Classification of mixed three-qubit states

Abstract

We introduce a classification of mixed three-qubit states, in which we define the classes of separable, biseparable, W- and GHZ-states. These classes are successively embedded into each other. We show that contrary to pure W-type states, the mixed W-class is not of measure zero. We construct witness operators that detect the class of a mixed state. We discuss the conjecture that all entangled states with positive partial transpose (PPTES) belong to the W-class. Finally, we present a new family of PPTES "edge" states with maximal ranks.

4 pages, 1 figure

Cited by in corpus (367)

• Quantum entanglement
• Entanglement detection
• Quantum metrology from a quantum information science perspective
• Geometric measure of entanglement and applications to bipartite and multipartite quantum states
• Fisher information and multiparticle entanglement
• Preparation and Measurement of Three-Qubit Entanglement in a Superconducting Circuit
• Multipartite entanglement and high precision metrology
• Witnessing multipartite entanglement
• Characterizing Entanglement
• Generation of Three-Qubit Entangled States using Superconducting Phase Qubits
• Everything You Always Wanted to Know About LOCC (But Were Afraid to Ask)
• Entanglement Certification $-$ From Theory to Experiment
• Taming multiparticle entanglement
• Separability criteria for genuine multiparticle entanglement
• Computing prime factors with a Josephson phase qubit quantum processor
• Open-System Dynamics of Entanglement
• Entanglement Detection in the Stabilizer Formalism
• Classification of multipartite entangled states by multidimensional determinants
• Detection of high-dimensional genuine multi-partite entanglement of mixed states
• Quantum teleportation via a W state
• Multipartite entanglement in spin chains
• A classification of entanglement in three-qubit systems
• The definition of multipartite nonlocality
• Quantitative entanglement witnesses
• Quantifying entanglement resources
• Acceleration-assisted entanglement harvesting and rangefinding
• Entropic uncertainty relations and entanglement
• Device-independent entanglement quantification and related applications
• Spin squeezing inequalities and entanglement of $N$ qubit states
• Separability Properties of Three-mode Gaussian States
• Entangled three-qubit states without concurrence and three-tangle
• Quantum Computing with NMR
• Entanglement Witnesses in Spin Models
• Quantum error correction with silicon spin qubits
• Measurement-Device-Independent Entanglement Witnesses for All Entangled Quantum States
• Genuine quantum correlations in quantum many-body systems: a review of recent progress
• Dynamical Casimir effect entangles artificial atoms
• Entanglement and permutational symmetry
• Optimal entanglement witnesses for continuous-variable systems
• Multipartite entanglement for entanglement teleportation
• Generation of cluster states
• Detection of multipartite entanglement in the vicinity of symmetric Dicke states
• Monogamy of quantum correlations - a review
• Full characterization of a three-photon GHZ state using quantum state tomography
• Multipartite entanglement measures
• Genuine quantum and classical correlations in multipartite systems
• Monogamy properties of quantum and classical correlations
• Experimental violation of a cluster state Bell inequality
• Imperfect measurements settings: implications on quantum state tomography and entanglement witnesses
• A Separability-Entanglement Classifier via Machine Learning
• Entanglement of three-qubit Greenberger-Horne-Zeilinger-symmetric states
• Sudden vanishing of spin squeezing under decoherence
• Partial separability and entanglement criteria for multiqubit quantum states
• Witnessing genuine multipartite entanglement with positive maps
• Evaluation of convex roof entanglement measures
• Entanglement negativity of fermions: monotonicity, separability criterion, and classification of few-mode states
• Quantum Correlation Without Classical Correlations
• Generalized spin squeezing inequalities in $N$ qubit systems: theory and experiment
• Testing the Structure of Multipartite Entanglement with Bell Inequalities
• Fusing multiple W states simultaneously with a Fredkin gate
• Generation of Massive Entanglement Through Adiabatic Quantum Phase Transition in a spinor condensate
• Determining lower bounds on a measure of multipartite entanglement from few local observables
• Three-tangle for mixtures of generalized GHZ and generalized W states
• Tri-partite Entanglement Witnesses and Sudden Death
• Local Conversion of Greenberger-Horne-Zeilinger States to Approximate W States
• Characterizing multipartite entanglement with moments of random correlations
• On the geometry of entangled states
• Multipartite entanglement in quantum spin chains
• Investigating three qubit entanglement with local measurements
