Entanglement of Formation of an Arbitrary State of Two Qubits

1997/09/13 by William K. Wootters · 8,368 citations
Computer Science · Mathematics · Physics and Astronomy · #Cluster state #Density matrix #Entanglement witness #Entropy (arrow of time) #Mathematics #Multipartite entanglement #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum entanglement #Quantum mechanics #Qubit #Squashed entanglement #State (computer science) #Statistical physics #W state #quant-ph

paper · pdf · doi:10.1103/physrevlett.80.2245

published in Physical Review Letters 80(10), 2245-2248 (American Physical Society) · 13 pages, LaTeX, no figures

arxiv created 1997/09/13 · openalex publication_date 1998/03/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

Abstract

The entanglement of a pure state of a pair of quantum systems is defined as the entropy of either member of the pair. The entanglement of formation of a mixed state \ensuremathρ is the minimum average entanglement of an ensemble of pure states that represents \ensuremathρ. An earlier paper conjectured an explicit formula for the entanglement of formation of a pair of binary quantum objects (qubits) as a function of their density matrix, and proved the formula for special states. The present paper extends the proof to arbitrary states of this system and shows how to construct entanglement-minimizing decompositions.

Citations

• Modern Quantum Mechanics
• Discussion of Probability Relations between Separated Systems
• Entanglement of a Pair of Quantum Bits
• On the Einstein Podolsky Rosen paradox
• Quantifying Entanglement

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• Macroscopic Einstein-Podolsky-Rosen pairs in superconducting circuits
• Entanglement of trapped-ion clock states
• Concurrence versus purity: Influence of local channels on Bell states of two qubits
• Groverian measure of entanglement for mixed states
• Quantum State Reconstruction of Many Body System Based on Complete Set of Quantum Correlations
• Controlling entanglement generation in external quantum fields
• Logarithmic Negativity: A Full Entanglement Monotone That is not Convex
• All (qubit) decoherences: Complete characterization and physical implementation
• Spectral conditions on the state of a composite quantum system implying its separability
• Entanglement evolution in a non-Markovian environment
• Exact entanglement cost of multiqubit bound entangled states
• Tensorial characterization and quantum estimation of weakly entangled qubits
• Resonant scattering can enhance the degree of entanglement
• Lower bounds of concurrence for tripartite quantum systems
• Parametrization of the feedback Hamiltonian realizing a pure steady state
• Modulated entanglement evolution via correlated noises
• Characterizing quantum correlations in the nonsignaling framework
• Local Conversion of Greenberger-Horne-Zeilinger States to ApproximateWStates
• Quantum-state transfer characterized by mode entanglement
• Three-qubit thermal entanglement via entanglement swapping on two-qubit HeisenbergXYchains
• Lower bounds on entanglement measures from incomplete information
• Dynamics of Quantum Entanglement in Reservoir with Memory Effects
• A Study of the Efficiency of the Class of W-States as a Quantum Channel
• Monogamy of quantum entanglement
• Entanglement of finite cyclic chains at factorizing fields
• Sudden death of entanglement and teleportation fidelity loss via the Unruh effect
• The parametric symmetry and numbers of the entangled class of 2 × M × N system
• Adaptive User Modeling in a Content-Based Music Retrieval System
• Multi-distributed entanglement in finitely correlated chains
• Entangled states of light and their robustness against photon absorption
• Control of the geometric phase and pseudospin dynamics on coupled Bose-Einstein condensates
• On-demand maximally entangled states with a parity meter and continuous feedback
• Spin decoherence from Hamiltonian dynamics in quantum dots
• Two-mode optical state truncation and generation of maximally entangled states in pumped nonlinear couplers
• Linear optical scheme to demonstrate genuine multipartite entanglement for single-particleWstates
• Optimal pumping of orbital entanglement with single-particle emitters
• The entanglement character between atoms in the non-degenerate two photons Tavis–Cummings model
• Entanglement dynamics for the double Tavis-Cummings model
• Quantum entanglement in nitrosyl iron complexes
• Limitations to sharing entanglement
• Fisher information of accelerated two-qubit system in the presence of the color and white noise channels
• A NOTE ON QUANTUM ENTANGLEMENT AND PPT
• Evolution equation for entanglement of assistance
• Classification of multiqubit mixed states: Separability and distillability properties
• Optimal simulation of a perfect entangler
• Spin-entangled two-particle dark state in quantum transport through coupled quantum dots
• Minimally entangled typical thermal state algorithms
• Symmetry in the open-system dynamics of quantum correlations
• Boundary and impurity effects on the entanglement of Heisenberg chains
