On the volume of the set of mixed entangled states

Abstract

A natural measure in the space of density matrices describing N-dimensional quantum systems is proposed. We study the probability P that a quantum state chosen randomly with respect to the natural measure is not entangled (is separable). We find analytical lower and upper bounds for this quantity. Numerical calculations give P = 0.632 for N=4 and P=0.384 for N=6, and indicate that P decreases exponentially with N. Analysis of a conditional measure of separability under the condition of fixed purity shows a clear dualism between purity and separability: entanglement is typical for pure states, while separability is connected with quantum mixtures. In particular, states of sufficiently low purity are necessarily separable.

10 pages in LaTex - RevTex + 4 figures in eps. submitted to Phys. Rev. A

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• Quantum Information Processing in Disordered and Complex Quantum Systems
• Anomalies of weight-based coherence measure and mixed maximally coherent states
• Unitary Invariants and Classification of Four-Qubit States via Negativity Fonts
• Finite-level systems, Hermitian operators, isometries, and a novel parameterization of Stiefel and Grassmann manifolds
• Residual effect on the robustness of multiqubit entanglement
• Convex politopes and quantum separability
• Entanglement Classification via Witness Operators generated by Support Vector Machine
• Subnormalized states and trace-nonincreasing maps
• Strengthened Bell Inequalities for Entanglement Verification
• Quantum noise and mixedness of a pumped dissipative non-linear oscillator
• Entanglement catalysis for quantum states and noisy channels
• Geometry of quantum state space and quantum correlations
• A simple model for a minimal environment: the two-atom Tavis-Cummings model revisited
• Bound entangled states with extremal properties
• Speed of disentanglement in multi-qubit systems under depolarizing channel
• Entanglement Echoes in Quantum Computation
• Measurement-based Multipartite Entanglement Inflation
• Single-experiment-detectable multipartite entanglement witness for ensemble quantum computing
• Kerr nonlinearity hinders symmetry-breaking states of coupled quantum oscillators
• Extended Studies of Separability Functions and Probabilities and the Relevance of Dyson Indices
• Quantum Throughput: Quantifying quantum communication with homodyne measurements
• Preserving quantum correlations and coherence with non-Markovianity
• Novae: An Important Source of Lithium in the Galaxy
• Relative volume of separable bipartite states
• Classical correlation and quantum entanglement in the mixed-spin Ising-XY model with Dzyaloshinskii-Moriya interaction
• A Proposal for Quantum Fisher Information Optimization and its Relation with Entanglement Measures
• Entanglement resource theory of quantum channel
• Holographic Entanglement negativity in flat space generalized minimal massive gravity
• Generation of field mediated three qubit entangled state shared by Alice and Bob
• Quantum metrology of rotations with mixed spin states
• Measurement of entropy and quantum coherence properties of two type-I entangled photonic qubits
• Rényi formulation of entanglement criteria for continuous variables
• Entanglement and spectra in topological many-body localized phases
• Fortran code for generating random probability vectors, unitaries, and quantum states
• Uncertainty Relation for Mutual Information
• Realization of the tradeoff between internal and external entanglement
• Inclusion relations among separability criteria
• Correlation constraints and the Bloch geometry of two qubits
• Absolute separability witnesses for symmetric multiqubit states
• Generalized Two-Qubit Whole and Half Hilbert-Schmidt Separability Probabilities
• Certifying nonlocality from separable marginals
• Numerical Computations of Separability Probabilities
• Entanglement dynamics for two-level quantum systems coupled with massive scalar fields
• Cycle Index Polynomials and Generalized Quantum Separability Tests
• Entangled states in the role of witnesses
• Bell-CHSH Violation Under Global Unitary Operations: Necessary and Sufficient conditions
