Separability criterion and inseparable mixed states with positive partial transposition

Abstract

It is shown that any separable state on Hilbert space $\mathcal{H}={\mathcal{H}}_1\otimes {\mathcal{H}}_2$, can be written as a convex combination of N pure product states with $N\le (dim\mathcal{H}{)}^2$. Then a new separability criterion for mixed states in terms of range of density matrix is obtained. It is used in construction of inseparable mixed states with positive partial transposition in the case of $3\times 3$ and $2\times 4$ systems. The states represent an entanglement which is hidden in a more subtle way than it has been known so far.

It is improved and extended version of the former manuscript, in particular the theorem concerning finite decomposition of separable states has been included, 14 pages, RevTeX

References in corpus (1)

• Broadcasting of entanglement via local copying

Cited by in corpus (725)

• Quantum entanglement
• A computable measure of entanglement
• Entanglement detection
• Peres-Horodecki separability criterion for continuous variable systems
• Inseparability criterion for continuous variable systems
• On the volume of the set of mixed entangled states
• Mixed-state entanglement and distillation: is there a ``bound'' entanglement in nature?
• Bell Inequalities and the Separability Criterion
• Entanglement in continuous variable systems: Recent advances and current perspectives
• Unextendible Product Bases and Bound Entanglement
• Optimization of entanglement witnesses
• Robustness of entanglement
• Research on Hidden Variable Theories: a review of recent progresses
• Characterizing Entanglement
• A complete family of separability criteria
• A Schmidt number for density matrices
• Fidelity and Concurrence of conjugated states
• Measures and dynamics of entangled states
• Bound entanglement can be activated
• Quantum optics in the phase space - A tutorial on Gaussian states
• Distinguishing separable and entangled states
• Unextendible Product Bases, Uncompletable Product Bases and Bound Entanglement
• Inseparability criteria for bipartite quantum states
• Quantum Communication With Zero-Capacity Channels
• Limits for entanglement measures
• Quantum non-locality in two three-level systems
• Concurrence of arbitrary dimensional bipartite quantum states
• Multiphoton Quantum Optics and Quantum State Engineering
• Classification of multi-qubit mixed states: separability and distillability properties
• Open-System Dynamics of Entanglement
• Computing quantum discord is NP-complete
• Detection of entanglement with few local measurements
• Multipartite Nonlocality without Entanglement in Many Dimensions
• Separability and distillability of multiparticle quantum systems
• Disentanglement and Decoherence by Open System Dynamics
• On the volume of the set of mixed entangled states II
• An experimental investigation of criteria for continuous variable entanglement
• Concurrence of mixed bipartite quantum states in arbitrary dimensions
• Experimental investigation of the dynamics of entanglement: Sudden death, complementarity, and continuous monitoring of the environment
• Quantifying Entanglement with Witness Operators
• Entangling operations and their implementation using a small amount of entanglement
• Quantum inseparability as local pseudomixture
• Evidence for Bound Entangled States with Negative Partial Transpose
• Schmidt number witnesses and bound entanglement
• Quantum discord and its allies: a review
• Distillability and partial transposition in bipartite systems
• A classification of entanglement in three-qubit systems
• Separability and entanglement of composite quantum systems
• Essential entanglement for atomic and molecular physics
• Entanglement witnesses: construction, analysis and classification
• Entanglement monogamy of multipartite higher-dimensional quantum systems using convex-roof extended negativity
• Characterizing the entanglement of bipartite quantum systems
• Quantifying entanglement resources
• Separability of n-particle mixed states: necessary and sufficient conditions in terms of linear maps
• Separability Properties of Three-mode Gaussian States
• Distillability Criterion for all Bipartite Gaussian States
• Separability Criterion for all bipartite Gaussian States
• Entanglement as a signature of quantum chaos
• Convex-roof extended negativity as an entanglement measure for bipartite quantum systems
• A four-party unlockable bound-entangled state
• Characterization of separable states and entanglement witnesses
• Entanglement and quantum tomography with top quarks at the LHC
• Standard Model Physics and the Digital Quantum Revolution: Thoughts about the Interface
• Variational Characterisations of Separability and Entanglement of Formation
• Local environment can enhance fidelity of quantum teleportation
• Quasi-probability representations of quantum theory with applications to quantum information science
• Negativity and steering: a stronger Peres conjecture
• Signatures of non-classicality in mixed-state quantum computation
• Separability in 2xN composite quantum systems
• Entanglement and permutational symmetry
• Operational criterion and constructive checks for the separability of low rank density matrices
• Inseparability inequalities for higher-order moments for bipartite systems
• Entangling two atoms via spontaneous emission
• On the quantification of entanglement in infinite-dimensional quantum systems
• The Structure of Bipartite Quantum States - Insights from Group Theory and Cryptography
• Quantum information with top quarks in QCD
• Protecting qutrit-qutrit entanglement by weak measurement and reversal
• Multipartite entangled coherent states
• Observation of quantum entanglement in top-quark pairs using the ATLAS detector
• Irreversibility in asymptotic manipulations of entanglement
• Evaluation of convex roof entanglement measures
• Quantitative measures of entanglement in pair coherent states
• Separability conditions from entropic uncertainty relations
• Improved tests of entanglement and Bell inequalities with LHC tops
• The generalized partial transposition criterion for separability of multipartite quantum states
• Construction of quantum states with bound entanglement
• Entanglement negativity of fermions: monotonicity, separability criterion, and classification of few-mode states