• Non-Markovian effect on the quantum discord
• Entanglement measures for intermediate separability of quantum states
• Effect of spin-orbit interaction on entanglement of two-qubit HeisenbergXYZsystems in an inhomogeneous magnetic field
• Giant enhancement of quantum decoherence by frustrated environments
• Three-qubit interpretation of BPS and non-BPSSTUblack holes
• Entanglement as a signature of quantum chaos
• Entanglement and quantum phases in the anisotropic ferromagnetic Heisenberg chain in the presence of domain walls
• Dynamics of quantum correlations and linear entropy in a multi-qubit-cavity system
• Entanglement harvesting from the electromagnetic vacuum with hydrogenlike atoms
• Dynamic entanglement in oscillating molecules and potential biological implications
• Geometric measure of entanglement and applications to bipartite and multipartite quantum states
• Entanglement between two superconducting qubits via interaction with nonclassical radiation
• Information transfer through a one-atom micromaser
• Strong subadditivity inequality for quantum entropies and four-particle entanglement
• Stochastic Resonance Phenomena in Quantum Many-Body Systems
• Rank-three bipartite entangled states are distillable
• The invariant-comb approach and its relation to the balancedness of multipartite entangled states
• Invariant-based entanglement monotones as expectation values and their experimental detection
• Understanding entanglement sudden death through multipartite entanglement and quantum correlations
• Colloquium: The Einstein-Podolsky-Rosen paradox: From concepts to applications
• Quantum entanglement and quantum discord in dimers in multiple quantum NMR experiments
• Entanglement dynamics in a quantum–classical hybrid of two q-bits and one oscillator
• DYNAMICS OF QUANTUM CORRELATIONS IN TWO-QUBIT SYSTEMS WITHIN NON-MARKOVIAN ENVIRONMENTS
• Environment-induced entanglement with a single photon
• Non-Markovian entanglement dynamics between two coupled qubits in the same environment
• Local and nonlocal properties of Werner states
• Quantumness of correlations, quantumness of ensembles and quantum data hiding
• Degree of entanglement in a quantum-measurement process
• Teleportation and Dense Coding with Genuine Multipartite Entanglement
• Quantum teleportation of an arbitrary two-qubit state and its relation to multipartite entanglement
• Violation of local uncertainty relations as a signature of entanglement
• Entanglement Certification - From Theory to Experiment
• Negative entanglement measure, and what it implies
• Teleportation of qubit states through dissipative channels: Conditions for surpassing the no-cloning limit
• Evolution of a quantum spin system to its ground state: Role of entanglement and interaction symmetry
• Rashba interferometers: Spin-dependent single- and two-electron interference
• Driven-dissipative entanglement of distant giant atoms
• The γ_c-Peak: Covariant Recovery on Four Organic Qubit Platforms
• Wave--particle transition and quantum Zeno effect in which-way experiments with a superconducting quantum processor
• Local qubit invariants on quantum computer
• Quantum adaptation of noisy channels
• Long-range quantum entanglement in dielectric mu-near-zero metamaterials
• Entanglement transfer via XXZ Heisenberg chain with DM interaction
• Reexamination of determinant-based separability test for two qubits
• Entanglement in a Valence-Bond Solid State
• Entanglement Probe of Two-Impurity Kondo Physics in a Spin Chain
• Effects of reservoir squeezing on quantum systems and work extraction
• Dual quantum-correlation paradigms exhibit opposite statistical-mechanical properties
• Quantum entanglement and order parameter in a paired finite Fermi system
• Two atoms in dissipative cavities in dispersive limit: entanglement sudden death and long-lived entanglement
• Optimal entanglement generation in cavity QED with dissipation
• Strings, black holes, and quantum information
• Complex dynamics of photon entanglement in the two-mode Jaynes–Cummings model
• Quantum modeling of ultrafast photoinduced charge separation
• Efficient numerical method to calculate the three-tangle of mixed states
• Entanglement-distribution maximization over one-sided Gaussian noisy channels
• Informational Mpemba Effect for Fast State Purification in Non-Hermitian System
• Dynamics of entanglement in the transverse Ising model
• Fading entanglement near an equilibrium state
• Efficient quantum filtering for quantum feedback control
• Two-spin entanglement distribution near factorized states
• Useful entanglement from the Pauli principle
• Proposed method for direct measurement of the non-Markovian character of the qubits coupled to bosonic reservoirs
• Evolution of pairwise entanglement in a coupledn-body system
• Tripartite entanglement dynamics in a system of strongly driven qubits
• Entanglement Scaling in the One-Dimensional Hubbard Model at Criticality
• Two interacting atoms in a cavity: exact solutions, entanglement and decoherence
• The Entanglement of theXYSpin Chain in a Random Magnetic Field