• The hierarchies of "witnesses" and the properties and characterization of entangled states as super entanglement witnesses
• Absolute fully entangled fraction from spectrum
• Complementarity and Entanglement in Quantum Information Theory
• Entanglement and coherence in a spin-s XXZ system under non-uniform fields
• Some measures for fermionic entanglement in the cosmological de Sitter spacetime
• Entanglement properties and ground-state statistics of free bosons
• Entanglement in bipartite quantum systems: Euclidean volume ratios and detectability by Bell inequalities
• Mixed state information theoretic measures in boosted black brane
• Negativity vs. Purity and Entropy in Witnessing Entanglement
• Monogamy of Logarithmic Negativity and Logarithmic Convex-Roof Extended Negativity
• Scale Invariant Entanglement Negativity at the Many-Body Localization Transition
• Measuring out quasi-local integrals of motion from entanglement
• Two-qubit mixed states and teleportation fidelity: Purity, concurrence, and beyond
• Perturbative expansion of entanglement negativity using patterned matrix calculus
• The Volume of Two-Qubit States by Information Geometry
• Probing Quantum Telecloning on Superconducting Quantum Processors
• Emergence of entanglement with temperature and time in factorization-surface states
• Steady-state entanglement enhanced by a dissipative ancilla
• Entanglement Negativity and Replica Symmetry Breaking in General Holographic States
• Thresholds for reduction-related entanglement criteria in quantum information theory
• Maximizing genuine multipartite entanglement of N mixed qubits
• Method for measuring the entanglement of formation for arbitrary-dimensional pure states
• Enhancement of nonclassical properties of two qubits via deformed operators
• Unbalanced gain and loss in a quantum photonic system
• Partial K-way Negativities of Pure Four qubit Entangled States
• Extracting an arbitrary relative phase from a multiqubit two-component entangled state
• Spectral Conditions on the State of a Composite Quantum System Implying its Separability
• On the comparison of volumes of quantum states
• On the Correlations Between Quantum Entanglement and q-Information Measures
• Schmidt numbers of low rank bipartite mixed states
• Entanglement enhancement and postselection for two atoms interacting with thermal light
• An Explicit Computation of the Bures Metric Over the Space of $N$-Dimensional Density Matrices
• Bures Geometry of the Three-Level Quantum Systems. I
• Upper Bound on the region of Separable States near the Maximally Mixed State
• Maximum entanglement of mixed symmetric states under unitary transformations
• Hierarchy of correlation quantifiers comparable to negativity
• Convex set of quantum states with positive partial transpose analysed by hit and run algorithm
• Entanglement distribution and quantum discord
• Noisy induced entanglement transition in one-dimensional random quantum circuits
• Quantitative characterization of several entanglement detection criteria
• Activation of Nonmonogamous Multipartite Quantum States
• The effect of channel decoherence on entangled coherent states: A theoretical analysis
• Maximally-Disordered Distillable Quantum States
• Bures and Hilbert-Schmidt 2 x 2 Determinantal Moments
• Formulas for Rational-Valued Separability Probabilities of Random Induced Generalized Two-Qubit States
• Interplay between nonclassicality and $\mathcal{P}\mathcal{T}$ symmetry in an effective two level system with open system effects
• Local Cloning of Entangled Qubits
• Separability Probability Formulas and Their Proofs for Generalized Two-Qubit X-Matrices Endowed with Hilbert-Schmidt and Induced Measures
• Generalizations of Quantum Discord
• Incompatibility probability of random quantum measurements
• The Essentially Entangled Component of Multipartite Mixed Quantum States, its Properties and an Efficient Algorithm for its Extraction
• Disappearance of entanglement: a topological point of view
• Negativity Fonts, multiqubit invariants and Four qubit Maximally Entangled States
• Evolution of two-mode quantum states under a dissipative environment: which quantum resource survives better, squeezing or entanglement?
