Entanglement Measures and Purification Procedures

Abstract

We generalize previously proposed conditions each measure of entanglement has to satisfy. We present a class of entanglement measures that satisfy these conditions and show that the Quantum Relative Entropy and Bures Metric generate two measures of this class. We calculate the measures of entanglement for a number of mixed two spin 1/2 systems using the Quantum Relative Entropy, and provide an efficient numerical method to obtain the measures of entanglement in this case. In addition, we prove a number of properties of our entanglement measure which have important physical implications. We briefly explain the statistical basis of our measure of entanglement in the case of the Quantum Relative Entropy. We then argue that our entanglement measure determines an upper bound to the number of singlets that can be obtained by any purification procedure and that distillable entanglement is in general smaller than the entanglement of creation.

40 pages, 2 figures, small changes, included references to Lieb and Ruskai for the proof of strong subadditivity

References in corpus (4)

• Entanglement of a Pair of Quantum Bits
• Quantifying Entanglement
• Statistical Inference, Distinguishability of Quantum States, And Quantum Entanglement
• Entanglement purification via separable superoperators

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• Optimal convex approximations of quantum states
• Entanglement and entropy rates in open quantum systems
• Towards an Entanglement Measure for Mixed States in CFTs Based on Relative Entropy
• Mixed-state additivity properties of magic monotones based on quantum relative entropies for single-qubit states and beyond
• Entangling remote microwave quantum computers with hybrid entanglement swap and variational distillation
• Highly-efficient estimation of entanglement measures for large experimentally created graph states via simple measurements
• Entanglement of resonantly coupled field modes in cavities with vibrating boundaries
• A nonstabilizerness monotone from stabilizerness asymmetry
• Remarks on the equivalence of full additivity and monotonicity for the entanglement cost
• Optimal Lewenstein-Sanpera Decomposition for some Biparatite Systems
• Quasi multipartite entanglement measure based on quadratic functions
• Chains of Quasi-Classical Informations for Bipartite Correlations and the Role of Twin Observables
• Epsilon-measures of entanglement
• Geometric approach to entanglement quantification with polynomial measures
• Geometric Rényi Divergence and its Applications in Quantum Channel Capacities
• Upper bounds for the secure key rate of decoy state quantum key distribution
• Geometric Entanglement of Symmetric States and the Majorana Representation
• Unification of quantum resources in distributed scenarios
• Optimal verification of entanglement in a photonic cluster state experiment
• Limited-control metrology approaching the Heisenberg limit without entanglement preparation
• Protecting quantum correlations in presence of generalised amplitude damping channel: the two-qubit case
• Quantum information science as an approach to complex quantum systems
• Using three-partite GHZ states for partial quantum error-detection in entanglement-based protocols
• Entanglement, EPR correlations and mesoscopic quantum superposition by the high-gain quantum injected parametric amplification
• All Inequalities for the Relative Entropy
• Overcoming entropic limitations on asymptotic state transformations through probabilistic protocols
• Relative entropy of entanglement of rotationally invariant states
• An analog of topological entanglement entropy for mixed states
• Coherence and entanglement in Grover and Harrow-Hassidim-Lloyd algorithm
• Preserving quantum correlations and coherence with non-Markovianity
• Complete Optimal Convex Approximations of Qubit States under $B_2$ Distance
• Entanglement resource theory of quantum channel
• Heat current and entropy production rate in local non-Markovian quantum dynamics of global Markovian evolution
• A Proposal for Quantum Fisher Information Optimization and its Relation with Entanglement Measures
• Magnetic shielding of quantum entanglement states
• Fundamental speed limits on entanglement dynamics of bipartite quantum systems
• On the units of bipartite entanglement: Is sixteen ounces of entanglement always equal to one pound?
