. Here, we give an affirmative answer to this question by providing examples of entangled states that scape detection by both the PPT and CCNR criteria whose entanglement is revealed by the CM condition. We also show that the CM can be used to measure the entanglement of pure states and obtain lower bounds for the entanglement measure known as tangle for general (mixed) states.

13 pages, no figures; added references, minor changes; section 4.3 added, to appear in J. Phys. A

References in corpus (35)

• 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
• Separability criterion and inseparable mixed states with positive partial transposition
• Universal state inversion and concurrence in arbitrary dimensions
• Unextendible Product Bases and Bound Entanglement
• Optimization of entanglement witnesses
• Measures and dynamics of entangled states
• Violation of local uncertainty relations as a signature of entanglement
• Bound entanglement can be activated
• Unextendible Product Bases, Uncompletable Product Bases and Bound Entanglement
• Concurrence of arbitrary dimensional bipartite quantum states
• Normal forms and entanglement measures for multipartite quantum states
• Quantitative entanglement witnesses
• I-concurrence and tangle for isotropic states
• A Note on Invariants and Entanglements
• Estimating entanglement measures in experiments
• Covariance matrices and the separability problem
• Entanglement of Formation of Bipartite Quantum States
• Lower bounds on concurrence and separability conditions
• When are correlations quantum? -- Verification and quantification of entanglement by simple measurements
• Optimal entanglement witnesses based on local orthogonal observables
• Construction of quantum states with bound entanglement
• Entanglement criteria based on local uncertainty relations are strictly stronger than the computable cross norm criterion
• Geometrical aspects of entanglement
• Separability criteria and bounds for entanglement measures
• Entanglement for rank-2 mixed states
• Separability criteria based on the Bloch representation of density matrices
• Concurrence via entanglement witnesses
• State space structure and entanglement of rotationally invariant spin systems
• Entanglement quantification through local observable correlations
• Constrained bounds on measures of entanglement
• Quasi multipartite entanglement measure based on quadratic functions
• Rotationally invariant bipartite states and bound entanglement

Cited by in corpus (44)

• Entanglement detection
• Multipartite entanglement detection from correlation tensors
• Unifying several separability conditions using the covariance matrix criterion
• Entanglement detection beyond the cross-norm or realignment criterion
• Characterizing multipartite entanglement with moments of random correlations
• Entanglement detection using mutually unbiased measurements
• Characterizing multipartite entanglement without shared reference frames
• Quantum Separability Criteria for Arbitrary Dimensional Multipartite States
• Observable estimation of entanglement for arbitrary finite-dimensional mixed states
• Heisenberg-Weyl Observables: Bloch vectors in phase space
• Bound entanglement from randomized measurements
• Quantifying entanglement with covariance matrices
• Bound of Entanglement of Assistance and Monogamy Constraints
• Entanglement detection via tighter local uncertainty relations
• Measure and detection of genuine multipartite entanglement for tripartite systems
• Genuine multipartite entanglement detection and lower bound of multipartite concurrence
• Analysing quantum systems with randomised measurements
• Quantum Entanglement: Separability, Measure, Fidelity of Teleportation and Distillation
• Entanglement characterization using quantum designs
• Entanglement detection via some classes of measurements
• Improved Separability Criteria Based on Bloch Representation of Density Matrices
• Characterizing correlation within multipartite quantum systems via local randomized measurements
• Maximum $N$-body correlations do not in general imply genuine multipartite entanglement
• Entanglement-Breaking Indices
• Mutually unbiased measurement based entanglement witnesses
• Entanglement criterion via general symmetric informationally complete measurements
• Separability criteria based on Bloch representation of density matrices
• Entanglement Witnesses Based on Symmetric Informationally Complete Measurements
• Entanglement Criteria Based on Quantum Fisher Information
• Using squeezed field to preserve two-atom entanglement against spontaneous emissions
• Monogamy relations of concurrence for any dimensional quantum systems
• Detection of bound entanglement in continuous variable systems
• Bounds on Multipartite Concurrence and Tangle
• Geometric representation of spin correlations and applications to ultracold systems
• Entanglement Capacity of Nonlocal Hamiltonians : A Geometric Approach
• Necessary conditions for classifying m-separability of multipartite entanglements
• Bound entangled Bell diagonal states of unequal local dimensions, and their witnesses
• Criteria of genuine multipartite entanglement based on correlation tensors
• Identifying non-k-separability of a class of N-qubit complete graph states using correlation tensors
• An Effective Way to Determine the Separability of Quantum State
• Separability criteria based on the correlation tensor moments for arbitrary dimensional states
• Using linear and nonlinear entanglement witnesses to generate and detect bound entangled states on an IBM quantum processor
• Quantum Separability Criteria Based on Symmetric Measurements
• Robustness of 2 x N x M entangled states against qubit loss