• Efficient Quantum Circuits for Non-Qubit Quantum Error-Correcting Codes
• Entanglement Detection by Local Orthogonal Observables
• Quantum Optomechanics in the Bistable Regime
• Qutrit Entanglement
• Linking a distance measure of entanglement to its convex roof
• Unifying several separability conditions using the covariance matrix criterion
• Separability and distillability in composite quantum systems -a primer-
• Convex geometry of quantum resource quantification
• A characterization of continuous variable entanglement
• Geometrical aspects of entanglement
• Understanding entanglement as resource: locally distinguishing unextendible product bases
• Towards resource theory of coherence in distributed scenarios
• Entanglement detection beyond the cross-norm or realignment criterion
• Testing entanglement and Bell inequalities in $H\to ZZ$
• Several nonlocal sets of multipartite pure orthogonal product states
• Witnessed entanglement and the geometric measure of quantum discord
• Gaussian bosonic synergy: quantum communication via realistic channels of zero quantum capacity
• Experimental bound entanglement in a four-photon state
• Enhanced entanglement criterion via symmetric informationally complete measurements
• Experimental single-setting quantum state tomography
• Structural approximations to positive maps and entanglement breaking channels
• Twisted and untwisted negativity spectrum of free fermions
• Many copies may be required for entanglement distillation
• Inseparability criteria based on matrices of moments
• Algorithmic construction of local hidden variable models for entangled quantum states
• Principles of Quantum Communication Theory: A Modern Approach
• Quantum states with a positive partial transpose are useful for metrology
• Further results on entanglement detection and quantification from the correlation matrix criterion
• Tighter monogamy relations in multipartite systems
• Activating bound entanglement in multi-particle systems
• Separable Multipartite Mixed States - Operational Asymptotically Necessary and Sufficient Conditions
• Probing Magnetic Excitations and Correlations in Single and Coupled Spin Systems with Scanning Tunneling Spectroscopy
• Quantum correlations and distinguishability of quantum states
• Decoherence effects in non-classicality tests of gravity
• Entanglement sudden death in qubit-qutrit systems
• Witnessing the non-classical nature of gravity in the presence of unknown interactions
• Geometric entanglement witnesses and bound entanglement
• Quantum entanglement in analogue Hawking radiation, when is the final state non-separable ?
• Spectral conditions for positive maps
• Optimal estimation of entanglement
• Entanglement in SU(2)-invariant quantum spin systems
• Observation of two-mode squeezing in a traveling wave parametric amplifier
• Quantum SMEFT tomography: top quark pair production at the LHC
• Entanglement witness operator for quantum teleportation
• Negativity and strong monogamy of multi-party quantum entanglement beyond qubits
• Qudits for Witnessing Quantum Gravity Induced Entanglement of Masses Under Decoherence
• Entanglement detection using mutually unbiased measurements
• Quantum interference and evolution of entanglement in a system of three-level atoms
• Generalized reduction criterion for separability of quantum states
• Quantum information and CP measurement in $H\to {\tau }^{+}{\tau }^{-}$ at future lepton colliders
• Bipartite entanglement in systems of identical particles: the partial transposition criterion
• Bounds on Quantum Correlations in Bell Inequality Experiments
• Polygamy of Distributed Entanglement
• Entanglement witnesses and geometry of entanglement of two--qutrit states
• Entangled states with positive partial transpose arising from indecomposable positive linear maps
• Measurement of Bell-type inequalities and quantum entanglement from $\Lambda$-hyperon spin correlations at high energy colliders
• Teleportation using coupled oscillator states
• When the Machine Chimes the Bell: Entanglement and Bell Inequalities with Boosted $t\bar{t}$
• Singularity in Entanglement Negativity Across Finite Temperature Phase Transitions
• Quantum Separability Criteria for Arbitrary Dimensional Multipartite States
• Entangled phonons in atomic Bose-Einstein condensates
• Binding entanglement channels
• QUBIT4MATLAB V3.0: A program package for quantum information science and quantum optics for MATLAB
• Entanglement negativity spectrum of random mixed states: A diagrammatic approach
• Entanglement Detection Based on Interference and Particle Counting
• Entanglement of a bipartite channel
• Quantum coherence of planar spin models with Dzyaloshinsky-Moriya interaction
• Detection of genuinely entangled and non-separable $n$-partite quantum states
• Class of PPT bound entangled states associated to almost any set of pure entangled states
• Four-qubit entangled symmetric states with positive partial transpositions
• Bound entanglement in the magic simplex of two--qutrits
• A completely entangled subspace of maximal dimension
• Monogamy of $\alpha$th Power Entanglement Measurement in Qubit Systems
• Bounds on entanglement in qudit subsystems
• Detecting two-party quantum correlations in quantum key distribution protocols
• Efficient $k$-separability criteria for mixed multipartite quantum states
• Concurrence in arbitrary dimensions
• Estimating entanglement monotones with a generalization of the Wootters formula
• Test for entanglement using physically observable witness operators and positive maps
• The Structure of Qubit Unextendible Product Bases
• Useful states and entanglement distillation
• Entanglement induced by a two-mode thermal field
• Distillability and positivity of partial transposes in general quantum field systems
• Bound entanglement from randomized measurements
• Entanglement and thermodynamics in general probabilistic theories
• On circulant states with positive partial transpose
• Entanglement thresholds for random induced states
• Genuinely entangled subspace with all-encompassing distillable entanglement across every bipartition
• Relativity of pure states entanglement
• Determination of the Schmidt number
• Entanglement of Orbital Angular Momentum in Non-Sequential Double Ionization
• Distillable entanglement and area laws in spin and harmonic-oscillator systems