• Loss tolerant device-independent quantum key distribution: a proof of principle
• Probing the structure of entanglement with entanglement moments
• Genuine-multipartite-entanglement trends in gapless-to-gapped transitions of quantum spin systems
• Quantum entanglement distribution using a magnetic field sensor
• Quantum entanglement and quantum phase transition in theXYmodel with staggered Dzyaloshinskii-Moriya interaction
• Entangled network and quantum communication
• Experimental Entanglement Redistribution under Decoherence Channels
• Dynamics of entanglement of two electron spins interacting with nuclear spin baths in quantum dots
• Monogamy and entanglement in tripartite quantum states
• Quantum transitions and quantum entanglement from Dirac-like dynamics simulated by trapped ions
• Experimental entanglement quantification and verification via uncertainty relations
• Enhancement of nearest-neighbor entanglement in one-dimensional disordered systems
• Multipartite entangled states in particle mixing
• Optimization approach to entanglement distillation
• Evaluating Convex Roof Entanglement Measures
• Nonequilibrium dissipation-driven steady many-body entanglement
• Constrained bounds on measures of entanglement
• Enhancement of entanglement transfer in a spin chain by phase-shift control
• Decoherence of geometric phase gates
• Underlining some limitations of the statistical formalism in quantum mechanics
• Two-mode excited entangled coherent states and their entanglement properties
• Monogamy equality in 2⊗2⊗d quantum systems
• Evolution of spin entanglement and an entanglement witness in multiple-quantum NMR experiments
• Tuning quantum tunneling and quantum information properties among the trion states in coupled quantum dots
• Mixed-state entanglement and quantum teleportation through noisy channels
• Thermal quantum and classical correlations in a two-qubit XX model in a nonuniform external magnetic field
• Spin squeezing, negative correlations, and concurrence in the quantum kicked top model
• Entanglement redistribution in the Schwarzschild spacetime
• Decoherence-free subspace and disentanglement dynamics for two qubits in a common non-Markovian squeezed reservoir
• Sudden Death, Birth and Stable Entanglement in a Two-Qubit Heisenberg XY Spin Chain
• Two-qubit separabilities as piecewise continuous functions of maximal concurrence
• Decoherence of two qubits in non-Markovian reservoirs without the rotating-wave approximation
• Local entanglement and quantum phase transition in spin models
• Entanglement dynamics and decoherence of an atom coupled to a dissipative cavity field
• Decoherence effect on quantum correlation and entanglement in a\n two-qubit spin chain
• Mixtures of maximally entangled pure states
• Spin correlation of hyperon-antihyperon systems in e⁺e^- annihilation
• Nonequilibrium dynamics of polariton entanglement in a cluster of coupled traps
• Generalized entropic measures of quantum correlations
• Quantum discord in finiteXYchains
• Thermal entanglement in fully connected spin systems and its random-phase-approximation description
• Entanglement versus quantum discord in two coupled double quantum dots
• QUBIT4MATLAB V3.0: A program package for quantum information science and quantum optics for MATLAB
• A decomposition of separable Werner states
• Berry phase and quantum criticality in Yang–Baxter systems
• Interplay between teleportation fidelity and basis-independent coherence in maximally sliced states under decoherence
• Three qubits in a symmetric environment: Dissipatively generated asymptotic entanglement
• Conical Designs and Categorical Jordan Algebraic Post-Quantum Theories
• Entanglement of collaboration
• Concurrence of superpositions
• Generation of maximally entangled mixed states of two atoms via on-resonance asymmetric atom-cavity couplings
• Single observable concurrence measurement without simultaneous copies
• Delocalized Entanglement of Atoms in Optical Lattices
• Coherent control in a decoherence-free subspace of a collective multilevel system
• Lower bounds on concurrence and separability conditions
• Entanglement, avoided crossings, and quantum chaos in an Ising model with a tilted magnetic field
• Experimental procedures for entanglement verification
• Entanglement generation and protection by detuning modulation
• Suppression of decoherence by bath ordering
• Full separability criterion for tripartite quantum systems
• Deterministic entanglement of assistance and monogamy constraints
• Entanglement between static and flying qubits in quantum wires
• A contour for the entanglement negativity of bosonic Gaussian states
• Spin frustration of a spin-1/2 Ising–Heisenberg three-leg tube as an indispensable ground for thermal entanglement
• Typical entanglement of stabilizer states
• Maximally genuine multipartite entangled mixed X-states ofN-qubits
• Heuristic for estimation of multiqubit genuine multipartite entanglement
• Concurrence vectors in arbitrary multipartite quantum systems
• Distinguishing the elements of a full product basis set needs only projective measurements and classical communication
