Mixed-state entanglement and distillation: is there a ``bound'' entanglement in nature?

Abstract

It is shown that if a mixed state can be distilled to the singlet form, it must violate partial transposition criterion [A. Peres, Phys. Rev. Lett. 76, 1413 (1996)]. It implies that there are two qualitatively different types of entanglement: ``free'' entanglement which is distillable, and ``bound'' entanglement which cannot be brought to the singlet form useful for quantum communication purposes. Possible physical meaning of the result is discussed.

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• Experimental quantum teleportation
• Experimental Realization of Teleporting an Unknown Pure Quantum State via Dual Classical and Einstein-Podolski-Rosen Channels

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• Multi-partite separable states with unique decompositions and construction of three qubit entanglement with positive partial transpose
• Detecting Quantum Entanglement
• Locally Accessible Information of Multisite Quantum Ensembles Violates Monogamy
• Annihilating Entanglement Between Cones
• John Bell and the Nature of the Quantum World
• Evaluation of two different entanglement measures on a bound entangled state
• Holographic Entanglement negativity in flat space generalized minimal massive gravity
• Preparation of bipartite bound entangled Gaussian states in quantum optics
• On two-distillable Werner states
• Every entangled state provides an advantage in classical communication
• Beating detection loophole in nonlinear entanglement witnesses
• Mutually Unbiased Bases and Bound Entanglement
• Fundamental speed limits on entanglement dynamics of bipartite quantum systems
• A Schmidt decomposition approach to quantum thermodynamics
• Entanglement transitions in random definite particle states
• Entanglement generation from athermality
• Unextendible entangled bases and more nonlocality with less entanglement
• Broadcasting of quantum correlations in qubit-qudit systems
• Generalized Entanglement Monogamy and Polygamy Relations for N -Qubit Systems
• Entanglement of disjoint blocks in the one dimensional Spin 1 VBS
• Special features of the Weyl-Heisenberg Bell basis imply unusual entanglement structure of Bell-diagonal states
• Rotationally invariant bipartite states and bound entanglement
• Experimental generation of complex noisy photonic entanglement
• The Power of LOCCq State Transformations
• Is bound entanglement Lorentz invariant?
• Halos and undecidability of tensor stable positive maps
• Entangled Qubits in a non-Gaussian Quantum State
• Determining quantum correlations in bipartite systems - from qubit to qutrit and beyond
• W-like bound entangled states and secure key distillation
• Generalised monogamy relation of convex-roof extended negativity in multi-level systems
• Product Bases in Quantum Information Theory
• Quantum privacy witness
• A general scheme for construction of scalar separability criteria from positive maps
• Weakly-entangled states are dense and robust
• Entangled state distillation from single copy mixed states beyond LOCC
• Negativity vs. Purity and Entropy in Witnessing Entanglement
• Symmetric quantum states: a review of recent progress
• Thresholds for reduction-related entanglement criteria in quantum information theory
• Perturbative expansion of entanglement negativity using patterned matrix calculus
• Strong NP-Hardness of the Quantum Separability Problem
• Non-distillable entanglement guarantees distillable entanglement
• Noiseless method for checking the Peres separability criterion by local operations and classical communication
• Second Law of Entanglement Manipulation with Entanglement Battery
• Optimized Correlation Measures in Holography
• Introduction to quantum entanglement in many-body systems
• Bipartite bound entanglement in continuous variables through deGaussification
• A Complete Hierarchy of Linear Systems for Certifying Quantum Entanglement of Subspaces
• Entanglement in the Bogoliubov vacuum
• Increasing distillable key rate from bound entangled states by using local filtration
• Superactivation, unlockability, and secrecy distribution of bound information
• Characterizing generalized axisymmetric quantum states in $d\times d$ systems
• Efficiency of Deterministic Entanglement Transformation
• Comparability of multipartite entanglement
