Entanglement detection
arXiv:0811.2803 · doi:10.1016/j.physrep.2009.02.004
Abstract
How can one prove that a given state is entangled? In this paper we review different methods that have been proposed for entanglement detection. We first explain the basic elements of entanglement theory for two or more particles and then entanglement verification procedures such as Bell inequalities, entanglement witnesses, the determination of nonlinear properties of a quantum state via measurements on several copies, and spin squeezing inequalities. An emphasis is given on the theory and application of entanglement witnesses. We also discuss several experiments, where some of the presented methods have been implemented.
review article, 90 pages, 22 figures. v2: more content, v3: small changes
References in corpus (66)
- Device-independent security of quantum cryptography against collective attacks
- Quantum computing with trapped ions
- Multi-party entanglement in graph states
- General Monogamy Inequality for Bipartite Qubit Entanglement
- A complete family of separability criteria
- An experimental test of non-local realism
- Bell inequality violation with two remote atomic qubits
- Detecting Genuine Multipartite Entanglement with Two Local Measurements
- Concurrence of arbitrary dimensional bipartite quantum states
- Testing the Hilbert space dimension
- Experimental entanglement of a six-photon symmetric Dicke state
- Experimental Analysis of a 4-Qubit Cluster State
- Entanglement Detection in the Stabilizer Formalism
- Symmetrised Characterisation of Noisy Quantum Processes
- Quantifying Entanglement with Witness Operators
- Multipartite entanglement in spin chains
- Bell Inequalities for Graph States
- Constructing N-qubit entanglement monotones from anti-linear operators
- Quantum Non-Demolition Detection of Strongly Correlated Systems
- Squashing Models for Optical Measurements in Quantum Communication
- Hyperentanglement of two photons in three degrees of freedom
- Unbounded violation of tripartite Bell inequalities
- Toolbox for entanglement detection and fidelity estimation
- All bipartite entangled states display some hidden nonlocality
- Realization and characterization of a 2-photon 4-qubit linear cluster state
- Detecting multipartite entanglement
- Partial separability and entanglement criteria for multiqubit quantum states
- Experimental observation of an entire family of four-photon entangled states
- Energy as an Entanglement Witness for Quantum Many-Body Systems
- Tripartite entanglement versus tripartite nonlocality in 3-qubit GHZ-class states
- Entanglement of multiparty stabilizer, symmetric, and antisymmetric states
- Testing Quantum Devices: Practical Entanglement Verification in Bipartite Optical Systems
- Entanglement monotones and maximally entangled states in multipartite qubit systems
- Spin dynamics for bosons in an optical lattice
- Majorization criterion for distillability of a bipartite quantum state
- Entanglement Detection in Optical Lattices of Bosonic Atoms with Collective Measurements
- Separable Multipartite Mixed States - Operational Asymptotically Necessary and Sufficient Conditions
- Entanglement witnesses and geometry of entanglement of two--qutrit states
- Thermal entanglement properties of small spin clusters
- Entanglement Detection Based on Interference and Particle Counting
- Lower bounds on entanglement measures from incomplete information
- A Robust Semidefinite Programming Approach to the Separability Problem
- Local commutativity versus Bell inequality violation for entangled states and versus non-violation for separable states
- Practical methods for witnessing genuine multi-qubit entanglement in the vicinity of symmetric states
- Verifying multi-partite mode entanglement of W states
- Analytic Expressions for Geometric Measure of Three Qubit States
- Generalized Ardehali-Bell inequalities for graph states
- Novel Schemes for Directly Measuring Entanglement of General States
- Quantum Non-locality and Partial Transposition for Continuous-Variable Systems
- Enhancing the Detection of Natural Thermal Entanglement with Disorder
- Addendum to "Sufficient conditions for three-particle entanglement and their tests in recent experiments"
- The joys of permutation symmetry: direct measurements of entanglement
- Parts and Wholes. An Inquiry into Quantum and Classical Correlations
- Multi-Partite Entanglement Inequalities via Spin Vector Geometry
- Two-message quantum interactive proofs are in PSPACE
- Witnessing Macroscopic Entanglement in a Staggered Magnetic Field
- The Jamiołkowski isomorphism and a conceptionally simple proof for the correspondence between vectors having Schmidt number and -positive maps
- Hyperentanglement witness
- Positive maps, majorization, entropic inequalities, and detection of entanglement
- Beyond the standard entropic inequalities: stronger scalar separability criteria and their applications
- A general scheme for construction of scalar separability criteria from positive maps
- Geometrically induced singular behavior of entanglement
- Entanglement detection via condition of quantum correlation
- Generalized Schmidt decomposition based on injective tensor norm
- Entangled multi-qubit states without higher-tangle
- Detecting and Quantifying Entanglement via Bayesian Updating
Cited by in corpus (10)
- Entanglement and permutational symmetry
- The geometric measure of entanglement for symmetric states
- Measuring Measurement: Theory and Practice
- Multipartite entanglement detection via structure factors
- Practical methods for witnessing genuine multi-qubit entanglement in the vicinity of symmetric states
- Verifying multi-partite mode entanglement of W states
- The joys of permutation symmetry: direct measurements of entanglement
- Probing the quantumness of channels with mixed states
- Positive maps, majorization, entropic inequalities, and detection of entanglement
- Decay of Entanglement for Solid-State Qubits