• Scheme for on-resonance generation of entanglement in time-dependent asymmetric two-qubit-cavity systems
• Entanglement generated between a single atom and a laser pulse
• Quasiparticle engineering and entanglement propagation in a quantum many-body system
• Time evolution of an entangled initial state in coupled quantum dots with Coulomb correlations
• Entangling polaritons via dynamical Casimir effect in circuit quantum electrodynamics
• Entanglement of flux qubits through a joint detection of photons
• Maximal entanglement versus entropy for mixed quantum states
• Entanglement swapping with quantum-memory-compatible photons
• Quantum relative positioning in Hilbert space
• Multipartite entanglement and quantum state exchange
• Experimental detection of steerability in Bell local states with two measurement settings
• Local description of quantum inseparability
• Entanglement evolution of a spin-chain bath coupled to a quantum spin
• Monogamy Equalities for Qubit Entanglement from Lorentz Invariance
• Observer-dependent entanglement
• Emergent radiation in an atom–field system at twice resonance
• Characterization of pure quantum states of multiple qubits using the Groverian entanglement measure
• Unveiling the internal entanglement structure of the Kondo singlet
• Coherence number as a discrete quantum resource
• Berry phase induced entanglement of hole-spin qubits in a microwave cavity
• Entanglement in the one-dimensional Kondo necklace model
• Quantum correlations in neutrino oscillation: Coherence and entanglement
• Entanglement of electron pairs extracted from a many-body system
• Projecting onto any two-photon polarization state using linear optics
• Photonic Heat Rectification in a System of Coupled Qubits
• On orthogonal bases in the Hilbert-Schmidt space of matrices
• Polygamy of entanglement in multipartite quantum systems
• Dynamics of entanglement and ‘attractor’ states in the Tavis–Cummings model
• Increase of entanglement by localPT-symmetric operations
• A Tunable Coupler with ScS Quantum Point Contact to Mediate Strong Interaction Between Flux Qubits
• Distilling one, two and entangled pairs of photons from a quantum dot with cavity QED effects and spectral filtering
• Characterizing qubit channels in the context of quantum teleportation
• Coupling nanocrystals to a high-Qsilica microsphere: Entanglement in quantum dots via photon exchange
• Remote Entanglement via Adiabatic Passage Using a Tunably Dissipative Quantum Communication System
• Study on Entanglement and its Utility in Information Processing
• Entropic and information inequality for nonlinearly transformed two-qubit X-states
• Concurrence of Mixed Multipartite Quantum States
• Universality in the Entanglement Structure of Ferromagnets
• Concurrence of quasipure quantum states
• Optimal copying of entangled two-qubit states
• Quantum-memory-assisted entropic uncertainty relation under noise
• 1D frustrated ferromagnetic model with added Dzyaloshinskii-Moriya interaction
• Constructive interference between disordered couplings enhances multiparty entanglement in quantum Heisenberg spin glass models
• Quantum steering ellipsoids, extremal physical states and monogamy
• Entanglement at the boundary of spin chains near a quantum critical point and in systems with boundary critical points
• Dynamics of entropic measurement-induced nonlocality in structured reservoirs
• Correlations and Werner states in finite spin linear arrays
• Quantum dynamics of two quantum dots coupled through localized plasmons: An intuitive and accurate quantum optics approach using quasinormal modes
• Relative entropy of entanglement of rotationally invariant states
• Entangled random pure states with orthogonal symmetry: exact results
• Decoherence control: Universal protection of two-qubit states and two-qubit gates using continuous driving fields
• Entanglement amplification via local weak measurements
• Entanglement dynamics for uniformly accelerated two-level atoms
• Quantum metrology and estimation of Unruh effect
• Entanglement between distant qubits in cyclicXXchains
• Entanglement, Bell Inequalities and Decoherence in Particle Physics
• Entanglement and tensor product decomposition for two fermions
• RELATIVISTIC, CAUSAL DESCRIPTION OF QUANTUM ENTANGLEMENT AND GRAVITY
• Triangle inequalities in coherence measures and entanglement concurrence
• Entanglement dynamics for two spins in an optical cavity – field interaction induced decoherence and coherence revival
• Detection and typicality of bound entangled states
• Generalized quantum telecloning
• Majorana Constellations: A Geometric Lens on Multipartite Entanglement and Geometric Phases
• Non-Markovian dynamics of quantum discord
• Bound of entanglement of assistance and monogamy constraints
• Interplay between entanglement and entropy in two-qubit systems
• Entanglement measure using Wigner function: Case of generalized vortex state formed by multiphoton subtraction
• On the `fake' inferred entanglement associated with the maximum entropy inference of quantum states