• Entanglement conditions for tripartite systems via indeterminacy relations
• Quantum entanglement in finite-dimensional Hilbert spaces
• Gaussian intrinsic entanglement: An entanglement quantifier based on secret correlations
• Experimental Detection of Qubit-Ququart Pseudo-Bound Entanglement using Three Nuclear Spins
• Einstein-Podolsky-Rosen uncertainty limits for bipartite multimode states
• Quantitative characterization of several entanglement detection criteria
• Entanglement theory with limited computational resources
• Bound entangled states are useful in prepare-and-measure scenarios
• Certification of genuine multipartite entanglement in spin ensembles with measurements of total angular momentum
• Negative result about the construction of genuinely entangled subspaces from unextendible product bases
• Entanglement distribution and quantum discord
• Activation of Nonmonogamous Multipartite Quantum States
• Canonical Distillation of Entanglement
• Product vectors in the ranges of multi-partite states with positive partial transposes and permanents of matrices
• Bose-Hubbard models with photon pairing in circuit-QED
• Constructing Entanglement Witness Via Real Skew-Symmetric Operators
• Accessibility of physical states and non-uniqueness of entanglement measure
• Indistinguishability-assisted two-qubit entanglement distillation
• Nonequivalence between absolute separability and positive partial transposition in the symmetric subspace
• Entanglement Detection and Distillation for Arbitrary Bipartite Systems
• Tighter generalized monogamy and polygamy relations for multiqubit systems
• A measure of quantum correlations that lies approximately between entanglement and discord
• Bounds on mixed state entanglement
• Computable entanglement conversion witness that is better than the negativity
• Relations among $k$-ME concurrence, negativity, polynomial invariants, and tangle
• Experimental distillation of tripartite quantum steering with an optimal local filtering operation
• Clustering of conditional mutual information and quantum Markov structure at arbitrary temperatures
• Simple permutation-based measure of quantum correlations and maximally-3-tangled states
• The Transition from Quantum to Classical in weak measurements and reconstruction of Quantum Correlation
• All incompatible measurements on qubits lead to multiparticle Bell nonlocality
• Bound entangled Bell diagonal states of unequal local dimensions, and their witnesses
• Generation and distribution of atomic entanglement in coupled-cavity arrays
• Bipartite Bound Entanglement
• Using Partial Transpose and Realignment to generate Local Unitary Invariants
• Key Distillation and the Secret-Bit Fraction
• Experimental single-copy distillation of quantumness from higher-dimensional entanglement
• Complementarity between decoherence and information retrieval from the environment
• The Adaptive Classical Capacity of a Quantum Channel, or Information Capacities of Three Symmetric Pure States in Three Dimensions
• Theoretical proposal for the experimental realization of realignment operation
• Quantifying subspace entanglement with geometric measures
• Gaussian multipartite bound information
• Distillation of entanglement by projection on permutationally invariant subspaces
• Entanglement detection and lower bound of convex-roof extension of negativity
• Low-dimensional quite noisy bound entanglement with cryptographic key
• Quantum-entangled light from localized emitters
• Algebraic Probability-Theoretic Characterization of Quantum Correlations
• Characterization of Nonlocal Resources Under Global Unitary Action
• General theory of detection and optimality
• Low-Fidelity Entanglement Distillation with FIMAX
• Investigating bound entangled two-qutrit states via the best separable approximation
• Hybrid quantum network design against unauthorized secret-key generation, and its memory cost
• Realignment separability criterion assisted with filtration for detecting continuous-variable entanglement
• A simplification of entanglement purification
• Unified Framework for Calculating Convex Roof Resource Measures
• Computable entanglement cost under positive partial transpose operations
• Measurement-device-independent verification of channel steering
• Comparative Dynamical Study of a Bound Entangled State
• Choi-Defined Resource Theories
• Are all noisy quantum states obtained from pure ones?