• Experimental analysis of decoherence of quantumness in a continuous variables bi-partite entangled system
• Three-by-three bound entanglement with general unextendible product bases
• High-Dimensional Entanglement in States with Positive Partial Transposition
• A Family of Norms With Applications In Quantum Information Theory
• Experimental Simultaneous Learning of Multiple Non-Classical Correlations
• Separability of diagonal symmetric states: a quadratic conic optimization problem
• Local and Nonlocal Properties of Werner States
• A new class of states with positive partial transposition
• Characterization and measurement of qubit-environment entanglement generation during pure dephasing
• A Survey of Finite Algebraic Geometrical Structures Underlying Mutually Unbiased Quantum Measurements
• Detecting and quantifying entanglement on near-term quantum devices
• Construction of entangled states with positive partial transposes based on indecomposable positive linear maps
• Witnessed Entanglement
• Separability criteria and entanglement witnesses for symmetric quantum states
• Entanglement Structure in Expanding Universes
• Symmetric Extension of Two-Qubit States
• Typical entanglement in multi-qubit systems
• Stationary two-atom entanglement induced by nonclassical two-photon correlations
• Qudit Entanglement
• Family of bound entangled states on the boundary of Peres set
• An Introduction to Quantum Entanglement: a Geometric Approach
• A (5,5) and (6,6) PPT edge state
• Geometry of quantum states: new construction of positive maps
• Separable approximations of density matrices of composite quantum systems
• Measurements of polarization and spin correlation and observation of entanglement in top quark pairs using lepton+jets events from proton-proton collisions at $\sqrt{s}$ = 13 TeV
• Local passivity and entanglement in shared quantum batteries
• Bound entangled states violate a non-symmetric local uncertainty relation
• Bipartite Mixed States of Infinite-Dimensional Systems are Generically Nonseparable
• Entanglement Distillation Protocols and Number Theory
• Multipartite continuous-variable entanglement
• Finite-time destruction of entanglement and non-locality by environmental influences
• Characterization of Distillable and Activable States using Entanglement Witnesses
• Witnessing Entanglement and Quantum Correlations in Condensed Matter: A Review
• Facial structures for various notions of positivity and applications to the theory of entanglement
• Entanglement detection via tighter local uncertainty relations
• Extreme points of the set of density matrices with positive partial transpose
• Characterizing multipartite entanglement classes via higher-dimensional embeddings
• Witness of mixed separable states useful for entanglement creation
• Distillability and PPT entanglement of low-rank quantum states
• Convex optimization over classes of multiparticle entanglement
• How to construct entanglement witnesses
• Tight Bell inequalities with no quantum violation from qubit unextendible product bases
• Einstein-Podolsky-Rosen Correlations of Ultracold Atomic Gases
• Entanglement due to noncommutativity in the phase-space
• Entanglement in SU(2)-invariant quantum systems: The positive partial transpose criterion and others
• Activating hidden metrological usefulness
• Concurrence via entanglement witnesses
• Nonclassicality Invariant of General Two-Mode Gaussian States
• Unique decompositions, faces, and automorphisms of separable states
• A two-way algorithm for the entanglement problem
• Generation and detection of bound entanglement
• Comparative study of nonclassicality, entanglement, and dimensionality of multimode noisy twin beams
• Qubit-qudit states with positive partial transpose
• When Do Composed Maps Become Entanglement Breaking?
• Bipartite quantum systems: on the realignment criterion and beyond
• A dimensionality and purity measure for high-dimensional entangled states
• Local hidden variable models for entangled quantum states using finite shared randomness
• Entanglement witnesses from mutually unbiased bases
• Distillation protocols: Output entanglement and local mutual information
• Complete positivity of nonlinear evolution: A case study
• A class of 2^N x 2^N bound entangled states revealed by non-decomposable maps
• Quantum states with strong positive partial transpose
• Construction of $3\otimes 3$ entangled edge states with positive partial transposes
• Improved algorithm for quantum separability and entanglement detection
• Bound Entanglement and Teleportation
• Low rank extremal PPT states and unextendible product bases
• A study of separability criteria for mixed three-qubit states
• Numerical studies of entangled PPT states in composite quantum systems
• Entanglement for a two-parameter class of states in $2\otimes n$ quantum system
• Rank three bipartite entangled states are distillable
• Nonclassical correlation in a multipartite quantum system: two measures and evaluation
• Optomechanical Entanglement in the Presence of Laser Phase Noise
• Squeezed light from microstructured fibres: towards free space quantum cryptography
• Quantum Entanglement: Separability, Measure, Fidelity of Teleportation and Distillation
• Entanglement Enhances Security in Secret Sharing
• Concurrence of quasi pure quantum states
• Separable states with unique decompositions
• On multipartite invariant states I. Unitary symmetry
• Interplay of nonclassicality and entanglement of two-mode Gaussian fields generated in optical parametric processes
• Rates of asymptotic entanglement transformations for bipartite mixed states: Maximally entangled states are not special
• Non-full rank bound entangled states satisfying the range criterion
• When different entanglement witnesses detect entangled states simultaneously
• New observables for testing Bell inequalities in $W$ boson pair production
• Spectral conditions for entanglement witnesses vs. bound entanglement
• Description of rank four PPT entangled states of two qutrits
• Non-negativity of conditional von Neumann entropy and global unitary operations
• Partial transpose criteria for symmetric states
• Entanglement between Collective Operators in a Linear Harmonic Chain
• Foundations of quantum theory and quantum information applications
• Searching for extremal PPT entangled states