• Physically realizable entanglement by local continuous measurements
• Infinitesimal-propagation equation for decoherence of an orbital-angular-momentum-entangled biphoton state in atmospheric turbulence
• Posner qubits: spin dynamics of entangled Ca₉(PO₄)₆ molecules and their role in neural processing
• Effect of the dipole-dipole interaction for two atoms with different couplings in a non-Markovian environment
• Three-tangle for rank-three mixed states: Mixture of Greenberger-Horne-Zeilinger,W, and flipped-Wstates
• Optimal Entanglement Enhancement for Mixed States
• Entanglement splitting of pure bipartite quantum states
• Optimal local preparation of an arbitrary mixed state of two qubits: Closed expression for the single-copy case
• Hidden entanglement, system-environment information flow and non-Markovianity
• Maximally discordant mixed states of two qubits
• Entanglement modes and topological phase transitions in superconductors
• Fluctuations of quantum entanglement
• Decoherence of entangled kaons and its connection to entanglement measures
• Distribution ofGconcurrence of random pure states
• Quantum channels in random spin chains
• Entanglement, coherence, and charging process of quantum batteries
• Measurement-induced long-distance entanglement of superconducting qubits using optomechanical transducers
• Amplitude tuning of steady-state entanglement in strongly driven coupled qubits
• Non-Hermitian Hamiltonians and no-go theorems in quantum information
• Enhancement of spontaneous entanglement generation via coherent quantum feedback
• Manipulation of multipartite entanglement in an array of quantum dots
• Spin correlation tensor for measurement of quantum entanglement in electron–electron scattering
• Geometric quantification of multiparty entanglement through orthogonality of vectors
• Quantum router based on ac control of qubit chains
• Characteristics and benchmarks of entanglement of mixed states: The two-qubit case
• Measurable concurrence of mixed states
• Anti- (conjugate) linearity
• Dissipative dynamics of quantum correlations in the strong-coupling regime
• Quantum entanglement of space domains occupied by interacting electrons
• Stable and metastable freezing of classical correlations in qutrits
• Sensitivity of entanglement decay of quantum-dot spin qubits to the external magnetic field
• Multipartite quantum correlation and entanglement in four-qubit pure states
• Sudden death and long-lived entanglement of two trapped ions
• Single-atom entropy squeezing for two two-level atoms interacting with a single-mode radiation field
• Bell-state diagonal entanglement witnesses for relativistic and nonrelativistic multispinor systems in arbitrary dimensions
• State determination for composite systems of two spatial qubits
• Natural Thermal and Magnetic Entanglement in the 1D Heisenberg Model
• Variational characterizations of separability and entanglement of formation
• Entanglement and collective flavor oscillations in a dense neutrino gas
• Quantum Open System Theory: Bipartite Aspects
• Decoherence effects on the quantum spin channels
• Local Unitary Invariants for Multipartite Quantum Systems
• Entangling two atoms via spontaneous emission
• Spin entanglement via scanning tunneling microscope current
• The optimal approximation of qubit states with limited quantum states
• Parity Deformed Jaynes-Cummings Model: “Robust Maximally Entangled States”
• Efficient Bipartite Entanglement Detection Scheme with a Quantum Adversarial Solver
• Finite-size scaling exponents in the Dicke model
• Quantum battery based on quantum discord at room temperature
• Quantum transport and spin dynamics on shearless tori
• Spin–orbit coupling in the presence of strong atomic correlations
• Purity as a witness for initial system-environment correlations in open-system dynamics
• Uniform cross-phase modulation for nonclassical radiation pulses
• Geometry in the Entanglement Dynamics of the Double Jaynes–Cummings Model
• Robust entanglement in antiferromagnetic Heisenberg chains by single-spin optimal control
• Quantum process estimation via generic two-body correlations
• Remarks on the Equivalence of Full Additivity and Monotonicity for the Entanglement Cost
• Remote control of quantum correlations in a two-qubit receiver by a three-qubit sender
• Quantum coherence, quantum Fisher information and teleportation in the Ising-Heisenberg spin chain model of a heterotrimetallic Fe − Mn − Cu coordination polymer with magnetic impurity
• Coherent and collective quantum optical effects in mesoscopic systems
• Quantum information and relativity theory
• Cayley's First Hyperdeterminant is an Entanglement Measure
• General pure multipartite entangled states and the Segre variety
• Simulating Zeno physics by a quantum quench with superconducting circuits
• Quantum Entanglement Autodistillation in Baryon Pair Decays
• Quantum correlations and entanglement in far-from-equilibrium spin systems
• METHOD OF CONSTRUCTING BRAID GROUP REPRESENTATION AND ENTANGLEMENT IN A 9 × 9 YANG–BAXTER SYSTEM
