Quantifying entanglement resources
arXiv:1402.6710 · doi:10.1088/1751-8113/47/42/424005
Abstract
We present an overview of the quantitative theory of single-copy entanglement in finite-dimensional quantum systems. In particular we emphasize the point of view that different entanglement measures quantify different types of resources which leads to a natural interdependence of entanglement classification and quantification. Apart from the theoretical basis, we outline various methods for obtaining quantitative results on arbitrary mixed states.
50+5 pages, 4 figures, contribution to Special Issue of J Phys A on 50 years of Bell's theorem. Typos corrected, various references added. Comments are welcome
References in corpus (58)
- Entanglement detection
- Scalable multi-particle entanglement of trapped ions
- 14-qubit entanglement: creation and coherence
- Entanglement in continuous variable systems: Recent advances and current perspectives
- General Monogamy Inequality for Bipartite Qubit Entanglement
- Entanglement versus Correlations in Spin Systems
- Multipartite entanglement, quantum-error-correcting codes, and entangling power of quantum evolutions
- Taming multiparticle entanglement
- Measure of genuine multipartite entanglement with computable lower bounds
- Monogamy Inequality in terms of Negativity for Three-Qubit States
- Experimental Observation of Four-Photon Entangled Dicke State with High Fidelity
- Localizable Entanglement
- Quantifying Entanglement with Witness Operators
- Constructing N-qubit entanglement monotones from anti-linear operators
- The structure of multidimensional entanglement in multipartite systems
- Entangled three-qubit states without concurrence and three-tangle
- Estimating entanglement measures in experiments
- General monogamy relation for the entanglement of formation in multiqubit systems
- Genuinely Multipartite Concurrence of N-qubit X-matrices
- Inductive Entanglement Classification of Four Qubits under SLOCC
- Multiqubit symmetric states with high geometric entanglement
- Four-qubit entanglement from string theory
- All Maximally Entangled Four Qubits States
- When are correlations quantum? -- Verification and quantification of entanglement by simple measurements
- Partial separability and entanglement criteria for multiqubit quantum states
- Optimal entanglement witnesses based on local orthogonal observables
- On the permutationally invariant part of a density matrix and nonseparability of N-qubit states
- On experimental procedures for entanglement verification
- Monogamy of entanglement of formation
- Separability criteria and bounds for entanglement measures
- Entanglement monotones and maximally entangled states in multipartite qubit systems
- Concurrence and a proper monogamy inequality for arbitrary quantum states
- Three-tangle for mixtures of generalized GHZ and generalized W states
- Determining lower bounds on a measure of multipartite entanglement from few local observables
- On polynomial invariants of several qubits
- Inductive classification of multipartite entanglement under SLOCC
- Tripartite entanglement transformations and tensor rank
- Analytical characterization of the genuine multiparticle negativity
- Polynomial invariants for discrimination and classification of four-qubit entanglement
- Tangles of superpositions and the convex-roof extension
- On the geometry of four qubit invariants
- Probability density function characterization of multipartite entanglement
- Estimating entanglement monotones with a generalization of the Wootters formula
- Three-Tangle for Rank-3 Mixed States: mixture of Greenberger-Horne-Zeilinger, W and flipped W states
- Lower bounds on entanglement measures from incomplete information
- Determination of the Schmidt number
- Highly Entangled Ground States in Tripartite Qubit Systems
- Measurable entanglement for tripartite quantum pure states of qubits
- Partial separability revisited: Necessary and sufficient criteria
- Topological phases and multiqubit entanglement
- Does three-tangle properly quantify the three-party entanglement for Greenberger-Horne-Zeilinger-type states?
- Geometric descriptions of entangled states by auxiliaries varieties
- SLOCC Convertibility between Two-Qubit States
- Entanglement of Collaboration
- Classification of Multipartite Entanglement via Negativity Fonts
- The mixed two qutrit system: local unitary invariants, entanglement monotones, and the SLOCC group SL(3,C)
- Unitary Invariants and Classification of Four-Qubit States via Negativity Fonts
- Comparability of multipartite entanglement
Cited by in corpus (100)
- The role of quantum information in thermodynamics --- a topical review
- Quantum information processing with superconducting circuits: a review
- Entanglement Certification From Theory to Experiment
- Measurements in two bases are sufficient for certifying high-dimensional entanglement
- Quantum Conference Key Agreement: A Review
- Multipartite entanglement measures
- Thermodynamic cost of creating correlations
- Convex geometry of quantum resource quantification
- Quantifying high dimensional entanglement with two mutually unbiased bases
- Transformations among Pure Multipartite Entangled States via Local Operations Are Almost Never Possible
- The thermodynamics of creating correlations: Limitations and optimal protocols
- Genuinely multipartite entangled quantum states with fully local hidden variable models and hidden multipartite nonlocality
- Relaxations of separability in multipartite systems: Semidefinite programs, witnesses and volumes
- Characterizing multipartite entanglement without shared reference frames
- Bipartite depolarizing channels
- Genuine-multipartite entanglement criteria based on positive maps
- Hierarchical monogamy relations for the squared entanglement of formation in multipartite systems
- Robust multipartite entanglement generation via a collision model
- Multipartite Entanglement Accumulation in Quantum States: Localizable Generalized Geometric Measure