• A Note on Resistance of NPT to Mixture of Separable States
• Qubit-environment entanglement in time-dependent pure dephasing
• Real randomized measurements for analyzing properties of quantum states
• The Schmidt number of a quantum state cannot always be device-independently certified
• Extremal entanglement witnesses
• Constructions of indecomposable positive maps based on a new criterion for indecomposability
• Self-testing composite measurements and bound entangled state in a single quantum network
• On the geometric distance between quantum states with positive partial transposition and private states
• Seven definitions of bipartite bound entanglement
• Creating multiphoton-polarization bound-entangled states
• Partial-transpose-guided entanglement classes and minimum noise filtering in many-body Gaussian quantum systems
• Entanglement and its Role in Shor's Algorithm
• Characterizing the Multipartite Entanglement Structure of Non-Gaussian Continuous-Variable States with a Single Evolution Operator
• Operational detection of entanglement via quantum designs
• Is absolute separability determined by the partial transpose?
• Generation of Mapping Cones from Small Sets
• Multipartite positive-partial-transpose inequalities exponentially stronger than local reality inequalities
• Dzyaloshinskii-Moriya interaction as a fast quantum information scrambler
• Loss of Information in Quantum Guessing Game
• Approximation, Proof Systems, and Correlations in a Quantum World
• Triangle-like inequalities related to coherence and entanglement negativity
• Birkhoff-James Orthogonality in the Trace Norm, with Applications to Quantum Resource Theories
• Absence of Entanglement Growth in Dicke Superradiance
• Iterative optimization in quantum metrology and entanglement theory using semidefinite programming
• Ground State Instabilities and Entanglement in the Detuned Dicke Model
• Correlations, Bell Inequality Violation & Quantum Entanglement
• One-shot rates for entanglement manipulation under non-entangling maps
• Bound on distributed entanglement
• Quantum Entanglement and Geometry
• Entangled edge states of corank one with positive partial transposes
• Decomposable Pauli diagonal maps and Tensor Squares of Qubit Maps
• On the state space structure of tripartite quantum systems
• Witnessing environment dimension through temporal correlations
• Measurement-invisible quantum correlations in scrambling dynamics
• Classical capacity of a noiseless quantum channel assisted by noisy entanglement
• Does connected wedge imply distillable entanglement?
• Robust entanglement measure for mixed quantum states
• Dicke subsystems are entangled
• Retrodiction of measurement outcomes on a single quantum system reveals entanglement with its environment
• Quantifying magic via quantum $(\alpha ,\beta )$ Jensen-Shannon divergence
• Generalized product-form monogamy relations in multi-qubit systems
• Entanglement-Enhanced Classical Communication
• State-witness contraction
• Entanglement and distillation from symmetric positive maps
• Entanglement bases and general structures of orthogonal complete bases
• Quantum-aware Transformer model for state classification
• Upper bounds on device-independent quantum key distribution rates and a revised Peres conjecture
• Quantum Separability of Thermal Spin One Boson Systems
• Markov Gap and Bound Entanglement in Haar Random State
• Measuring outcome correlation for spin-s Bell cat-state and geometric phase induced spin parity effect
• A non-distillability criterion for secret correlations
• Bound entanglement and distillability of multipartite quantum systems
• Necessary criterion for extracting thermodynamical work from qudit-entangled state
• Quantum discord protection of a two-qutrit V-type atomic system from decoherence by partially collapsing measurements
• Quantum state merging with bound entanglement
• On two maximally entangled couples
• Fate of entanglement in quadratic Markovian dissipative systems
• Entanglement cost hierarchies in quantum fragmented mixed states
• Group-Theoretic Perspective on the PPT and Realignment Criteria in the Magic Simplex for Bipartite Qutrits
• Localised Systems in Relativistic Quantum Information
• A Measure of Stregth of an Unextendible Product Basis
• Convex-roof entanglement measures of density matrices block diagonal in disjoint subspaces for the study of thermal states
• Immense Fidelity Enhancement of Encoded Quantum Bell Pairs at Short and Long-distance Communication along with Generalized Design of Circuit