• Entanglement sudden birth of two trapped ions interacting with a time-dependent laser field
• Anisotropic Invariance and the Distribution of Quantum Correlations
• Symmetry resolved entanglement: exact results in 1D and beyond
• All-optical non-Markovian stroboscopic quantum simulator
• Universal entanglement decay of photonic-orbital-angular-momentum qubit states in atmospheric turbulence
• Symmetry-protected topological entanglement
• Genuine multipartite entanglement in the cluster-Ising model
• Assisted optimal state discrimination without entanglement
• Entanglement in a second-order quantum phase transition
• Finite-Size Scaling Exponents of the Lipkin-Meshkov-Glick Model
• Entanglement in a first-order quantum phase transition
• Sudden death and sudden birth of entanglement in common structured reservoirs
• Requirement of Dissonance in Assisted Optimal State Discrimination
• Simulation of collective neutrino oscillations on a quantum computer
• Entanglement, Quantum Phase Transitions, and Density Matrix Renormalization
• Communications: Entanglement switch for dipole arrays
• Magnetic entanglement in spin-1/2 XY chains
• THERMAL DISCORD AND NEGATIVITY IN A TWO-SPIN-QUTRIT SYSTEM UNDER DIFFERENT MAGNETIC FIELDS
• Comparative study of quantum discord and geometric discord for generic bipartite states
• Entanglement versus Gaussian quantum discord in a double-cavity opto-mechanical system
• Demonstration of Einstein–Podolsky–Rosen steering with enhanced subchannel discrimination
• Speed of disentanglement in multiqubit systems under a depolarizing channel
• Gaussian intrinsic entanglement for states with partial minimum uncertainty
• Quantum correlations and entanglement in a Kitaev-type spin chain
• The Lindblad equation for the decay of entanglement due to atmospheric scintillation
• Additivity of entanglement of formation via an entanglement-breaking space
• Quantum imaging as an ancilla-assisted process tomography
• The bell inequality: A measure of entanglementa?
• Entanglement dynamics in random media
• Local uncertainty relations serving as measures of entanglement in a bipartite two-level system
• Exact one- and two-site reduced dynamics in a finite-size quantum Ising ring after a quench: A semianalytical approach
• Quantum Fisher Information and the Curvature of Entanglement
• More nonlocality with less entanglement in Clauser-Horne-Shimony-Holt experiments using inefficient detectors
• Perturbative expansion of entanglement negativity using patterned matrix calculus
• Dark periods and revivals of entanglement in a two-qubit system
• Entanglement dynamics of qubits in a common environment
• Quantifying entanglement in two-mode Gaussian states
• Thermal entanglement of spins in mean-field clusters
• Relation between two measures of entanglement in spin-1∕2and spinless fermion quantum chain systems
• A simple spectral condition implying separability for states of bipartite quantum systems
• Relative information encoded in the degree of entanglement to discriminate bipartite states
• Disentangling theorem and monogamy for entanglement negativity
• Separability and Entanglement of a Spin-1 Particle
• Measuring two-photon orbital angular momentum entanglement
• System-time entanglement in a discrete-time model
• Stabilizing coherence with nested environments: a numerical study using kicked Ising models
• Entanglement dynamics of two-bipartite system under the influence of dissipative environments
• Efficient superdense coding in the presence of non-Markovian noise
• Localization properties of the disordered XY spin chain
• Quantum state transfer in aXXchain with impurities
• Coupling-assisted Landau-Majorana-Stückelberg-Zener transition in a system of two interacting spin qubits
• Entanglement of Formation for an Arbitrary Two-Mode Gaussian State
• Numerical hardware-efficient variational quantum simulation of a soliton solution
• Entanglement properties of topological color codes
• ENTROPY OPERATOR AND ASSOCIATED WIGNER FUNCTION
• Nonlocal magnon entanglement generation in coupled hybrid cavity systems
• Polygamy of distributed entanglement
• Separability conditions and limit temperatures for entanglement detection in two-qubit HeisenbergXYZmodels
• The role of quantum coherence in dimer and trimer excitation energy transfer
• Bipartite quantum channels using multipartite cluster-type entangled coherent states
• Carboxylate-based molecular magnet: One path toward achieving stable quantum correlations at room temperature
• Singularity in entanglement negativity across finite-temperature phase transitions
• Universal feedback control of two-qubit entanglement
• Quantum entanglement in the two-impurity Kondo model
• Entanglement dynamics modified by an effective atomic environment
• Dissipative entanglement swapping in the presence of detuning and Kerr medium: Bell state measurement method
• A scheme for direct detection of qubit–environment entanglement generated during qubit pure dephasing
• Generalized Kraus Operators for the One-Qubit Depolarizing Quantum Channel
• Maximization of thermal entanglement of arbitrarily interacting two qubits