• Entanglement detection via some classes of measurements
• Quantum entanglement and disentanglement of multi-atom systems
• Quantum Separability and Entanglement Detection via Entanglement-Witness Search and Global Optimization
• Bell states diagonal entanglement witnesses
• Separability problem for multipartite states of rank at most four
• Unextendible maximally entangled bases in ${\mathbb{C}}^d⨂{\mathbb{C}}^{d^{\prime }}$
• Entanglement in stationary nonequilibrium states at high energies
• Functional Bell inequalities can serve as a stronger entanglement witness
• Improved Separability Criteria Based on Bloch Representation of Density Matrices
• Entanglement and violation of classical inequalities in the Hawking radiation of flowing atom condensates
• Distinguishability classes, resource sharing, and bound entanglement distribution
• Entanglement in quantum information theory
• Separability and entanglement in 2x2xN composite quantum systems
• Unextendible product bases from tile structures and their local entanglement-assisted distinguishability
• $\alpha$-Logarithmic negativity
• Spin squeezing as a measure of entanglement in a two qubit system
• Group theoretical approach to entanglement
• Unextendible maximally entangled bases in dxd
• Quantum information
• Bell-Correlated Activable Bound Entanglement in Multiqubit Systems
• Weakly coupled local particle detectors cannot harvest entanglement
• New classes of n-copy undistillable quantum states with negative partial transposition
• Quantum channel detection
• The nonequilibrium cost of accurate information processing
• Disentanglement and decoherence in a pair of qutrits under dephasing noise
• Coherence, entanglement and quantumness in closed and open systems with conserved charge, with an application to many-body localisation
• A Traversable Wormhole Teleportation Protocol in the SYK Model
• Efficient Online Quantum Generative Adversarial Learning Algorithms with Applications
• A class of positive atomic maps
• A Class of Bound Entangled States
• Positive maps and entanglement in real Hilbert spaces
• Nonclassicality of pure two-qutrit entangled states
• Better detection of Multipartite Bound Entanglement with Three-Setting Bell Inequalities
• Generalized Circulant Densities and a Sufficient Condition for Separability
• Generating entangled quantum microwaves in a Josephson-photonics device
• On the P-representable subset of all bipartite Gaussian separable states
• Entanglement Theory and the Quantum Simulation of Many-Body Physics
• Tensor of coherences parameterization of multiqubit density operators for entanglement characterization
• Quantum dynamical semigroups and non-decomposable positive maps
• Multiqubit entanglement witness
• A class of inequalities inducing new separability criteria for bipartite quantum systems
• Classification of bi-qutrit positive partial transpose entangled edge states by their ranks
• General Monogamy Relations of Quantum Entanglement for Multiqubit W-class States
• Does inflation squeeze cosmological perturbations?
• Entanglement of a Quantum Optical Elliptic Vortex
• Efficient Bipartite Entanglement Detection Scheme with a Quantum Adversarial Solver
• A nonextensive critical phenomenon scenario for quantum entanglement
• Two-way and three-way negativities of three qubit entangled states
• Estimating entanglement in teleportation experiments
• Simple and maximally robust processes with no classical common-cause or direct-cause explanation
• Separability, entanglement and full families of commuting normal matrices
• Mixed-State Entanglement and Quantum Teleportation through Noisy Channels
• Inequalities Detecting Quantum Entanglement for $2\otimes d$ Systems
• Mixed State Entanglement Classification using Artificial Neural Networks
• Spontaneously generated atomic entanglement in free space: reinforced by incoherent pumping
• Construction of noisy bound entangled states and the range criterion
• Dual entanglement measures based on no local cloning and no local deleting
• Non-classical correlations in quantum mechanics and beyond
• Dimensions, lengths and separability in finite-dimensional quantum systems
• Algorithmic construction of local models for entangled quantum states: optimization for two-qubit states
• Entanglement of a class of mixed two - qutrit states
• Positive Maps Which Are Not Completely Positive
• Concurrence Vectors for Entanglement of High-dimensional Systems
• Minimal tomography with entanglement witnesses
• Entanglement detection in arbitrary dimensional bipartite quantum systems through partial realigned moments
• A simple class of bound entangled states based on the properties of the antisymmetric subspace
• Quantum Entanglement and Quantum Computational Algorithms
• Characterizing mixed state entanglement through single-photon interference
• Qudit Hypergraph States
• Detection and typicality of bound entangled states
• Improved separability criteria via some classes of measurements
• Continuous-Variable Entangled States of Light carrying Orbital Angular Momentum
• Best Separable Approximation of multipartite diagonal symmetric states
• Optimal discrimination between real and complex quantum theories
• Hierarchy of Nonlinear Entanglement Dynamics for Continuous Variables
• Entanglement of Coarse Grained Quantum Field in the Expanding Universe
• A Variational Approach to the Quantum Separability Problem
• Sufficient separability criteria and linear maps
• Numerical construction of multipartite entanglement witnesses
• Properties and construction of extreme bipartite states having positive partial transpose
• Non-linear and quantum optics of a type II OPO containing a birefringent element Part 2 : bright entangled beams generation
• Bipartite separability and non-local quantum operations on graphs
• When only two thirds of the entanglement can be distilled
• Entanglement and spin squeezing in the two-atom Dicke model
• Simultaneous amplitude and phase damping of a kind of Gaussian states and their separability
• Entanglement between smeared field operators in the Klein-Gordon vacuum
• Quantum Correlation with Sandwiched Relative Entropies: Advantageous as Order Parameter in Quantum Phase Transitions
• Quantum Discord Surge Heralds Entanglement Revival in an Infinite Spin Chain
• How many mutually unbiased bases are needed to detect bound entangled states?