• Genuine three-partite entangled states with a local hidden variable model
• Detecting quantum entanglement with unsupervised learning
• Multipartite entanglement in 2 x 2 x n quantum systems
• Operational determination of multi-qubit entanglement classes via tuning of local operations
• The Lorentz singular value decomposition and its applications to pure states of 3 qubits
• A lower bound of concurrence for multipartite quantum states
• Entanglement detection in the vicinity of arbitrary Dicke states
• Distillation of multipartite entanglement by complementary stabilizer measurements
• QUBIT4MATLAB V3.0: A program package for quantum information science and quantum optics for MATLAB
• Generalized Criterion of Maximally Multi-Qubit Entanglement
• Energy and multipartite entanglement in multidimensional and frustrated spin models
• Class of PPT bound entangled states associated to almost any set of pure entangled states
• Detection of genuinely entangled and non-separable $n$-partite quantum states
• Four-qubit entangled symmetric states with positive partial transpositions
• Experimental Quantum Networking Protocols via Four-Qubit Hyperentangled Dicke States
• Efficient $k$-separability criteria for mixed multipartite quantum states
• Detection of genuine tripartite entanglement by multiple sequential observers
• High-fidelity entanglement swapping and generation of three-qubit GHZ state using asynchronous telecom photon pair sources
• Detecting multipartite entanglement structure with minimal resources
• Negativity for two blocks in the one dimensional Spin 1 AKLT model
• Tripartite entanglement: Foundations and applications
• Representation of Berry phase by the trajectories of Majorana stars
• Entangled symmetric states of N qubits with all positive partial transpositions
• Entanglement Sudden Death in Three Qubit X-States
• Convexity of momentum map, Morse index, and quantum entanglement
• Generation of Three-Qubit Entangled W-State by Nonlinear Optical State Truncation
• Genuine Einstein-Podolsky-Rosen steering of three-qubit states by multiple sequential observers
• Correlation tensor criteria for genuine multiqubit entanglement
• On the definition and characterisation of multipartite causal (non)separability
• Scaling of tripartite entanglement at impurity quantum phase transitions
• Multisetting Bell-type inequalities for detecting genuine tripartite entanglement
• Exchange Symmetry and Multipartite Entanglement
• Multiqubit symmetric states with maximally mixed one-qubit reductions
• Detecting metrologically useful entanglement in the vicinity of Dicke states
• Practical methods for witnessing genuine multi-qubit entanglement in the vicinity of symmetric states
• Finite-time destruction of entanglement and non-locality by environmental influences
• Experimental construction of generic three-qubit states and their reconstruction from two-party reduced states on an NMR quantum information processor
• A note on the optimality of decomposable entanglement witnesses and completely entangled subspaces
• Quantifying genuine multipartite correlations and their pattern complexity
• Multipartite entanglement generation and contextuality tests using non-destructive three-qubit parity measurements
• Characterizing multipartite entanglement classes via higher-dimensional embeddings
• Experimentally accessible lower bounds for genuine multipartite entanglement and coherence measures
• Entanglement of three-qubit pure states in terms of teleportation capability
• Multi-qubit entanglement engineering via projective measurements
• Convex optimization over classes of multiparticle entanglement
• Partial separability revisited: Necessary and sufficient criteria
• Robust and Fragile Entanglement of Three Qubits: Relation to Permutation Symmetry
• Characterizing Quantum Networks: Insights from Coherence Theory
• Generation and detection of bound entanglement
• Linear and nonlinear Stark effect in triangular molecule
• Global Entanglement for Multipartite Quantum States
• Scheme for implementing quantum information sharing via tripartite entangled state in cavity QED
• Enhancing a Many-body Dipolar Rydberg Tweezer Array with Arbitrary Local Controls
• Analysing quantum systems with randomised measurements
• k-stretchability of entanglement, and the duality of k-separability and k-producibility
• Demonstrating shareability of multipartite Einstein-Podolsky-Rosen steering
• A study of separability criteria for mixed three-qubit states
• Genuine Multipartite Entanglement in Time
• Generalized X states of N qubits and their symmetries
• Long-range multipartite entanglement close to a first order quantum phase transition
• Experimental generation of pseudo bound entanglement
• Flow of Quantum Correlations from a Two-Qubit System to its Environment
• Entanglement characterization using quantum designs
• Does three-tangle properly quantify the three-party entanglement for Greenberger-Horne-Zeilinger-type states?