• Entanglement dynamics of the ultrastrong-coupling three-qubit Dicke model
• Open quantum system description of singlet-triplet qubits in quantum dots
• Optimal manipulations with qubits: Universal quantum entanglers
• Experimental demonstration of robust entanglement distribution over reciprocal noisy channels assisted by a counter-propagating classical reference light
• Quantum correlations and distinguishability of quantum states
• An uncertainty view on complementarity and a complementarity view on uncertainty
• Entanglement witnesses: construction, analysis and classification
• Correlation-induced non-Abelian quantum holonomies
• Controllable generation of mixed two-photon states
• Hidden entanglement in the presence of random telegraph dephasing noise
• Entanglement in a molecular three-qubit system
• Improving autonomous thermal entanglement generation using a common reservoir
• Switching Exciton Pulses Through Conical Intersections
• Tunable quantum entanglement of three qubits in a nonstationary cavity
• A composite parameterization of unitary groups, density matrices and subspaces
• Effects of partial measurements on quantum resources and quantum Fisher information of a teleported state in a relativistic scenario
• Tripartite thermal correlations in an inhomogeneous spin–star system
• Experimental control of the transition from Markovian to non-Markovian dynamics of open quantum systems
• Measuring polynomial invariants of multiparty quantum states
• Self-calibrating quantum state tomography
• Quantum decoherence in noninertial frames
• Measurements in two bases are sufficient for certifying high-dimensional entanglement
• Unified theory of consequences of spontaneous emission in aΛsystem
• Quantum energy teleportation across a three-spin Ising chain in a Gibbs state
• Concurrence of assistance and Mermin inequality on three-qubit pure states
• Observation of Strong and Weak Thermalization in a Superconducting Quantum Processor
• Correlations in the Grover search
• Geometry of quantum state space and entanglement
• Entanglement percolation in quantum networks
• Mapping photonic entanglement into and out of a quantum memory
• Analytical solution and entanglement swapping of a double Jaynes–Cummings model in non-Markovian environments
• Recovering the lost steerability of quantum states within non-Markovian environments by utilizing quantum partially collapsing measurements
• Adiabatic approximation for three qubits ultrastrongly coupled to a harmonic oscillator
• Noise-assisted preparation of entangled atoms
• Thermal geometric discords in a two-qutrit system
• Quantum discord in spin-1/2 Heisenberg chains with Dzyaloshinkii–Moriya interaction
• Absolutely covert quantum communication
• Current and entanglement in a three-site Bose-Hubbard ring
• Entanglement preparation using symmetric multiports
• Long-lived spin entanglement induced by a spatially correlated thermal bath
• Quantum coherence and uncertainty in the anisotropic XY chain
• Geometry of a two-qubit state and intertwining quaternionic conformal mapping under local unitary transformations
• Dynamics of entanglement in a two-dimensional spin system
• Numerical study of two-body correlation in a 1D lattice with perfect blockade
• Dicke model and environment-induced entanglement in ion-cavity QED
• Dynamics of non-classically-reproducible entanglement
• Stimulated emission tomography for entangled photon pairs with different detection spectral ranges
• Statistical mixtures of states can be more quantum than their superpositions: Comparison of nonclassicality measures for single-qubit states
• The quantum entropic uncertainty relation and entanglement witness in the two-atom system coupling with the non-Markovian environments
• Factorization and entanglement in generalXYZspin arrays in nonuniform transverse fields
• Quantum dynamics as a physical resource
• The generalized partial transposition criterion for separability of multipartite quantum states
• Stereographic geometry of coherence and which-path information
• Conditions for a Class of Entanglement Transformations
• Creating nuclear spin entanglement using an optical degree of freedom
• Partial transposition as a direct link between concurrence and negativity
• Probabilistic Teleportation of a Single Qubit: Unearthing New W-Class of States
• Problem of quantifying quantum correlations with non-commutative discord
• DYNAMICS OF ENTANGLEMENT FOR ONE-DIMENSIONAL SPIN SYSTEMS IN AN EXTERNAL TIME-DEPENDENT MAGNETIC FIELD
• Asymptotic Entanglement Sudden Death in Two Atoms with Dipole–Dipole and Ising Interactions Coupled to a Radiation Field at Non-Zero Detuning
• Origins and optimization of entanglement in plasmonically coupled quantum dots
• Dynamics of global entanglement under decoherence
• Entangled photon pairs from a quantum-dot cascade decay: The effect of time reordering
• Observable estimation of entanglement for arbitrary finite-dimensional mixed states
• Experimental Verification of Entanglement Generated in a Plasmonic System
• Two-channel spin-chain communication line and simple quantum gates