• Teleportation: from probability distributions to quantum states
• Entanglement of pair cat states and teleportation
• Fortran code for generating random probability vectors, unitaries, and quantum states
• Uniform Quantification of Correlations for Bipartite Systems
• Bounds on localisable information via semidefinite programming
• Realization of the tradeoff between internal and external entanglement
• A Theory of Entanglement
• Monogamy inequality in terms of entanglement measures based on distance for pure multiqubit states
• Realism-based nonlocality: Invariance under local unitary operations and asymptotic decay for thermal correlated states
• Estimating Parameterized Entanglement Measure
• Improving the lower bound to the secret-key capacity of the thermal amplifier channel
• Entanglement dynamics governed by time-dependent quantum generators
• An Explicit Computation of the Bures Metric Over the Space of $N$-Dimensional Density Matrices
• Continuity of entropies via integral representations
• Alternatives of entanglement depth and metrological entanglement criteria
• Hierarchy of correlation quantifiers comparable to negativity
• Correlations in Quantum Physics
• The dynamical $\alpha$-Rényi entropies of local Hamiltonians grow at most linearly in time
• Dynamics and Quantum correlations in Two independently driven Rydberg atoms with distinct laser fields
• Accessible bounds for general quantum resources
• Investigating entropic dynamics of multiqubit cavity QED system
• The resource theory of coherence for quantum channels
• An Extention of Entanglement Measures for Pure States
• Quantifying quantum coherence based on the Tsallis relative operator entropy
• Monogamy of Entanglement Measures Based on Fidelity in Multiqubit Systems
• The Meta-Structures Project
• Coherent and incoherent contents of correlations
• Complementarity of Entanglement and Interference
• Relative entropy of entanglement of a kind of two qubit entangled states
• Characterizing randomness in parameterized quantum circuits through expressibility and average entanglement
• Quantum entanglement and Hawking temperature
• Local Cloning of Entangled Qubits
• Complete Genuine Multipartite Entanglement Monotone
• Entropic Diagram Characterization of Quantum Coherence: Degenerate Distillation and the Maximum Eigenvalue Uncertainty Bound
• Optimization free measures of quantum resources
• Path-entangling evolution and quantum gravitational interaction
• Genuine Multiparty Quantum Entanglement Suppresses Multiport Classical Information Transmission
• Entanglement and perfect quantum error correction
• Quantum Characterization of a Werner-like Mixture
• Non-Markovianity and Clauser-Horne-Shimony-Holt (CHSH)-Bell inequality violation in quantum dissipative systems
• Interplay between nonclassicality and $\mathcal{P}\mathcal{T}$ symmetry in an effective two level system with open system effects
• Maximal Overlap with a Fully Separable State and Translational Invariance in Multipartite Entangled States
• Hierarchy of continuous-variable quantum resource theories
• Entanglement distribution and quantum discord
• Quantifying the unextendibility of entanglement
• Generation of entanglement via squeezing on a tripartite-optomechanical system
• Entangling efficiency of linear-optical quantum gates
• Modification of polarization through de-Gaussification
• Entanglement properties of a measurement-based entanglement distillation experiment
• Quantum Coherence, Coherent Information and Information Gain in Quantum Measurement
• Multipartite entanglement in fermionic systems via a geometric measure
• Upper bounds for relative entropy of entanglement based on active learning
• Delayed creation of entanglement in superconducting qubits interacting with a microwave field
• Improvement of stabilizer based entanglement distillation protocols by encoding operators
• Characterizing entanglement using quantum discord over state extensions
• Relation between the Greenberger-Horne-Zeilinger--entanglement cost of preparing a multipartite pure state and its quantum discord
• Additivity relations in quantum correlations
• Controlling gain with loss: Bounds on localizable entanglement in multi-qubit systems
• Partial-Norm of Entanglement: Entanglement Monotones That are not Monogamous
• Resource Theory of Non-absolute Separability
• The reduction of the closest disentangled states