• Quantum coherences, K-way negativities and multipartite entanglement
• Geometric discord and Measurement-induced nonlocality for well known bound entangled states
• Non-Markovian Dynamics and Entanglement in Quantum Brownian Motion
• Distance between Bound Entangled States from Unextendible Product Bases and Separable States
• Tighter monogamy relations of quantum entanglement for multiqubit W-class states
• Ghost imaging with intense fields from chaotically-seeded parametric downconversion
• Quasilocal entanglement across the Mott-Hubbard transition
• Geometry for separable states and construction of entangled states with positive partial transposes
• Separability of rank two quantum states on multiple quantum spaces
• Mutually unbiased measurement based entanglement witnesses
• Existence of product vectors and their partial conjugates in a pair of spaces
• Entanglement Witnesses and Characterizing Entanglement Properties of Some PPT States
• Five open problems in quantum information
• Bound entanglement in quantum phase transitions
• Discrete Wigner distribution for two qubits: a characterization of entanglement properties
• Low rank positive partial transpose states and their relation to product vectors
• Measuring spin correlation between quarks during QCD confinement
• Manipulation of Multimode Squeezing in a Coupled Waveguide Array
• Continuous variable polarization entanglement, experiment and analysis
• Uncertainty under Quantum Measures and Quantum Memory
• Entanglement Distillation; A Discourse on Bound Entanglement in Quantum Information Theory
• Correlations enable lossless ergotropy transport
• Quantum correlation via quantum coherence
• Deep learning the hierarchy of steering measurement settings of qubit-pair states
• On the Bures Volume of Separable Quantum States
• Non-linear and quantum optics of a type II OPO containing a birefringent element Part 1: Classical operation
• Entanglement witnesses in the XY chain: Thermal equilibrium and postquench nonequilibrium states
• Witness for edge states and its characteristics
• Entanglement properties of quantum grid states
• Quantum separability criteria based on realignment moments
• Canonical Leggett-Garg Inequality: Nonclassicality of temporal quantum correlations under energy constraint
• Absolute Non-Violation of a Three-Setting Steering Inequality by Two-Qubit States
• Nonlocal Activation of Bound Entanglement via Local Quantum Zeno Dynamics
• Separability and entanglement in 2x3xN composite quantum systems
• Robustness of entangled states that are positive under partial transposition
• Detecting three-qubit bound MUB diagonal entangled states via Nonlinear optimal entanglement witnesses
• Entanglement criterion via general symmetric informationally complete measurements
• Thermometry by correlated dephasing of impurities in a 1D Fermi gas
• Exposedness of Choi type entanglement witnesses and applications to lengths of separable states
• Unextendible product bases, bound entangled states, and the range criterion
• Positive maps, majorization, entropic inequalities, and detection of entanglement
• Entanglement control in coupled two-mode boson systems
• Quantumness and Entanglement Witnesses
• Many body physics from a quantum information perspective
• Detecting the inseparability and distillability of continuous variable states in Fock space
• There is no direct generalization of positive partial transpose criterion to the three-by-three case
• Assessing the role of initial correlations in the entropy production rate for non-equilibrium harmonic dynamics
• On Estimation of Fully Entangled Fraction
• Entanglement generation between a charge qubit and its bosonic environment during pure dephasing - dependence on environment size
• Vacuum - induced stationary entanglement in radiatively coupled three - level atoms
• Distillation of free entanglement from bound entangled states using weak measurements
• Distillation Protocols that Involve Local Distinguishing: Composing Upper and Lower Bounds on Locally Accessible Information
• Inertias of entanglement witnesses
• Reducing Computational Complexity of Quantum Correlations
• Dense Coding with Locality Restriction for Decoder: Quantum Encoders vs. Super-Quantum Encoders
• Norms and Cones in the Theory of Quantum Entanglement
• Tripartite Entanglement of Hawking Radiation in Dispersive Model
• Finding semi-optimal measurements for entanglement detection using Autoencoder Neural Networks
• Improved monogamy relations with concurrence of assistance and negativity of assistance for multiqubit W-class states
• On the two-dimensional time-dependent anisotropic harmonic oscillator in a magnetic field
• Attainability and lower semi-continuity of the relative entropy of entanglement, and variations on the theme
• On multipartite invariant states II. Orthogonal symmetry
• An Upper Bound of Fully Entangled Fraction of Mixed States
• Frontier between separability and quantum entanglement in a many spin system
• Construction of optimal teleportation witness operators from entanglement witnesses
• Entanglement Witnesses Based on Symmetric Informationally Complete Measurements
• Essentially All Gaussian Two-Party Quantum States are a priori Nonclassical but Classically Correlated
• Quantum Atom Optics: Theory and Applications to Quantum Technology
• A class of Bell diagonal entanglement witnesses in ${\mathbb{C}}^4\otimes {\mathbb{C}}^4$: optimization and the spanning property
• Efficient nonlinear witnessing of non-absolutely separable states with lossy detectors
• Polarization and frequency disentanglement of photons via stochastic polarization mode dispersion
• Learning entanglement breakdown as a phase transition by confusion
• Quantum Wasserstein distance based on an optimization over separable states
• Generalized uncertainty relations and entanglement dynamics in quantum Brownian motion models
• Delayed birth of distillable entanglement in the evolution of bound entangled states
• Qubit-environment Negativity versus Fidelity of conditional environmental states for an NV-center spin qubit interacting with a nuclear environment
• Tracking the variation of entanglement Rényi negativity: a quantum Monte Carlo study
• Unextendible and uncompletable product bases in every bipartition
• Quantum entanglement of decohered two-mode squeezed states in absorbing and amplifying environment
• Entanglement Criteria Based on Quantum Fisher Information
• The role of phases in detecting three-qubit entanglement
• Maximum entangled states and quantum Teleportation via Single Cooper pair Box
• Characterizing entanglement with geometric entanglement witnesses
• Generating and detecting bound entanglement in two-qutrits using a family of indecomposable positive maps
• Entanglement in bipartite generalized coherent states
• Optimal Lewenstein-Sanpera Decomposition for some Biparatite Systems
