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 (201)
- Quantum entanglement
- Quantum Cryptography
- Entanglement of Formation of an Arbitrary State of Two Qubits
- Mixed State Entanglement and Quantum Error Correction
- Separability Criterion for Density Matrices
- A computable measure of entanglement
- Quantum information with continuous variables
- Separability of Mixed States: Necessary and Sufficient Conditions
- Three qubits can be entangled in two inequivalent ways
- Concentrating Partial Entanglement by Local Operations
- Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels
- Entanglement of a Pair of Quantum Bits
- Bell nonlocality
- Distributed Entanglement
- Entanglement detection
- Quantum Communication
- Quantifying Entanglement
- Persistent entanglement in arrays of interacting particles
- Scaling of Entanglement close to a Quantum Phase Transitions
- Measurement-based quantum computation with cluster states
- Entanglement in a simple quantum phase transition
- Entanglement Measures and Purification Procedures
- On the volume of the set of mixed entangled states
- Separability criterion and inseparable mixed states with positive partial transposition
- Scalable multi-particle entanglement of trapped ions
- Mixed-state entanglement and distillation: is there a ``bound'' entanglement in nature?
- 14-qubit entanglement: creation and coherence
- Conditions for a class of entanglement transformations
- Universal state inversion and concurrence in arbitrary dimensions
- Bell Inequalities and the Separability Criterion
- Entanglement in continuous variable systems: Recent advances and current perspectives
- General Monogamy Inequality for Bipartite Qubit Entanglement
- Geometric measure of entanglement and applications to bipartite and multipartite quantum states
- Unextendible Product Bases and Bound Entanglement
- Entanglement monotones
- Quantum Information and Relativity Theory
- Optimization of entanglement witnesses
- Four qubits can be entangled in nine different ways
- Robustness of entanglement
- Superadditivity of communication capacity using entangled inputs
- Classification of mixed three-qubit states
- Generalized Schmidt decomposition and classification of three-quantum-bit states
- Global entanglement in multiparticle systems
- Entanglement Measures under Symmetry
- Entanglement versus Correlations in Spin Systems
- Characterizing Entanglement
- "Squashed Entanglement" - An Additive Entanglement Measure
- Exact and Asymptotic Measures of Multipartite Pure State Entanglement
- Observation of eight-photon entanglement
- A Schmidt number for density matrices
- Bell's theorem for general N-qubit states
- Entanglement of pure states for a single copy
- Fidelity and Concurrence of conjugated states
- Multipartite entanglement, quantum-error-correcting codes, and entangling power of quantum evolutions
- The asymptotic entanglement cost of preparing a quantum state
- Taming multiparticle entanglement
- Separability criteria for genuine multiparticle entanglement
- Measure of genuine multipartite entanglement with computable lower bounds
- Entanglement in Quantum Information Theory
- A potential multipartide entanglement measure
- The entanglement cost under operations preserving the positivity of partial transpose
- Monogamy Inequality in terms of Negativity for Three-Qubit States
- Normal forms and entanglement measures for multipartite quantum states
- Classification of multipartite entangled states by multidimensional determinants
- Bell inequality, Bell states and maximally entangled states for n qubits
- Experimental Observation of Four-Photon Entangled Dicke State with High Fidelity
- Detection of high-dimensional genuine multi-partite entanglement of mixed states
- Multi-particle entanglement and its applications to cryptography
- The Entanglement of Formation for Isotropic States
- The Schmidt Measure as a Tool for Quantifying Multi-Particle Entanglement
- Localizable Entanglement
- Quantifying Entanglement with Witness Operators
- Absolute Maximal Entanglement and Quantum Secret Sharing
- Monotones and invariants for multi-particle quantum states
- Schmidt number witnesses and bound entanglement
- Geometry of entangled states
- Quantitative entanglement witnesses
- Separability and entanglement of composite quantum systems
- Essential entanglement for atomic and molecular physics
- I-concurrence and tangle for isotropic states
- Entanglement versus Bell violations and their behaviour under local filtering operations
- Partial Teleportation of Entanglement in the Noisy Environment
- Local filtering operations on two qubits
- A comparison of the entanglement measures negativity and concurrence
- 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
- A Note on Invariants and Entanglements
- The polynomial invariants of four qubits
- Convex-roof extended negativity as an entanglement measure for bipartite quantum systems
- Estimating entanglement measures in experiments
- Variational Characterisations of Separability and Entanglement of Formation
- Computing Local Invariants of Qubit Systems
- Operational Families of Entanglement Classes for Symmetric -Qubit States
- An observable entanglement measure for unknown mixed quantum states
- General monogamy relation for the entanglement of formation in multiqubit systems
- Entanglement Polytopes: Multiparticle Entanglement from Single-Particle Information
- How robust is a quantum gate in the presence of noise?