• Continuous variable port-based teleportation
• Schrödinger as a Quantum Programmer: Estimating Entanglement via Steering
• Continuity of the relative entropy of resource
• Generating pseudo-random discrete probability distributions
• Entanglement Measures with Asymptotic Weak-Monotonicity as Lower (Upper) Bound for the Entanglement of Cost (Distillation)
• Quantum channels that destroy negative conditional entropy
• Entanglement cost for infinite-dimensional physical systems
• Genuine Secret-Sharing States
• Partitioning optical solitons for generating entangled light beams
• Quantifying the particle aspect of quantum systems
• Multiqubits Entanglement Based on Optimal Witness
• Role of matter coherence in entanglement due to gravity
• One-shot manipulation of coherence in dynamic quantum resource theory
• A smallest computable entanglement monotone
• Two-mode light states before and after delocalized single-photon addition
• Entanglement detection and lower bound of convex-roof extension of negativity
• Minkowski structure for purity and entanglement of Gaussian bipartite states
• Experimental Entanglement Quantification for Unknown Quantum States in a Semi-Device-Independent Manner
• Quantum discord of 2n-dimensional Bell-diagonal states
• Hermitian Schmidt Decomposition and Twin Observables of Bipartite Mixed States
• All multipartite entanglements are quantum coherences in locally distinguishable bases
• Role of quantum state texture in probing resource theories and quantum phase transition
• Quantum-classical entropy analysis for nonlinearly-coupled continuous-variable bipartite systems
• Negative entanglement measure for bipartite separable mixed states
• Distillable entanglement in $d\otimes d$ dimension
• Entanglement measures for two-particle quantum histories
• Impacts of Intrinsic Noise and Quantum Entanglement on the Geometric and Dynamical Properties of the XXZ Heisenberg Interacting Spin Model
• Are all noisy quantum states obtained from pure ones?
• Local cloning of genuine entangled states of three qubit
• Dynamics of quantum entanglement in the reservoir with memory effects
• Resource reduction via repeaters in entanglement distribution
• Entanglement rates for bipartite open systems
• Distributed Compression and Squashed Entanglement
• Entanglement dynamics in finite qudit chain in consistent magnetic field
• Approximation, Proof Systems, and Correlations in a Quantum World
• Correlation based entanglement criteria for bipartite systems
• Impossibility Criterion for Obtaining Pure Entangled States From Mixed States By Purifying Protocols
• Information-theoretic aspects of the generalized amplitude damping channel
• Finding maximal quantum resources
• Quantum coherence with incomplete set of pointers and corresponding wave-particle duality
• An entanglement measure based on the capacity of dense coding
• Quantum Entanglement and Geometry
• Correlations, Bell Inequality Violation & Quantum Entanglement
• Entanglement bound for multipartite pure states based on local measurements
• Nonlocality of two-qubit and three-qubit Schmidt-Correlated states
• Monogamous property of generalized W states in three-qubit systems in terms of relative entropy of entanglement
• Biphoton ququarts as either pure or mixed states, features and reconstruction from coincidence measurements
• Mode-Invisibility as a non-Destructive Probe of Entangled QUBIT-CAT States
• Hallmarking quantum states: unified framework for coherence and correlations
• Visualization of correlations in hybrid quantum systems
• On directional derivatives of trace functionals of the form $A\mapsto\Tr(Pf(A))$
• Quantifying Multipartite Quantum Entanglement in a Semi-Device-Independent Manner
• Multipartite quantum correlations in a two-mode Dicke model
• Preservation of entanglement in local noisy channels
• Resource theories with completely passive states and passive states as free states
• Measurement-induced entanglement entropy of gravitational wave detections
• Generation of polarization-entangled photon pairs from two interacting quantum emitters
• Parameterized bipartite entanglement measures and entanglement constraints
• Path superposition activating perfect quantum teleportation ability for separable states
• Aperiodic Dissipation as a Mechanism for Steady-State Localization
• Tighter monogamy relations of entanglement measures based on fidelity
• Limits of Detecting Extraterrestrial Civilizations