• Relaxation Method For Calculating Quantum Entanglement
• Analogous Hawking radiation and quantum entanglement in two-component Bose-Einstein condensates: the gapped excitations
• Some aspects of separability
• Nonclassicality of noisy quantum states
• Coupling bosonic modes with a qubit: entanglement dynamics at zero and finite-temperatures
• Detection of entanglement during pure dephasing evolutions for systems and environments of any size
• Necessary And Sufficient Condition of Separability of Any System
• Bound entanglement in the Jaynes-Cummings model
• Hydrogenic entanglement
• Two-message quantum interactive proofs and the quantum separability problem
• Mapping cone of $k$-Entanglement Breaking Maps
• A generic framework for genuine multipartite entanglement detection
• A note on bound entanglement and local realism
• Detecting Quantum Entanglement
• Certifying Quantum Separability with Adaptive Polytopes
• Single-qubit measurement of two-qubit entanglement in generalized Werner states
• Long-range multipartite quantum correlations and factorization in a one-dimensional spin-1/2 $XY$ chain
• Using non-positive maps to characterize entanglement witnesses
• Separability of Multipartite Quantum States with Strong Positive Partial Transpose
• Every entangled state provides an advantage in classical communication
• Boundary of the set of separable states
• Detecting separable states via semidefinite programs
• Preparation of bipartite bound entangled Gaussian states in quantum optics
• Separability criteria based on Heisenberg-Weyl representation of density matrices
• Beating detection loophole in nonlinear entanglement witnesses
• Dynamical creation of entanglement versus disentanglement in a system of three - level atoms with vacuum - induced coherences
• Neutrinos as qubits and qutrits
• Usefulness of classical communication for local cloning of entangled states
• Analytic solution of the separability criterion for continuous variable systems
• Separability criteria for continuous variable systems
• Entropic characterization of Separability in Gaussian states
• Locally Accessible Information of Multisite Quantum Ensembles Violates Monogamy
• A new bound of concurrence
• Broadcasting of quantum correlations in qubit-qudit systems
• Entangled states in the role of witnesses
• Schmidt number criterion via general symmetric informationally complete measurements
• Estimating Concurrence via Entanglement Witnesses
• Quantum Entanglement: Criteria and Collective Tests
• Different operational meanings of continuous variable Gaussian entanglement criteria and Bell inequalities
• Entanglement detection beyond the CCNR criterion for infinite-dimensions
• The hierarchies of "witnesses" and the properties and characterization of entangled states as super entanglement witnesses
• Detection loophole in measurement-device-independent entanglement witness
• Rotationally invariant bipartite states and bound entanglement
• Equivalence classes and canonical forms for two-qutrit entangled states of rank four having positive partial transpose
• Low rank separable states are a set of measure zero within the set of low rank states
• Unextendible entangled bases and more nonlocality with less entanglement
• A general scheme for construction of scalar separability criteria from positive maps
• Generalised monogamy relation of convex-roof extended negativity in multi-level systems
• Evaluating measures of nonclassical correlation in a multipartite quantum system
• Generalized Entanglement Monogamy and Polygamy Relations for N -Qubit Systems
• Analog de Sitter universe in quantum Hall systems with an expanding edge
• A Complete Hierarchy of Linear Systems for Certifying Quantum Entanglement of Subspaces
• Entanglement without Dissipation: A Touchstone for an exact Comparison of Entanglement Measures
• Entanglement of positive definite functions on compact groups
• Dvoretzky's Theorem and the Complexity of Entanglement Detection
• Censorship of Quantum Resources in Quantum Networks
• Phase-space quantum profile of Pöschl-Teller two-level systems
• Superadditivity of distillable entanglement From Quantum Teleportation
• Geometry on the manifold of Gaussian quantum channels
• Hierarchy of quantum operations in manipulating coherence and entanglement
• Symmetric measurement-induced lower bounds of concurrence
• A complete picture of the four-party linear inequalities in terms of the 0-entropy
• Noiseless method for checking the Peres separability criterion by local operations and classical communication
• Introduction to quantum entanglement in many-body systems
• Schmidt numbers of low rank bipartite mixed states
• Constructing unextendible product bases from the old ones
• Bipartite bound entanglement in continuous variables through deGaussification
• On the comparison of volumes of quantum states
• $C^{\ast }$-extreme points of entanglement breaking maps
• Noisy quantum input loophole in measurement-device-independent entanglement witnesses
• D-concurrence bounds for pair coherent states
• Characteristics and benchmarks of entanglement of mixed states -- the two qubit case
• Hermitian Tensor Product Approximation of Complex Matrices and Separability
• Negative result about the construction of genuinely entangled subspaces from unextendible product bases
• Witness Operator Provides Better Estimate of the Lower Bound of Concurrence of Bipartite Bound Entangled States in $d_1\otimes d_2$ Dimensional System
• Characterizing generalized axisymmetric quantum states in $d\times d$ systems
• Internal Boundary between Entanglement and Separability Within a Quantum State
• An Inverse Mass Expansion for the Mutual Information in Free Scalar QFT at Finite Temperature
• Geometric Local Hidden State Model for Some Two-qubit States
• Polynomial measure of coherence
• Entanglement distribution and quantum discord
• Activation of Nonmonogamous Multipartite Quantum States
• Computing linear sections of varieties: quantum entanglement, tensor decompositions and beyond
• Two and Three-Qubits Geometry, Quaternionic and Octonionic Conformal Maps, and Intertwining Stereographic Projection
• Canonical Distillation of Entanglement
• Product vectors in the ranges of multi-partite states with positive partial transposes and permanents of matrices
• Entanglement witnesses with variable number of local measurements
• Constructing Entanglement Witness Via Real Skew-Symmetric Operators
• Quantum Entanglement is Quantum: ZZ Production at the LHC
• Sufficient and Necessary Condition of Separability for Generalized Werner States
• A Family of Bipartite Separability Criteria Based on Bloch Representation of Density Matrices
• Nonlinear Improvement of Qubit-qudit Entanglement Witnesses
• Experimental Detection of Qubit-Ququart Pseudo-Bound Entanglement using Three Nuclear Spins
• Maximally-Disordered Distillable Quantum States
• Quantum entanglement in finite-dimensional Hilbert spaces