- Coherence number as a discrete quantum resource
- Measures of imaginarity and quantum state order
- Witnessing Entanglement and Quantum Correlations in Condensed Matter: A Review
- Entanglement swapping and swapped entanglement
- Energetics of correlations in interacting systems
- k-stretchability of entanglement, and the duality of k-separability and k-producibility
- Analysing quantum systems with randomised measurements
- Strong monogamy inequalities for four qubits
- Multipartite entanglement outperforming bipartite entanglement under limited quantum system sizes
- Certification of high-dimensional entanglement and Einstein-Podolsky-Rosen steering with cold atomic quantum memory
- Semi-device-independent characterisation of multipartite entangled states and measurements
- Partial transpose as a direct link between concurrence and negativity
- Experimental construction of a W-superposition state and its equivalence to the GHZ state under local filtration
- Distribution of entanglement and correlations in all finite dimensions
- Generalized concurrence in boson sampling
- Evaluating the geometric measure of multiparticle entanglement
- Entanglement in highly symmetric multipartite quantum states
- Entanglement quantification made easy: Polynomial measures invariant under convex decomposition
- Quantifying entanglement of maximal dimension in bipartite mixed states
- Polynomial Monogamy Relations for Entanglement Negativity
- Practical measurement-device-independent entanglement quantification
- Quantum entanglement in strong-field ionization
- Entanglement of four-qubit systems: a geometric atlas with polynomial compass II (the tame world)
- A Variational Approach to the Quantum Separability Problem
- Criticality-enhanced quantum sensor at finite temperature
- Triplet-Triplet Decoherence in Singlet Fission
- Trade-off Between Work and Correlations in Quantum Thermodynamics
- Time evolution of coupled spin systems in a generalized Wigner representation
- Symmetries and entanglement of stabilizer states
- Multipartite correlations in mutually unbiased bases
- Deterministic Generation of Multipartite Entanglement via Causal Activation in the Quantum Internet
- Locally Maximally Entangled States of Multipart Quantum Systems
- The classification of multipartite quantum correlation
- Matrix Product States: Entanglement, symmetries, and state transformations
- Forbidden regimes in the distribution of bipartite quantum correlations due to multiparty entanglement
- Quantitative bound entanglement in two-qutrit states
- Coherent control of multipartite entanglement
- Multipartite entanglement transfer in spin chains
- Maximally entangled mixed states for a fixed spectrum do not always exist
- Measurement-based local quantum filters and their ability to transform quantum entanglement
- Geometric approach to entanglement quantification with polynomial measures
- Entanglement Classification via Witness Operators generated by Support Vector Machine
- Lower bounds of concurrence for -qubit systems and the detection of -nonseparability of multipartite quantum systems
- Entanglement production by statistical operators
- The Entanglement Hierarchy 2 x m x n Systems
- A -partite entanglement measure of -partite quantum states
- Diagnosing Quantum Phases Using Long-Range Two-Site Quantum Resource Behaviors
- A link between symmetries of critical states and the structure of SLOCC classes in multipartite systems
- Hierarchy of quantum operations in manipulating coherence and entanglement
- Classification of four qubit states and their stabilisers under SLOCC operations
- Entangled States are Harder to Transfer than Product States
- Polynomial measure of coherence
- Generalized Phase-Space Techniques to Explore Quantum Phase Transitions in Critical Quantum Spin Systems
- General Monogamy and polygamy properties of quantum systems
- Classification of multipartite systems featuring only and genuine entangled states
- Entanglement and entropy in multipartite systems: a useful approach
- An introductory review on resource theories of generalized nonclassical light
- A geometric formulation to measure global and genuine entanglement in three-qubit systems
- Relations among -ME concurrence, negativity, polynomial invariants, and tangle
- Multipartite Gaussian Entanglement of Formation
- Entanglement and measurement-induced nonlocality of mixed maximally entangled states in multipartite dynamics
- Criteria of genuine multipartite entanglement based on correlation tensors
- Higher order singular value decomposition and the reduced density matrices of three qubits
- Quantifying entanglement from the geometric perspective
- Mixture of entangled pure states with maximally mixed one-qudit reduced density matrices
- The verification of a requirement of entanglement measures
- Uncertainty relations between quantum Fisher information and entanglement monotones
- Entanglement Classification via Single Entanglement Measure
- Finite-Function-Encoding Quantum States
- Long-distance genuine multipartite Entanglement between Magnetic Defects in Spin Chains
- Measurement-device-independent Schmidt number certification of all entangled states
- The Role of Localizable Concurrence in Quantum Teleportation Protocols
- Approximate and ensemble local entanglement transformations for multipartite states
- On two maximally entangled couples
- Systematics and symmetry in molecular phylogenetic modelling: perspectives from physics
- Absolutely maximally entangled pure states of multipartite quantum systems
- Threetangle in the XY-model class with a non-integrable field background
- Monogamy and polygamy for multi-qudit generalized -class states based on concurrence of assistance and Tsallis- entanglement of assistance
- Nonexistence of maximally entangled mixed states for a fixed spectrum
- Lorentz invariants of pure three-qubit states
- Optimal finite-dimensional probe states for quantum phase estimation