• A matrix inequality related to the entanglement distillation problem
• How to fool the GHZ and W witnesses
• Certifying the dimensionality of any quantum channel with minimal assumptions
• Measurement-device-independent nonlinear entanglement witnesses
• Hierarchy of quantum correlations in qubit-qutrit axially symmetric states
• New Partial Trace Inequalities and Distillability of Werner States
• Effect of Quantum Information Scrambling on Bound Entangled States
• Measurement and feedforward induced entanglement negativity transition
• Bound entanglement-assisted prepare-and-measure scenarios based on four-dimensional quantum messages
• Geometry of two-body correlations in three-qubit states
• Partial Transposition in a Finite-Dimensional Hilbert Space: Physical Interpretation, Measurement of Observables and Entanglement
• Computing partial transposes and related entanglement functions
• Dzyaloshinskii-Moriya interaction as an agent to free the bound entangled states
• Construction and properties of a class of private states in arbitrary dimensions
• Geometry of the faces for separable states arising from generalized Choi maps
• Spin polarized induction of quantum correlations-entanglement using a 2 MeV proton beam channeling
• Non-Bilocal Measurement via Entangled State
• A comment on "A semiconductor source of entangled photons"
• Bipartite entanglement of localized separated systems
• Generalized distillability conjecture and generalizations of Cauchy-Bunyakovsky-Schwarz inequality and Lagrange identity
• Scalable Ellipsoidal Classification for Bipartite Quantum States
• Analysis of the Entanglement Cost and Calculation of the Holevo Capacity
• Two-particle Hadamard walk on dynamically percolated line and circle
• Revealing effects of local dimension on variable-range interacting model by connecting Lieb-Robinson bounds and multipartite entanglement
• Many-to-one remote information concentration for qudits and multipartite entanglement
• Unveiling NPT bound problem: From Distillability Sets to Inequalities and Multivariable Insights
• Detecting Entanglement by Pure Bosonic Extension
• Closing loopholes of measurement-device-independent nonlinear entanglement witnesses
• Hidden nonmacrorealism: reviving the Leggett-Garg inequality with stochastic operations
• A Novel Stabilizer-based Entanglement Distillation Protocol for Qudits
• Creating two-qudit maximally entangled quantum link through bulk
• Threshold (Q, P) Quantum Distillation
• Attainable entanglement of unitary transformed thermal states in liquid-state nuclear magnetic resonance with the chemical shift
• Characterizing multipartite entanglement by violation of CHSH inequalities
• Geometrical aspects of qudits concerning Bell inequalities
• Entanglement - A Queer In The World Of Quantum : Some Perspectives
• Entanglement in bipartite X-states: Analytical results for the volume of states with positive partial transpose
• On the temperature dependence of the interaction-induced entanglement
• A Non-Convex Optimization Strategy for Computing Convex-Roof Entanglement
• Noisy dynamics of Gaussian entanglement: a transient bound entangled phase before separability
• Unlimited quantum correlation advantage from bound entanglement
• Distillation of multipartite entangled states for arbitrary subsets of parties in noisy quantum networks of increasing size
• Rank-based entanglement detection for bound entangled states
• Progress in the study of the (non)existence of genuinely unextendible product bases
• Generalized Entanglement of Purification Criteria for 2-Producible States in Multipartite Systems
• Maximal extension on converse monogamy of entanglement for tripartite pure states
• Bound entanglement in symmetric random induced states
• Noisy Monitored Quantum Circuits
• Protocols for sharing genuine multipartite entanglement by employing copies of biseparable states
• Unital Kadison-Schwarz Maps
• Entanglement Protection of Classically Driven Qubits in a Lossy Cavity
• Entanglement transitions induced by large deviations
• Study on Entanglement and its Utility in Information Processing
• Quantum Information Approaches to Quantum Gravity
• Some aspects of the interplay between bipartite correlations and quantum channels
• Practical construction of positive maps which are not completely positive
• Thermodynamics of bipartite entanglement
• Generation and Detection of Quantum Correlations and Entanglement on a Spin-Based Quantum Information Processor