• Generation of four-qubit cluster of entangled coherent states in bimodal QED cavities
• Bound entanglement in the XY model
• Identification of three-qubit entanglement
• Partial transpose criteria for symmetric states
• Scheme for sharing classical information via tripartite entangled states
• Multipartite entanglement measures: a review
• Controlled State Reconstruction and Quantum Secret Sharing
• Separability problem for multipartite states of rank at most four
• On the entanglement structure in quantum cloning
• Experimentally implementable criteria revealing substructures of genuine multipartite entanglement
• Searching for extremal PPT entangled states
• Quantification of entanglement via uncertainties
• Algorithm for characterizing stochastic local operations and classical communication classes of multiparticle entanglement
• Separability and entanglement in 2x2xN composite quantum systems
• Minimal control power of the controlled teleportation
• Photonic multipartite entanglement conversion using nonlocal operations
• Identification and control of electron-nuclear spin defects in diamond
• Tripartite entanglement transfer from flying modes to localized qubits
• Demonstrating multipartite entanglement of single-particle W states: linear optical schemes
• Entanglement quantification made easy: Polynomial measures invariant under convex decomposition
• Optimal decomposable witnesses without the spanning property
• Device-independent tests of structures of measurement incompatibility
• Detection of multipartite entanglement with two-body correlations
• Hilbert-Schmidt distance and entanglement witnessing
• Fast entanglement detection for unknown states of two spatial qutrits
• Experimental Classification of Entanglement in Arbitrary Three-Qubit States on an NMR Quantum Information Processor
• Lorentz invariance of entanglement classes in multipartite systems
• Entangled graphs: A classification of four-qubit entanglement
• Bounding Polynomial Entanglement Measures for Mixed States
• Nonlinear entanglement witnesses, covariance matrices and the geometry of separable states
• Generating entangled quantum microwaves in a Josephson-photonics device
• Multiqubit entanglement witness
• Which multiphoton states are related via linear optics?
• Exchange symmetry and global entanglement and full separability
• Multipartite states under local unitary transformations
• Genuine Distributed Coherence
• Manipulating Multi-qudit Entanglement Witnesses by Using Linear Programming
• Tensor of coherences parameterization of multiqubit density operators for entanglement characterization
• Operational multipartite entanglement classes for symmetric photonic qubit states
• Nonlocal Advantages of Quantum Imaginarity
• Witnessing Light-Driven Entanglement using Time-Resolved Resonant Inelastic X-Ray Scattering
• Production of multipartite entanglement for electron spins in quantum dots
• Construction of multi-qubit optimal genuine entanglement witnesses
• Equivalence of Quantum States under Local Unitary Transformations
• Entanglement in a class of multiqubit mixed states without multipartite tangles
• Proving the Generation of Genuine Multipartite Entanglement in a Single-Neutron Interferometer Experiment
• Practical method to obtain a lower bound to the three-tangle
• Entanglement and magnetic order
• Generalization of port-based teleportation and controlled teleportation capability
• Detecting genuine multipartite entanglement via machine learning
• Estimating multipartite entanglement measures
• Minimax optimization of entanglement witness operator for the quantification of three-qubit mixed-state entanglement
• Operational Entanglement Families of Symmetric Mixed N-Qubit States
• Experimental high-intensity three-photon entangled source
• Measuring the integrated information of a quantum mechanism
• Machine-Learning-Derived Entanglement Witnesses
• Bell-states diagonal entanglement witnesses for relativistic and non-relativistic multispinor systems in arbitrary dimensions
• Randomized Graph States and their Entanglement Properties
• Optimal quantum communication using multiparticle partially entangled states
• Impacts of Noise and Structure on Quantum Information Encoded in a Quantum Memory
• Genuine tripartite entanglement in the non-interacting Fermi gas
• Three-qubit entanglement witnesses with the full spanning properties
• Activation of metrologically useful genuine multipartite entanglement