- Genuinely Multipartite Concurrence of N-qubit X-matrices
- Entanglement of Formation of Bipartite Quantum States
- The maximally entangled set of multipartite quantum states
- Non-local properties of multi-particle density matrices
- Detection of multipartite entanglement in the vicinity of symmetric Dicke states
- On local invariants of pure three-qubit states
- Family of Concurrence Monotones and its Applications
- Local unitary equivalence of multipartite pure states
- Inductive Entanglement Classification of Four Qubits under SLOCC
- Separability properties of tripartite states with UxUxU-symmetry
- Observer dependent entanglement
- Multiqubit symmetric states with high geometric entanglement
- Four-qubit entanglement from string theory
- Measurement-based quantum computation with trapped ions
- All Maximally Entangled Four Qubits States
- Entanglement of three-qubit Greenberger-Horne-Zeilinger-symmetric states
- Local symmetry properties of pure 3-qubit 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
- The entropy vector formalism and the structure of multidimensional entanglement in multipartite systems
- On the permutationally invariant part of a density matrix and nonseparability of N-qubit states
- On experimental procedures for entanglement verification
- Geometrical aspects of entanglement
- Monogamy of entanglement of formation
- The classical communication cost of entanglement manipulation: Is entanglement an inter-convertible resource?
- Measure of multipartite entanglement with computable lower bounds
- Entanglement for rank-2 mixed states
- Separability criteria and bounds for entanglement measures
- Classification of multipartite entanglement in all dimensions
- A comparative study of relative entropy of entanglement, concurrence and negativity
- Entanglement monotones and maximally entangled states in multipartite qubit systems
- Concurrence and a proper monogamy inequality for arbitrary quantum states
- A General Fidelity Limit for Quantum Channels
- Concurrence Vectors in Arbitrary Multipartite Quantum Systems
- Degree of entanglement for two qubits
- 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
- Entanglement Equivalence of -qubit Symmetric States
- Analytical characterization of the genuine multiparticle negativity
- Roofs and Convexity
- Polynomial invariants for discrimination and classification of four-qubit entanglement
- Negativity as a counter of entangled dimensions
- Tangles of superpositions and the convex-roof extension
- Obtain -state from three-qubit -state on rate 1
- Multipartite entanglement in 2 x 2 x n quantum systems
- On the geometry of four qubit invariants
- The Lorentz singular value decomposition and its applications to pure states of 3 qubits
- Probability density function characterization of multipartite entanglement
- Algebraic invariants of five qubits
- Classification of general n-qubit states under stochastic local operations and classical communication in terms of the rank of coefficient matrix
- A complete set of covariants of the four qubit system
- Estimating entanglement monotones with a generalization of the Wootters formula
- Concurrence in arbitrary dimensions
- The moduli space of three qutrit states
- Three-Tangle for Rank-3 Mixed States: mixture of Greenberger-Horne-Zeilinger, W and flipped W states
- Determination of the Schmidt number
- Lower bounds on entanglement measures from incomplete information
- Quantifying entanglement with covariance matrices
- Why Two Qubits Are Special
- Evolution and Symmetry of Multipartite Entanglement
- Highly Entangled Ground States in Tripartite Qubit Systems
- Qudit Entanglement
- Measurable entanglement for tripartite quantum pure states of qubits
- On Strong Superadditivity of the Entanglement of Formation
- Multipartite pure-state entanglement and the generalized GHZ states
- Partial separability revisited: Necessary and sufficient criteria
- Collective Uncertainty Entanglement Test
- Topological phases and multiqubit entanglement
- Does three-tangle properly quantify the three-party entanglement for Greenberger-Horne-Zeilinger-type states?