• Entanglement of one-magnon Schur-Weyl states
• Entanglement versus mixedness for coupled qubits under a phase damping channel
• A gap for PPT entanglement
• Separability of qubit-qudit quantum states with strong positive partial transposes
• Entanglement in phase-space distribution for an anisotropic harmonic oscillator in noncommutative space
• Economical realization of phase covariant devices in arbitrary dimensions
• Estimating the Schmidt numbers of quantum states via symmetric measurements
• Separability Criterion for Quantum Effects
• Bound entangled Bell diagonal states of unequal local dimensions, and their witnesses
• An asymptotical separability criterion for bipartite density operators
• Entanglement Detection and Distillation for Arbitrary Bipartite Systems
• Reflection Symmetries for Multiqubit Density Operators
• A bipartite separable ball and its applications
• Bipartite Bound Entanglement
• Entanglement of quantum oscillators coupled to different heat baths
• Statistical-mechanical description of quantum entanglement
• Entanglement and nonclassicality in four-mode Gaussian states generated via parametric down-conversion and frequency up-conversion
• Quantum channels that destroy negative conditional entropy
• Correlation Minor Norms, Entanglement Detection and Discord
• Tighter generalized monogamy and polygamy relations for multiqubit systems
• Detectors interacting through quantum fields: Non-Markovian effects, non-perturbative generation of correlations and apparent non-causality
• Upper bounds for relative entropy of entanglement based on active learning
• Physical realization of realignment criteria using structural physical approximation
• Optimal Time-Reversal of Multi-phase Equatorial States
• Entanglement properties of a measurement-based entanglement distillation experiment
• Bounds on bipartite entanglement from fixed marginals
• Quantifying subspace entanglement with geometric measures
• Theoretical proposal for the experimental realization of realignment operation
• Minkowski structure for purity and entanglement of Gaussian bipartite states
• Computing finite-dimensional bipartite quantum separability
• Unified Framework for Calculating Convex Roof Resource Measures
• Quasi-polynomial time algorithms for free quantum games in bounded dimension
• Entanglement detection and lower bound of convex-roof extension of negativity
• Computable entanglement cost under positive partial transpose operations
• Linear maps as sufficient criteria for entanglement depth and compatibility in many-body systems
• Detecting entanglement from macroscopic measurements of the electric field and its fluctuations
• Mode Entanglement in Fermionic and Bosonic Harmonium
• Work drives time evolution
• Characterization of Nonlocal Resources Under Global Unitary Action
• A family of generalized Horodecki-like entangled states
• Degree of separability of bipartite quantum states
• Separability criteria with angular and Hilbert space averages
• Construction of Bound Entangled States Based on Permutation Operators
• Multi-copy activation of genuine multipartite entanglement in continuous-variable systems
• Unbreakable and breakable quantum censorship
• Quantum-entangled light from localized emitters
• Nonexistence of entangled continuous-variable Werner states with positive partial transpose
• Entanglement partners and monogamy in de Sitter universes
• A Note on Resistance of NPT to Mixture of Separable States
• Multipartite entanglement detection via generalized Wigner-Yanase skew information
• Comparative Dynamical Study of a Bound Entangled State
• Detecting genuine multipartite entanglement using moments of positive maps
• Entanglement and separability in the noncommutative phase-space scenario
• Extremal entanglement witnesses
• Triangle-like inequalities related to coherence and entanglement negativity
• Capacities of a two-parameter family of noisy Werner-Holevo channels
• Approximation, Proof Systems, and Correlations in a Quantum World
• Detection methods to rule out completely co-positive and bi-entangling operations
• Creating multiphoton-polarization bound-entangled states
• Quantum entanglement in phase space
• Sinkhorn-Knopp Theorem for PPT states
• Quantum correlations for anonymous metrology
• Visualizing extremal positive maps in unital and trace preserving form
• Is absolute separability determined by the partial transpose?
• Quantumness and its hierarchies in PT-symmetric down-conversion models
• Separability of Multi-Partite Quantum States
• Real randomized measurements for analyzing properties of quantum states
• Finite-temperature quantum discordant criticality
• Correlation based entanglement criteria for bipartite systems
• Derivation of the robustness from the concurrence
• Operational detection of entanglement via quantum designs
• On separable decompositions of quantum states with strong positive partial transposes
• Dicke subsystems are entangled
• Robust entanglement measure for mixed quantum states
• Bound on distributed entanglement
• On the extreme points of sets of absolulely separable and PPT states
• Correlations, Bell Inequality Violation & Quantum Entanglement
• On Global Effects Caused by Locally Noneffective Unitary Operations
• Studies on the Role of Entanglement in Mixed-state Quantum Computation
• Construction of PPT entangled state and its detection by using second-order moment of the partial transposition
• Separable states and positive maps
• On the state space structure of tripartite quantum systems
• Not all entangled states are useful for ancilla-assisted quantum process tomography
• The Role of Entanglement in Quantum Communication, and Analysis of the Detection Loophole
• Quantification of Quantum Entanglement in a Multiparticle System of Two-Level Atoms Interacting with a Squeezed Vacuum State of the Radiation Field
• Experimental pre-assessing entanglement in Gaussian states mixing
• Scaling maps of $s$-ordered quasiprobabilities are either nonpositive or completely positive
• Entanglement Universality of TGX States in Qubit-Qutrit Systems
• Quantum Grid States and Hybrid Graphs
• Entanglement in the bimodal Jaynes-Cummings model with the two-mode squeezed vacuum state
• Iterative optimization in quantum metrology and entanglement theory using semidefinite programming
• Entangled edge states of corank one with positive partial transposes
• Search for an efficient entanglement witness operator for bound entangled states in bipartite quantum systems
• Separability and Entanglement of Identical Bosonic Systems
• Decomposable Pauli diagonal maps and Tensor Squares of Qubit Maps
• Initial-state randomness as a universal source of decoherence
• On the symmetry of the seminal Horodecki state
• Quantum Entanglement and Geometry
• Three qubit separable states of length ten with unique decompositions
• Entanglement-Enhanced Classical Communication