• The Role of Entanglement in Quantum Communication, and Analysis of the Detection Loophole
• Discord, quantum knowledge and private communications
• Testing the Monogamy Relations via Rank-2 Mixtures
• REE From EOF
• Entanglement measure for multipartite pure states and its numerical calculation
• Production of Information and Entropy in measurement of entangled states
• Voronoi Diagrams for Quantum States and Its Application to a Numerical Estimation of a Quantum Channel Capacity
• Global quantum discord and von Neumann entropy in multipartite two-level atomic systems
• Entangled states from simple quantum graphs
• A Sharp Geometric Measure of Entanglement
• Entanglement preservation in tripartite quantum systems under dephasing dynamics
• Geometric measures of quantum nonlocality: characterization, quantification, and comparison by distances and operations
• Diffusion and entanglement of a kicked particle in an infinite square well under frequent measurements
• Classifying fermionic states via many-body correlation measures
• Holographic Limitations and Corrections to Quantum Information Protocols
• Irrversibility of Entanglement Manipulations: Vagueness of the Entanglement of Cost and Entanglement of Distillation
• Entanglement quantification from collective measurements processed by machine learning
• Upper bounds on the leakage of private data and operational approach to markovianity
• Geometric measure of entanglement compared to measures based on fidelity
• Max- Relative Entropy of Entanglement, alias Log Robustness
• Transformation properties and entanglement of relativistic qubits under space-time and gauge transformations
• The landscape of quantum transitions driven by single-qubit unitary transformations with implications for entanglement
• Bures measure of entanglement of an arbitrary state of two qubits
• Superactivation of Bell nonlocality in pure anyonic states
• Variational-toolbox-based separability detection of multiqubit states
• Algorithm for evaluating distance-based entanglement measures
• Computable Measure of Total Quantum Correlation of Multipartite Systems
• Maximal Atom-Photon Entanglement in a Double-Lambda Quantum System
• Shareability of Quantum Correlations in a Many-Body Spin System with Two- and Three-Body Interactions
• Atom- photon entanglement beyond the multi-photon resonance condition
• Entanglement of Four-Qubit Rank-$2$ Mixed States
• Optimal Interpolation of Entanglement Purification Protocols
• Some aspects of the interplay between bipartite correlations and quantum channels
• Relative Entropy of Entanglement for Two-Qubit State with $z$-directional Bloch Vectors
• Entanglement as the cross-symmetric part of quantum discord
• Quantum-state block texture and its quantification
• Entanglement - A Queer In The World Of Quantum : Some Perspectives
• Unified monogamy relations for the generalized $W$-class states beyond qubits
• Entanglement Entropy in CFT and Modular Nuclearity
• Absolutely maximally entangled pure states of multipartite quantum systems
• How confused can an entanglement witness be to be still persuasive
• Partitewise Entanglement
• Characterization of PPT states and measures of entanglement
• Generation and Manipulation of Entanglement in Quantum Optical Systems
• Quantum correlations and ergotropy
• Classification of two-particle quantum channels of information transfer
• Method of convex rigid frames and applications in studies of multipartite quNit pure-states
• Dephasing-Induced Distribution of Entanglement in Tripartite Quantum Systems
• Quantum Resource Theories of Anyonic Entanglement
• Lower bounds on distances between a given quantum channel and certain classes of channels
• Study on Entanglement and its Utility in Information Processing
• Local Purity Distillation in Quantum Systems: Exploring the Complementarity Between Purity and Entanglement
• Floating Entanglement Witness Measure and Genetic Algorithm
• Generation and Detection of Quantum Correlations and Entanglement on a Spin-Based Quantum Information Processor
• Qubit-qunit decomposition of quantum channel
• From Quantum Optics to Quantum Technologies
• Atom- Photon Entanglement in Double- Lambda Quantum System by using femtosecond Gaussian pulses
• Is monogamy of entanglement geometrical?
• Generalized Entanglement of Purification Criteria for 2-Producible States in Multipartite Systems