• Computable entanglement conversion witness that is better than the negativity
• Magnetic Field Effect on Dynamics of Entanglement for Time-dependent Harmonic Oscillator
• Generating pseudo-random discrete probability distributions
• Distinguishing Phases via Non-Markovian Dynamics of Entanglement in Topological Quantum Codes under Parallel Magnetic Field
• Criteria for reliable entanglement quantification with finite data
• The Transfer of Entanglement Negativity at the Onset of Interactions
• Optimal quantum speed for mixed states
• Role of interference and entanglement in quantum neural processing
• Instantaneous phase synchronization of two decoupled quantum limit-cycle oscillators induced by conditional photon detection
• QSlack: A slack-variable approach for variational quantum semi-definite programming
• Experimental relative entanglement potentials of single-photon states
• Kenfack Zyczkowski indicator of nonclassicality for two non-equivalent representations of Wigner function of qutrit
• Lower bounds on concurrence and negativity from a trace inequality
• Entanglement robustness in trace decreasing quantum dynamics caused by depolarization and polarization dependent losses
• Entanglement Distribution and Entangling Power of Quantum Gates
• A bipartite separable ball and its applications
• Entanglement and teleportation via chaotic system
• Controlling gain with loss: Bounds on localizable entanglement in multi-qubit systems
• Nearly Markovian maps and entanglement-based bound on corresponding non-Markovianity
• Simple permutation-based measure of quantum correlations and maximally-3-tangled states
• Numerical and Exact Analyses of Bures and Hilbert-Schmidt Separability and PPT-Probabilities
• Long-lived entanglement with Pulsed-driven initially entangled qubit pair
• Ratios of maximal concurrence-parameterized separability functions, and generalized Peres-Horodecki conditions
• Bipartite Bound Entanglement
• Upper bounds for relative entropy of entanglement based on active learning
• Invariance of Bipartite Separability and PPT-Probabilities over Casimir Invariants of Reduced States
• Sufficient criteria for absolute separability in arbitrary dimensions via linear map inverses
• Degree of separability of bipartite quantum states
• Investigating bound entangled two-qutrit states via the best separable approximation
• State-Agnostic Approach to Certifying Electron-Photon Entanglement in Electron Microscopy
• The statistics of the entanglement changes generated by the Hadamard-CNOT quantum circuit
• Localizing genuine multiparty entanglement in noisy stabilizer states
• Linear maps as sufficient criteria for entanglement depth and compatibility in many-body systems
• Entanglement distribution revealed by macroscopic observations
• A smallest computable entanglement monotone
• Dynamics of single-mode nonclassicalities and quantum correlations in the Jaynes-Cummings model
• A new entanglement measure based on the total concurrence
• Computing finite-dimensional bipartite quantum separability
• Noise resilience in path-polarization hyperentangled probe states
• Relation Between Stereographic Projection and Concurrence Measure in Bipartite Pure States
• Entanglement quantifiers and phase transitions
• Entanglement detection and lower bound of convex-roof extension of negativity
• Problem of quantifying quantum correlations with non-commutative discord
• Sequential generation of Polynomial Invariants and N-body non-local correlations
• Low-Fidelity Entanglement Distillation with FIMAX
• Holographic entanglement entropy and complexity for the cosmological braneworld model
• Generators of nonclassical states by combination of the linear coupling of boson modes, Kerr nonlinearity and the strong linear losses
• Curvature from multipartite entanglement in quantum gravity states
• Glassy disorder-induced effects in noisy dynamics of Bose-Hubbard and Fermi-Hubbard systems
• Quantum deficits and correlations of two superconducting charge qubits
• Extensions of Generalized Two-Qubit Separability Probability Analyses to Higher Dimensions, Additional Measures and New Methodologies
• Complementarity between micro-micro and micro-macro entanglement in a Bose-Einstein condensate with two Rydberg impurities
• User-specified random sampling of quantum channels and its applications
• On Symmetric Sets of Projectors for Reconstruction of a Density Matrix
• Quantum channels and some absolute properties of quantum states
• Upper bound on three tangles of reduced states of four-qubit pure states
• Effective approaches to the dynamical properties of two distinguishable Bose polarons
• Correlation based entanglement criteria for bipartite systems
• Maximum Violation of Monogamy of Entanglement for Indistinguishable Particles by Measures that are Monogamous for Distinguishable Particles
• Volume of the set of locally diagonalizable bipartite states
• Multipartite Entanglement in the Random Ising Chain
• Negative entanglement measure for bipartite separable mixed states
• Quantum Features of the Thermal Two-Qubit Quantum Rabi Model in Ultra- and Deep-Strong Regimes
• Advances in delimiting the Hilbert-Schmidt separability probability of real two-qubit systems