• Tensor network representations from the geometry of entangled states
• New Bell inequalities for three-qubit pure states
• Optimal quantum control via genetic algorithms for quantum state engineering in driven-resonator mediated networks
• Analyzing quantum entanglement with the Schmidt decomposition in operator space
• Role of many-body entanglement in decoherence processes
• A unified approach to entanglement criteria using the Cauchy-Schwarz and Hölder inequalities
• Witness for edge states and its characteristics
• Structural physical approximations and entanglement witnesses
• Efficient measurement-device-independent detection of multipartite entanglement structure
• The classification of multipartite quantum correlation
• A dissipative scheme to approach the boundary of two-qubit entangled mixed states
• Entanglement witnesses in the XY chain: Thermal equilibrium and postquench nonequilibrium states
• Fusing atomic $W$ states via quantum Zeno dynamics
• Generation of energy-entangled W states via parametric fluorescence in integrated devices
• Many-region vacuum entanglement: Distilling a W state
• Entanglement increase from local interactions with not-completely-positive maps
• Greenberger-Horne-Zeilinger States in Quantum Dot Molecule
• Genuine Multipartite Entanglement of Superpositions
• Various notions of positivity for bi-linear maps and applications to tri-partite entanglement
• Quantum correlation via quantum coherence
• Detecting three-qubit bound MUB diagonal entangled states via Nonlinear optimal entanglement witnesses
• Genuine multipartite entanglement is not a precondition for secure conference key agreement
• Distinguishing different classes of entanglement of three-qubit pure states
• Observables suitable for restricting the fidelity to multipartite maximally entangled states
• Distillation of genuine tripartite Einstein-Podolsky-Rosen steering
• Construction of three-qubit biseparable states distinguishing kinds of entanglement in a partial separability classification
• Generation of a time-bin Greenberger--Horne--Zeilinger state with an optical switch
• Entanglement measure for general pure multipartite quantum states
• Inertias of entanglement witnesses
• Investigating a Class of $2\otimes 2\otimes d$ Chessboard Density Matrices via Linear and Non-linear Entanglement Witnesses Constructed by Exact Convex Optimization
• Criteria to detect genuine multipartite entanglement using spin measurements
• Experimental sample-efficient quantum state tomography via parallel measurements
• Attainability and lower semi-continuity of the relative entropy of entanglement, and variations on the theme
• Construction of genuine multipartite entangled states
• Constructions of genuinely entangled multipartite states with applications to local hidden variables (LHV) and states (LHS) models
• Realism and single-quanta nonlocality
• State complexity and quantum computation
• Experimental determination of multipartite entanglement with incomplete information
• Mapping the spatial distribution of entanglement in optical lattices
• Norms and Cones in the Theory of Quantum Entanglement
• Quantifying mixed-state quantum entanglement by optimal entanglement witness
• Linear optical scheme to demonstrate genuine multipartite entanglement for single-particle W states
• Resource conversion between operational coherence and multipartite entanglement in many-body systems
• Tripartite Entanglement Extraction from the Black Hole Vacuum
• Decay of Entanglement for Solid-State Qubits
• Experimentally identifying the entanglement class of pure tripartite states
• General entanglement
• A priori probability that a qubit-qutrit pair is separable
• Multipartite entanglement transfer in spin chains
• A Moment for Random Measurements
• Geometric approach to entanglement quantification with polynomial measures
• Concurrence of assistance and Mermin inequality on three-qubit pure states
• The role of phases in detecting three-qubit entanglement
• Characterizing entanglement with geometric entanglement witnesses
• Entanglement Classification via Witness Operators generated by Support Vector Machine
• Criterion for SLOCC Equivalence of Multipartite Quantum States
• Structural change in multipartite entanglement sharing: a random matrix approach
• Minimal control power of controlled dense coding and genuine tripartite entanglement
• Quantum LOSR networks cannot generate graph states with high fidelity