• Geometric Discord of any arbitrary dimensional bipartite system and its application in quantum key distribution
• Group-Theoretic Perspective on the PPT and Realignment Criteria in the Magic Simplex for Bipartite Qutrits
• Measurement of spin correlation and entanglement in ATLAS and CMS
• The Origin of Separable States and Separability Criteria from Entanglement-breaking Channels
• Particle Creation and Entanglement in Dispersive Model with Step Velocity Profile
• Tuning the separability in noncommutative space
• Constructing unextendible product bases from multiqubit ones
• Characterization of the quantum state of top quark pairs produced in proton-proton collisions at $\sqrt{s}$ = 13 TeV using the beam and helicity bases
• Necessary criterion for extracting thermodynamical work from qudit-entangled state
• Efficient detection for quantum states containing fewer than $k$ unentangled particles in multipartite quantum systems
• Bound entanglement and distillability of multipartite quantum systems
• The Classical Harmonic Vibrations of the Atomic Centers of Mass with Micro Amplitudes and Low Frequencies Monitored by the Entanglement between the Two Two-level Atoms in a Single mode Cavity
• Convex-roof entanglement measures of density matrices block diagonal in disjoint subspaces for the study of thermal states
• Matrix convex sets over the Euclidean ball and polar duals of real free spectrahedra
• Generalized product-form monogamy relations in multi-qubit systems
• Role of qubits in quantum entanglement and quantum teleportation
• Efficient Characterization of N-Beam Gaussian Fields Through Photon-Number Measurements: Quantum Universal Invariants
• Entanglement in the Dicke subspace
• An Effective Way to Determine the Separability of Quantum State
• Recovery of resources through sequential noisy measurements
• Measurement-device-independent nonlinear entanglement witnesses
• Algorithm for evaluating distance-based entanglement measures
• Construction of exposed indecomposable positive linear maps between matrix algebras
• Remarks on Lewenstein-Sanpera Decomposition
• Experimental characterization of the hierarchy of quantum correlations in top quark pairs
• Effect of Quantum Information Scrambling on Bound Entangled States
• Degradable Strongly Entanglement Breaking Maps
• Coherence measure of ensembles with nonlocality without entanglement
• A variational quantum algorithm for entanglement quantification
• Constructing quantum circuits for maximally entangled multi-qubit states using the genetic algorithm
• Variational-toolbox-based separability detection of multiqubit states
• Mathematical framework for detection and quantification of nonclassical correlation
• Limitation for linear maps in a class for detection and quantification of bipartite nonclassical correlation
• Convicting emergent multipartite entanglement with evidence from a partially blind witness
• Maximum Dimension of Subspaces with No Product Basis
• On the covariance matrix for Gaussian states
• Measure of tripartite quantum correlation in multiqubit symmetric pure state
• Practical construction of positive maps which are not completely positive
• An experimental proposal for a Gaussian amendable quantum channel
• Separability for Weak Irreducible matrices
• Rényi and von Neumann entropies for various Bipartite Gaussian States
• On the geometric phase for Gaussian states
• Local Purity Distillation in Quantum Systems: Exploring the Complementarity Between Purity and Entanglement
• Entangled Kernels -- Beyond Separability
• Generation and Detection of Quantum Correlations and Entanglement on a Spin-Based Quantum Information Processor
• Partial Transposition in a Finite-Dimensional Hilbert Space: Physical Interpretation, Measurement of Observables and Entanglement
• Nongeneric positive partial transpose states of rank five in $3\times 3$ dimensions
• Entanglement groups
• The number of product vectors and their partial conjugates in a pair of spaces
• Colliders are not Testing Locality via Bell's Inequality nor Providing an Unconditional Proof of Entanglement
• Dzyaloshinskii-Moriya interaction as an agent to free the bound entangled states
• Separability Properties for a Class of Block Matrices
• Certifying the activation of Bell nonlocality with finite data
• Global geometric difference between separable and Positive partial transpose states
• Separable State Decompositions for a Class of Mixed States
• Revealing effects of local dimension on variable-range interacting model by connecting Lieb-Robinson bounds and multipartite entanglement
• Quantum Separability Criteria Based on Symmetric Measurements
• On the separability criterion of bipartite states with certain non-Hermitian operators
• Entropic Uncertainty Principle and Information Exclusion Principle for multiple measurements in the presence of quantum memory
• Entropy Production and the Role of Correlations in Quantum Brownian Motion
• Brief Theory of Multiqubit Measurement
• Entanglement Generalization in Coupled Harmonic Oscillators
• On the temperature dependence of the interaction-induced entanglement
• Thermodynamics of bipartite entanglement
• Some aspects of the interplay between bipartite correlations and quantum channels
• Exposed faces for decomposable positive linear maps arising from completely positive maps
• Nonexistence of maximally entangled mixed states for a fixed spectrum
• Experimental verification of multi-copy activation of genuine multipartite entanglement
• Useful variants and perturbations of completely entangled subspaces and spans of unextendible product bases
• Bound entanglement in symmetric random induced states
• Maximal extension on converse monogamy of entanglement for tripartite pure states
• Spectral characterizations of entanglement witnesses
• Rank-based entanglement detection for bound entangled states
• Steady-state dynamics of quantum frequency combs in microring resonators
• Population-only decay map for n-qubit n-partite inseparability detection
• Bipartite entanglement of localized separated systems
• Entanglement - A Queer In The World Of Quantum : Some Perspectives
• Convex Hulls of Varieties and Entanglement Measures Based on the Roof Construction
• Optical Quantum Computing
• Closing loopholes of measurement-device-independent nonlinear entanglement witnesses
• Three-Party Entanglement in Tripartite Teleportation Scheme through Noisy Channels
• Scalable Ellipsoidal Classification for Bipartite Quantum States
• Entanglement distillation in terms of a conjectured matrix inequality
• Detection of $d_1\otimes d_2$ Dimensional Bipartite Entangled State: A Graph Theoretical Approach
• Noisy dynamics of Gaussian entanglement: a transient bound entangled phase before separability
• Attainable entanglement of unitary transformed thermal states in liquid-state nuclear magnetic resonance with the chemical shift