• Information theoretic measures for Lifshitz system
• Birman-Wenzl-Murakami Algebra and the Topological Basis
• Quantum entanglement in phase space
• The verification of a requirement of entanglement measures
• Local cloning of genuine entangled states of three qubit
• Adiabatic freezing of entanglement with insertion of defects in a one-dimensional Hubbard model
• Convex bodies of states and maps
• Exploring the possibility of a complex-valued non-Gaussianity measure for quantum states of light
• Creating multiphoton-polarization bound-entangled states
• Tetrahedron genuine entanglement measure of four-qubit systems
• Pair entanglement in dimerized spin-s chains
• Restrictions on shareability of classical correlations for random multipartite quantum states
• Separable Ball around any Full-Rank Multipartite Product State
• Mixedness timescale in non-Hermitian quantum systems
• Dynamics of impurity, local and non-local information for two non identical qubits
• Environmental effects on nonlocal correlations
• Loop State-preparation-and-measurement tomography of a two-qubit system
• Nonclassical correlations in subsystems of globally entangled quantum states
• Approximation, Proof Systems, and Correlations in a Quantum World
• Existence of maximally correlated states
• Inducing critical phenomena in spin chains through sparse alternating fields
• Extremal entanglement witnesses
• Derivative coupling enables genuine entanglement harvesting in causal communication
• Fermionic entanglement in the presence of background electric and magnetic fields
• Dissipative phase transition: from qubits to qudits
• Quantum correlations in general qubit-qudit axially symmetric states
• Geometrically induced singular behavior of entanglement
• A simple spectral condition implying separability for states of bipartite quantum systems
• Length filtration of the separable states
• Entanglement generation and transfer between remote atomic qubits interacting with squeezed field
• Correlations and energy in mediated dynamics
• Tighter Constraints of Multi-Qubit Entanglement in Terms of Nonconvex Entanglement Measures LCREN and LCRENoA
• Rényi and Tsallis formulations of separability conditions in finite dimensions
• Formulas for Generalized Two-Qubit Separability Probabilities
• Competition of Direct and Indirect Sources of Thermal Entanglement in a spin star network
• Ground state separability and criticality in interacting many-particle systems
• Spin flip of multiqubit states in discrete phase space
• Entanglement, Complexity, and Causal Asymmetry in Quantum Theories
• Gravity induced entanglement of multiple massive particles with large spin
• Applications of differential geometry and representation theory to description of quantum correlations
• Parameterized bipartite entanglement measures and entanglement constraints
• Eigenlevel statistics of the quantum adiabatic algorithm
• Superdense Coding with Uniformly Accelerated Particle
• Generating multi-hops entangled network via spin Dipolar interaction
• Estimating entanglement in 2D Heisenberg model in the strong rung-coupling limit
• A geometric approach to the distribution of quantum states in bipartite physical systems
• Complementarity relations for design-structured POVMs in terms of generalized entropies of order $\alpha \in (0,2)$
• Geometry of quantum state space and entanglement
• The surface code beyond Pauli channels: Logical noise coherence, information-theoretic measures, and errorfield-double phenomenology
• Certifying nonlocal properties of noisy quantum operations
• Correlations, Bell Inequality Violation & Quantum Entanglement
• Entanglement gain in measurements with unknown results
• Entanglement hierarchies in multipartite scenarios
• Quantum hyperspins: Highly nonclassical collective behavior in quantum optical parametric oscillators
• Two-Qubit Separabilities as Piecewise Continuous Functions of Maximal Concurrence
• Entanglement in the Quantum Spherical Model -- a Review
• On the extreme points of sets of absolulely separable and PPT states
• Construction of PPT entangled state and its detection by using second-order moment of the partial transposition
• Quantifying multipartite quantum states by ($k+1$)-partite entanglement measures
• Violations of local realism by two entangled quNits
• Polytope structures for Greenberger-Horne-Zeilinger diagonal states
• Separable ellipsoids around multipartite states
• Entanglement generation in weakly-driven arrays of multilevel atoms via dipolar interactions
• Quantifying Multipartite Quantum Entanglement in a Semi-Device-Independent Manner
• Entanglement and fidelity across quantum phase transitions in locally perturbed topological codes with open boundaries
• Initial-state randomness as a universal source of decoherence
• Entanglement dynamics in dissipative photonic Mott insulators
• Multiparty Entanglement Microscopy of Quantum Ising models in 1d, 2d and 3d
• Convex-roof entanglement measures of density matrices block diagonal in disjoint subspaces for the study of thermal states
• Optimal quantum precision in noise estimation: Is entanglement necessary?