• Generation of cluster states with Josephson charge qubits
• Certifying Quantum Separability with Adaptive Polytopes
• Entanglement Witness for Indistinguishable Electrons using Solid-State Spectroscopy
• Single-experiment-detectable multipartite entanglement witness for ensemble quantum computing
• Multi-partite separable states with unique decompositions and construction of three qubit entanglement with positive partial transpose
• Separability of three qubit Greenberger-Horne-Zeilinger diagonal states
• Efficient creation of multipartite entanglement in flux qubits
• Entanglement in a three spin system controlled by electric and magnetic field
• GHZ and W Entanglement Witnesses for the Non-interacting Fermi gas
• Predicting Features of Quantum Systems from Very Few Measurements
• Entanglement generation from athermality
• Nilpotent polynomials approach to four-qubit entanglement
• Genuine Entanglement of Four Qubit Cluster Diagonal States
• Exclusion principle for nonlocal advantage of quantum coherence
• Separability criterion for three-qubit states with a four dimensional norm
• Entanglement classification and \emph{non-k}-separability certification via Greenberger-Horne-Zeilinger-class fidelity
• Robust construction of entangled coherent GHZ and W states in a cavity QED system
• Introduction to quantum entanglement in many-body systems
• Extremal states of positive partial transpose in a system of three qubits
• Multi-linear Monogamy Relations for Three Qubit States
• Alternatives of entanglement depth and metrological entanglement criteria
• Concurrence classes for general pure multipartite states
• Internal Boundary between Entanglement and Separability Within a Quantum State
• Genuine Multipartite Entanglement induced by a Thermal Acoustic Reservoir
• On the convex cones arising from classifications of partial entanglement in the three qubit system
• Deterministic transformations of three-qubit entangled pure states
• Quantum Thermal Amplifiers with Engineered Dissipation
• Experimental Detection of Qubit-Ququart Pseudo-Bound Entanglement using Three Nuclear Spins
• Product vectors in the ranges of multi-partite states with positive partial transposes and permanents of matrices
• A heat bath can generate all classes of three-qubit entanglement
• Quantum dissonance provide power to deterministic quantum computation with single qubit
• Energy spectra of three electrons in SiGe/Si/SiGe laterally coupled triple quantum dots
• Conversion of entangled states with nitrogen-vacancy centers coupled to microtoroidal resonators
• Optimal indecomposable witnesses without extremality as well as spanning property
• Spin Squeezing by means of Driven Superradiance
• Study of controlled dense coding with some discrete tripartite and quadripartite states
• Generation of two-photon EPR and Wstates
• Tripartite separability conditions exponentially violated by Gaussian states
• Group structures and representations of graph states
• All incompatible measurements on qubits lead to multiparticle Bell nonlocality
• Classification and Quantification of Entanglement Through Wedge Product and Geometry
• Concurrence classes for an arbitrary multi-qubit state based on positive operator valued measure
• Quantum Information Aspects on Bulk and Nano Interacting Fermi System: Spin-Space Density Matrix Approach
• Canonical operators and the optimal concentration of three-qubit Greenberger-Horne-Zeilinger states
• Criteria for SLOCC and LU Equivalence of Generic Multi-qudit States
• The Essentially Entangled Component of Multipartite Mixed Quantum States, its Properties and an Efficient Algorithm for its Extraction
• Tripartite quantum state mapping and discontinuous entanglement transfer in a cavity QED open system
• State mapping and discontinuous entanglement transfer in a multipartite open system
• Classification witness operator for the classification of different subclasses of three-qubit GHZ class
• Experimental characterization of a non-local convertor for quantum photonic networks
• Locality of three-qubit Greenberger-Horne-Zeilinger-symmetric states
• Stretching the limits of multiparticle entanglement
• Decoherence-free subspace and entanglement sudden death of multi-photon polarization states in fiber channels
• Detection of tripartite entanglement based on principal basis matrix representations
• Geometric Multiaxial Representation of N-qubit Mixed Symmetric Separable States
• Maximal tree size of few-qubit states
