Multiparticle covariance matrices and the impossibility of detecting graph state entanglement with two-particle correlations

Abstract

We present a criterion for multiparticle entanglement based on covariance matrices. On the one hand, the criterion allows to detect bound entangled states which are not detected by other criteria; on the other hand, some strongly entangled pure states such as the GHZ states are not detected. We show, however, that this is a general phenomenon: No separability criterion based on two-particle correlations can recognize the entanglement in the family of graph states, to which the GHZ states belong.

10 pages, 3 figures

References in corpus (19)

• Quantum entanglement
• Separability Criterion for Density Matrices
• A computable measure of entanglement
• Entanglement detection
• Generalized Schmidt decomposition and classification of three-quantum-bit states
• Violation of local uncertainty relations as a signature of entanglement
• Optimal spin squeezing inequalities detect bound entanglement in spin models
• Spin squeezing and entanglement
• Magnetic Susceptibility as a Macrosopic Entaglement Witness
• Entanglement Witnesses in Spin Models
• Covariance matrices and the separability problem
• Not all pure entangled states are useful for sub shot-noise interferometry
• Energy as an Entanglement Witness for Quantum Many-Body Systems
• Unifying several separability conditions using the covariance matrix criterion
• Entanglement detection beyond the cross-norm or realignment criterion
• Multipartite entanglement detection via structure factors
• Entanglement Detection in Optical Lattices of Bosonic Atoms with Collective Measurements
• Quantifying entanglement with covariance matrices
• Entanglement detection via tighter local uncertainty relations

Cited by in corpus (32)

• Multipartite entanglement detection from correlation tensors
• Measure of multipartite entanglement with computable lower bounds
• Enhanced entanglement criterion via symmetric informationally complete measurements
• Scalable Bell inequalities for qubit graph states and robust self-testing
• Nonlocality in many-body quantum systems detected with two-body correlators
• Semidefinite programming relaxations for quantum correlations
• Efficient $k$-separability criteria for mixed multipartite quantum states
• Probing quantum correlations in many-body systems: a review of scalable methods
• Entanglement criteria and full separability of multi-qubit quantum states
• Detection of $k$-partite entanglement and $k$-nonseparability of multipartite quantum states
• Useful multipartite correlations from useless reduced states
• Unveiling quantum entanglement in many-body systems from partial information
• Improved Separability Criteria Based on Bloch Representation of Density Matrices
• Parameterized multipartite entanglement measures
• Bounding entanglement dimensionality from the covariance matrix
• Complementarity between Tripartite Quantum Correlation and Bipartite Bell Inequality Violation in Three Qubit States
• Relationship among locally maximally entanglable states, W states and hypergraph states under local unitary transformations
• Entanglement transitivity problems
• Separability criteria based on Heisenberg-Weyl representation of density matrices
• A Family of Bipartite Separability Criteria Based on Bloch Representation of Density Matrices
• All multipartite entanglements are quantum coherences in locally distinguishable bases
• Negative entanglement measure for bipartite separable mixed states
• Identifying non-k-separability of a class of N-qubit complete graph states using correlation tensors
• Discrimination strategies for inequivalent classes of multipartite entangled states
• Minimal criteria for continuous-variable genuine multipartite entanglement
• $su(d)$-squeezing and many-body entanglement geometry in finite-dimensional systems
• The Foliage Partition: An Easy-to-Compute LC-Invariant for Graph States
• Quantifying multipartite quantum states by ($k+1$)-partite entanglement measures
• Entanglement hierarchies in multipartite scenarios
• The additivity of states uniquely determined by marginals
• Distinguishing Graph States by the Properties of Their Marginals
• On Ergotropic Gap of Tripartite Separable Systems