• Manipulation of tripartite-to-bipartite entanglement localization under quantum noises and its application to entanglement distribution
• Superradiant Phase Transition and Statistical Properties in the Dicke-Stark Model
• Adding Photonic Entanglement to Superradiance by Using Multilevel Atoms
• Quantum spin van der Pol oscillator -- a spin-based limit-cycle oscillator exhibiting quantum synchronization
• Quantum state merging with bound entanglement
• Experimental test of the majorization uncertainty relation with mixed states
• Local correlations of mixed two-qubit states
• Mathematical framework for detection and quantification of nonclassical correlation
• Full Bell locality of a noisy state for $N\ge 3$ nonlocally entangled qudits
• The Role of Localizable Concurrence in Quantum Teleportation Protocols
• Minimal-error quantum state discrimination versus robustness of entanglement:More indistinguishability with less entanglement
• A Cooper-pair beam splitter as a feasible source of entangled electrons
• Separability and entanglement in the Hilbert space reference frames related through the generic unitary transform for four level system
• Geometry of two-body correlations in three-qubit states
• Local entanglement transfer to multiple pairs of spatially separated observers
• Upper bounds on the leakage of private data and operational approach to markovianity
• Logarithmic growth of peripheral entanglement concentrated via noisy measurements in a star network of spins
• Typical Gaussian Quantum Information
• Role of external fields in enhancing long-distance entanglement at finite temperatures
• Optimal quantum resource generation in coupled transmons immersed in Markovian baths
• Conditional states and entropy in qudit-qubit systems
• Constructing quantum circuits for maximally entangled multi-qubit states using the genetic algorithm
• Mixed State Parametrization and Two-qubit Entanglement
• Local cloning of CAT states
• Quasirandom estimations of two-qubit operator-monotone-based separability probabilities
• Some Comments on Entanglement and Local Thermofield Theory
• Constructing a ball of separable and absolutely separable states for $2\otimes d$ quantum system
• Local entanglement of multidimensional continuous-variable systems
• Quantum-aware Transformer model for state classification
• Sudden Decoherence by Resonant Particle Excitation for Testing Gravity-Induced Entanglement
• Entanglement quantification from collective measurements processed by machine learning
• A Differential-Geometric Approach to Quantum Ignorance Consistent with Entropic Properties of Statistical Mechanics
• Resource-efficient quantum correlation measurements via multicopy neural network methods
• Optical remote control of a charge qubit
• On the $\mathcal{P}\mathcal{T}$-symmetric parametric amplifier
• Quantum causal models via QBism
• Detecting false correlations: Uncovering a faked Bell-inequality violation
• Quantum entanglement and classical separability in NMR computing
• On the temperature dependence of the interaction-induced entanglement
• A Note on Quantum Separability
• Generation and Detection of Quantum Correlations and Entanglement on a Spin-Based Quantum Information Processor
• Quantum correlations in composite systems under global unitary operations
• Attainable entanglement of unitary transformed thermal states in liquid-state nuclear magnetic resonance with the chemical shift
• Shareability of Quantum Correlations in a Many-Body Spin System with Two- and Three-Body Interactions
• Confident entanglement detection via separable numerical range
• Absolutely entangled sets of pure states for bipartitions and multipartitions
• Witnessing entanglement via the geometric phase in a impurity-doped Bose-Einstein condensate
• Conditional steering under von-Neumann scenario
• Entanglement in bipartite X-states: Analytical results for the volume of states with positive partial transpose
• Generation and nonclassicality of entangled states via the interaction of two three-level atoms with a quantized cavity field assisted by a driving external classical field
• On the tensor convolution and the quantum separability problem
• Quantum Deep Sets and Sequences
• Detecting entanglement from few partial transpose moments and their decay via weight enumerators
• Effective sample size approximations as entropy measures
• Yang-Baxter $\breve{R}$ matrix, Entanglement and Yangian
• Generation and Manipulation of Entanglement in Quantum Optical Systems
• Entanglement and swap of quantum states in two qubits
• Two-electron quantum walks can probe entanglement and decoherence in an electron microscope
• Detection of nonabsolute separability in quantum states and channels through moments
• Unbounded entanglement-sustaining sequential local quantum state discrimination
• One application of Duistermaat-Heckman measure in quantum information theory
• On Sufficient and Necessary Criteria of Multipartite Quantum Entanglement
• Geometric Measure of Entanglement and Schmidt Decomposition of Multipartite Systems
• The mixing of internal gravity waves and lithium production in intermediate-mass AGB stars
• NMR Quantum Information Processing and Entanglement
• Any Two Qubit State Has Non Zero Quantum Discord Under Global Unitary Operations
• Photon Induced Entanglement in Atom-Cavity Systems
• Parametrization of projector-based witnesses for bipartite systems
• On Ruelle transfer operators and completely positive maps