• Tests of quantum contextuality in particle physics
• Quantum spin squeezing
• Entanglement of Formation for Isotropic States
• Teleportation using coupled oscillator states
• Exponential Speedup of Entanglement Generation by Quantum Mpemba Effects
• Majorana representation of symmetric multiqubit states
• Quantum deficits and correlations of two superconducting charge qubits
• Dressed-state master equation for two strongly coupled two-level atoms with long-lived entanglement
• Relative quantum coherence, incompatibility, and quantum correlations of states
• Many-Body Topological Invariants for Fermionic Symmetry-Protected Topological Phases
• Teleportation of a qubit using entangled non-orthogonal states: a comparative study
• Upper bound and shareability of quantum discord based on entropic uncertainty relations
• The quantum Rabi model for two qubits
• Entanglement dynamic of arbitrary number qubit in the open quantum systems
• Computable entanglement conversion witness that is better than the negativity
• Entanglement of systems of dipolar coupled nuclear spins at the adiabatic demagnetization
• Entanglement Evolution of a Two-Qubit System beyond Rotating-Wave Approximation
• CDJ-Pontryagin Optimal Control for General Continuously Monitored Quantum Systems
• Estimating the best separable approximation of non-pure spin-squeezed states
• MEASUREMENT-INDUCED NONLOCALITY OVER TWO-SIDED PROJECTIVE MEASUREMENTS
• Ratios of maximal concurrence-parameterized separability functions, and generalized Peres–Horodecki conditions
• Exact quantification of bipartite entanglement in unresolvable spin ensembles
• Polarization insensitive frequency conversion for an atom-photon entanglement distribution via a telecom network
• Hiding and masking quantum information in complex and real quantum mechanics
• Equivalence of qubit-environment entanglement and discord generation via pure dephasing interactions and the resulting consequences
• Quantum proportional-integral (PI) control
• Voltage probe model of spin decay in a chaotic quantum dot with applications to spin-flip noise and entanglement production
• Controlled secret sharing protocol using a quantum cloning circuit
• Entanglement switching via the Kondo effect in triple quantum dots
• Experimental demonstration of quantum correlations over more than 10 km
• Concurrence (quantum computing) [wikipedia]
• Strong coupling among semiconductor quantum dots induced by a metal nanoparticle. [europepmc]
• Quantum coherence and correlations in quantum system. [europepmc]
• Using non-Markovian measures to evaluate quantum master equations for photosynthesis. [europepmc]
• Orbital angular momentum of photons and the entanglement of Laguerre-Gaussian modes. [europepmc]
• Generation of photonic entanglement in green fluorescent proteins. [europepmc]
• Quantum Correlations and Coherence of Polar Symmetric Top Molecules in Pendular States. [europepmc]
• High-fidelity entanglement swapping and generation of three-qubit GHZ state using asynchronous telecom photon pair sources. [europepmc]
• A CNOT gate between multiphoton qubits encoded in two cavities. [europepmc]
• Polarization insensitive frequency conversion for an atom-photon entanglement distribution via a telecom network. [europepmc]
• Entanglement in a 20-Qubit Superconducting Quantum Computer. [europepmc]
• Non-locality Correlation in Two Driven Qubits Inside an Open Coherent Cavity: Trace Norm Distance and Maximum Bell Function. [europepmc]
• Quantum process capability. [europepmc]
• Quantum Correlation Dynamics in Controlled Two-Coupled-Qubit Systems. [europepmc]
• Mutual Information and Quantum Discord in Quantum State Discrimination with a Fixed Rate of Inconclusive Outcomes. [europepmc]
• Probing resonating valence bond states in artificial quantum magnets. [europepmc]
• Quantum semantics of text perception. [europepmc]
• Entanglement Robustness via Spatial Deformation of Identical Particle Wave Functions. [europepmc]
• Experimental classical entanglement in a 16 acoustic qubit-analogue. [europepmc]
• Almost complete solution for the NP-hard separability problem of Bell diagonal qutrits. [europepmc]
• Magnetic field effects in biology from the perspective of the radical pair mechanism. [europepmc]
• Programmable frequency-bin quantum states in a nano-engineered silicon device. [europepmc]
• Loophole-free Bell inequality violation with superconducting circuits. [europepmc]
• Quantum simulation of Hawking radiation and curved spacetime with a superconducting on-chip black hole. [europepmc]
• Spatially correlated classical and quantum noise in driven qubits. [europepmc]
• A tunable transition metal dichalcogenide entangled photon-pair source. [europepmc]

Related

• Entanglement of a Pair of Quantum Bits
• Entanglement of formation from optimal decomposition
• Entanglement of Formation of an Arbitrary State of Two Rebits
• An efficient numerical method for calculating the entanglement of formation of arbitrary mixed quantum states of any dimension
• A necessary and sufficient condition for optimal decompositions