- The invariant-comb approach and its relation to the balancedness of multipartite entangled states
- Entanglement of four qubit systems: a geometric atlas with polynomial compass I (the finite world)
- Possibility of generalized monogamy relations for multipartite entanglement beyond three qubits
- Geometric descriptions of entangled states by auxiliaries varieties
- Complete set of operational measures for the characterization of 3-qubit entanglement
- Efficient numerical method to calculate three-tangle of mixed states
- A quantitative witness for Greenberger-Horne-Zeilinger entanglement
- Bounding Polynomial Entanglement Measures for Mixed States
- Rescaling multipartite entanglement measures for mixed states
- Multipartite Entanglement and Quantum State Exchange
- Practical method to obtain a lower bound to the three-tangle
- Lower Bound of Concurrence and Distillation for Arbitrary Dimensional Bipartite Quantum States
- Estimating multipartite entanglement measures
- Concurrence Vectors for Entanglement of High-dimensional Systems
- Entanglement of Collaboration
- A bipartite class of entanglement monotones for N-qubit pure states
- SLOCC Convertibility between Two-Qubit States
- Invariant-based entanglement monotones as expectation values and their experimental detection
- Three-tangle for high-rank mixed states
- Classification scheme of pure multipartite states based on topological phases
- Classification of Multipartite Entanglement via Negativity Fonts
- Classification of qubit entanglement: SL(2,C) versus SU(2) invariance
- Three-qubit topological phase on entangled photon pairs
- Proof of the Gour-Wallach conjecture
- 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
- Guide to Mathematical Concepts of Quantum Theory
- Comparability of multipartite entanglement
- Negativity Fonts, multiqubit invariants and Four qubit Maximally Entangled States
- Freudenthal ranks: GHZ vs. W
Cited by in corpus (101)
- 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
- Genuine-multipartite entanglement criteria based on positive maps
- Bipartite depolarizing channels
- 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
- Entanglement swapping and swapped entanglement
- Witnessing Entanglement and Quantum Correlations in Condensed Matter: A Review
- Energetics of correlations in interacting systems
- k-stretchability of entanglement, and the duality of k-separability and k-producibility
- Strong monogamy inequalities for four qubits
- Analysing quantum systems with randomised measurements
- 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
- Experimental construction of a W-superposition state and its equivalence to the GHZ state under local filtration
- Partial transpose as a direct link between concurrence and negativity
- Generalized concurrence in boson sampling
- Distribution of entanglement and correlations in all finite dimensions
- Evaluating the geometric measure of multiparticle entanglement
- Quantifying entanglement of maximal dimension in bipartite mixed states
- Entanglement quantification made easy: Polynomial measures invariant under convex decomposition
- Entanglement in highly symmetric multipartite quantum 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
- Locally Maximally Entangled States of Multipart Quantum Systems
- Time evolution of coupled spin systems in a generalized Wigner representation
- Deterministic Generation of Multipartite Entanglement via Causal Activation in the Quantum Internet
- Multipartite correlations in mutually unbiased bases
- Symmetries and entanglement of stabilizer states
- Matrix Product States: Entanglement, symmetries, and state transformations
- The classification of multipartite quantum correlation
- Quantitative bound entanglement in two-qutrit states
- Forbidden regimes in the distribution of bipartite quantum correlations due to multiparty entanglement
- Maximally entangled mixed states for a fixed spectrum do not always exist
- Multipartite entanglement transfer in spin chains
- Coherent control of multipartite entanglement
- Geometric approach to entanglement quantification with polynomial measures
- Entanglement Classification via Witness Operators generated by Support Vector Machine
- Measurement-based local quantum filters and their ability to transform quantum entanglement
- Entanglement production by statistical operators
- Lower bounds of concurrence for -qubit systems and the detection of -nonseparability of multipartite quantum systems
- The Entanglement Hierarchy 2 x m x n Systems
- Diagnosing Quantum Phases Using Long-Range Two-Site Quantum Resource Behaviors
- A -partite entanglement measure of -partite quantum states
- Entangled States are Harder to Transfer than Product States
- 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
- Generalized Phase-Space Techniques to Explore Quantum Phase Transitions in Critical Quantum Spin Systems
- General Monogamy and polygamy properties of quantum systems
- Polynomial measure of coherence
- Classification of multipartite systems featuring only and genuine entangled states
- Relations among -ME concurrence, negativity, polynomial invariants, and tangle
- An introductory review on resource theories of generalized nonclassical light
- A geometric formulation to measure global and genuine entanglement in three-qubit systems
- Entanglement and measurement-induced nonlocality of mixed maximally entangled states in multipartite dynamics
- Entanglement and entropy in multipartite systems: a useful approach
- Adventures in Invariant Theory
- Multipartite Gaussian Entanglement of Formation
- Criteria of genuine multipartite entanglement based on correlation tensors
- Higher order singular value decomposition and the reduced density matrices of three qubits
- Mixture of entangled pure states with maximally mixed one-qudit reduced density matrices
- Quantifying entanglement from the geometric perspective
- The verification of a requirement of entanglement measures
- Finite-Function-Encoding Quantum States
- Long-distance genuine multipartite Entanglement between Magnetic Defects in Spin Chains
- Uncertainty relations between quantum Fisher information and entanglement monotones
- Entanglement Classification via Single Entanglement Measure
- The Role of Localizable Concurrence in Quantum Teleportation Protocols
- On two maximally entangled couples
- Approximate and ensemble local entanglement transformations for multipartite states
- Measurement-device-independent Schmidt number certification of all entangled states
- Threetangle in the XY-model class with a non-integrable field background
- Optimal finite-dimensional probe states for quantum phase estimation
- Lorentz invariants of pure three-qubit states
- Nonexistence of maximally entangled mixed states for a fixed spectrum
- Absolutely maximally entangled pure states of multipartite quantum systems
- Systematics and symmetry in molecular phylogenetic modelling: perspectives from physics
- Monogamy and polygamy for multi-qudit generalized -class states based on concurrence of assistance and Tsallis- entanglement of assistance