• Linear semi-infinite programming approach for entanglement quantification
• Discrimination strategies for inequivalent classes of multipartite entangled states
• Entanglement detection via condition of quantum correlation
• Metrology-assisted entanglement distribution in noisy quantum networks
• Quantum fidelity of symmetric multipartite states
• Genuine three qubit Einstein-Podolsky-Rosen steering under decoherence: Revealing hidden genuine steerability via pre-processing
• Characterizing Entanglement via Uncertainty Relations
• "All-versus-nothing" proof of genuine tripartite steering and entanglement certification in the two-sided device-independent scenario
• Tight bounds from multiple-observable entropic uncertainty relations
• Majorana stellar representation for mixed-spin $(s,\frac{1}{2})$ systems
• Creating multiphoton-polarization bound-entangled states
• There exist infinitely many kinds of partial separability/entanglement
• W state generation and effect of cavity photons on the purification of dot-like single quantum well excitons
• Maximal Secret Reconstruction, Teleportation and Bell's Inequality
• Dicke subsystems are entangled
• Separable ellipsoids around multipartite states
• Entanglement Classification of Restricted Greenberger-Horne-Zeilinger Symmetric States in Four-Qubit System
• Correlations, Bell Inequality Violation & Quantum Entanglement
• Mirrored Entanglement Witnesses for Multipartite and High-Dimensional Quantum Systems
• Randomized hypergraph states and their entanglement properties
• Non-locality and entanglement in multi-qubit systems from a unified framework
• Constructing three-qubit unitary gates in terms of Schmidt rank and CNOT gates
• Long-distance genuine multipartite Entanglement between Magnetic Defects in Spin Chains
• Polytope structures for Greenberger-Horne-Zeilinger diagonal states
• Positive maps from the walled Brauer algebra
• Generation and evaluation of multipartite entanglement with multi-rail encoding in linear optics networks
• Persistent Tensors and Multiqudit Entanglement Transformation
• Multipartite entanglement distribution in a topological photonic network
• Classifying Entanglement by Algebraic Geometry
• Entanglement-Constrained Quantum Metrology: Rapid Low-Entanglement Gains, Tapered High-Level Growth
• Detecting a set of entanglement measures in an unknown tripartite quantum state by local operations and classical communication
• Algorithm for evaluating distance-based entanglement measures
• Uniform Entanglement Frames
• A Note on Normal Forms of Quantum States and Separability
• The additivity of states uniquely determined by marginals
• Multipartite entanglement classes of a multiport beam-splitter
• Minimal-error quantum state discrimination versus robustness of entanglement:More indistinguishability with less entanglement
• The detection power of real entanglement witnesses under local unitary equivalence
• Convicting emergent multipartite entanglement with evidence from a partially blind witness
• The Role of Localizable Concurrence in Quantum Teleportation Protocols
• A Complete Set of Local Invariants for a Family of Multipartite Mixed States
• Tripartite State Characterization via Activated Bipartite Entanglement
• Environment engineering to protect quantum coherence in tripartite systems under dephasing noise
• Matrix Tensor Product Approach to the Equivalence of Multipartite States under Local Unitary Transformations
• Entanglement bases and general structures of orthogonal complete bases
• Entanglement witnesses for stabilizer states and subspaces beyond qubits
• Two- and three-mode squeezing in a three-qubit entangled system
• Generation and Detection of Quantum Correlations and Entanglement on a Spin-Based Quantum Information Processor
• Bipartite and tripartite entanglement in pure dephasing relativistic spin-boson model
• Criteria for partial entanglement of three qubit states arising from distributive rules
• Entanglement criterion for pure $M\otimes N$ bipartite quantum states
• Greenberger-Horne-Zeilinger Symmetry in Four Qubit System
• Entanglement of Four-Qubit Rank-$2$ Mixed States
• Entanglement Classification of extended Greenberger-Horne-Zeilinger-Symmetric States
• Structural physical approximation of partial transposition makes possible to distinguish SLOCC inequivalent classes of three-qubit system
• Identifying local unitary equivalence based on reduction of quantum states