Evidence for Bound Entangled States with Negative Partial Transpose

Abstract

We exhibit a two-parameter family of bipartite mixed states ${\rho }_{bc}$, in a $d\otimes d$ Hilbert space, which are negative under partial transposition (NPT), but for which we conjecture that no maximally entangled pure states in $2\otimes 2$ can be distilled by local quantum operations and classical communication (LQ+CC). Evidence for this undistillability is provided by the result that, for certain states in this family, we cannot extract entanglement from any arbitrarily large number of copies of ${\rho }_{bc}$ using a projection on $2\otimes 2$. These states are canonical NPT states in the sense that any bipartite mixed state in any dimension with NPT can be reduced by LQ+CC operations to an NPT state of the ${\rho }_{bc}$ form. We show that the main question about the distillability of mixed states can be formulated as an open mathematical question about the properties of composed positive linear maps.

Revtex, 19 pages, 2 eps figures. v2,3: very minor changes, submitted to Phys. Rev. A. v4: minor typos corrected

References in corpus (1)

• Distillability and partial transposition in bipartite systems

Cited by in corpus (158)

• Quantum entanglement
• Quantum information with continuous variables
• Entanglement detection
• The Role of Relative Entropy in Quantum Information Theory
• Bell Inequalities and the Separability Criterion
• Entanglement in continuous variable systems: Recent advances and current perspectives
• General Entanglement Breaking Channels
• Characterizing Entanglement
• A Schmidt number for density matrices
• Quantum Data Hiding
• Unextendible Product Bases, Uncompletable Product Bases and Bound Entanglement
• Fundamentals of Quantum Information Theory
• Open-System Dynamics of Entanglement
• Hiding bits in Bell states
• Characterizing the entanglement of symmetric many-particle spin-1/2 systems
• Distillability and partial transposition in bipartite systems
• Convex resource theory of non-Gaussianity
• Disproving the Peres conjecture: Bell nonlocality from bipartite bound entanglement
• Irreversibility for all bound entangled states
• Nonadditivity of Bipartite Distillable Entanglement follows from Conjecture on Bound Entangled Werner States
• The Structure of Bipartite Quantum States - Insights from Group Theory and Cryptography
• Multipartite bound entangled states that violate Bell's inequality
• A Generalization of Quantum Stein's Lemma
• Irreversibility in asymptotic manipulations of entanglement
• Separability and distillability in composite quantum systems -a primer-
• Quantum Capacities of Channels with small Environment
• The quantum capacity with symmetric side channels
• A few steps more towards NPT bound entanglement
• Concurrence and a proper monogamy inequality for arbitrary quantum states
• Many copies may be required for entanglement distillation
• Principles of Quantum Communication Theory: A Modern Approach
• Activating bound entanglement in multi-particle systems
• Distillability via protocols respecting the positivity of partial transpose
• Non-local Operations: Purification, storage, compression, tomography, and probabilistic implementation
• Dynamical Entanglement
• Dense coding with multipartite quantum states
• Entanglement of a bipartite channel
• Separability and Fourier representations of density matrices
• Concurrence in arbitrary dimensions
• Activating NPPT distillation with an infinitesimal amount of bound entanglement
• Distillability and positivity of partial transposes in general quantum field systems
• On circulant states with positive partial transpose
• Genuinely entangled subspace with all-encompassing distillable entanglement across every bipartition
• Distillable entanglement and area laws in spin and harmonic-oscillator systems
• A Family of Norms With Applications In Quantum Information Theory
• A new class of states with positive partial transposition
• Three-by-three bound entanglement with general unextendible product bases
• Restricted numerical range: a versatile tool in the theory of quantum information
• Sudden death of distillability in qutrit-qutrit systems
• Distillability sudden death in qutrit-qutrit systems under global decoherence
• Family of bound entangled states on the boundary of Peres set
• An Introduction to Quantum Entanglement: a Geometric Approach
• Quantum Conical Designs
• Positivity of linear maps under tensor powers
• Distillability sudden death in qutrit-qutrit systems under amplitude damping
• Characterization of Distillable and Activable States using Entanglement Witnesses
• Entanglement Distillation Protocols and Number Theory
• Study of the Distillability of Werner States Using Entanglement Witnesses and Robust Semidefinite Programs
• A composite parameterization of unitary groups, density matrices and subspaces
• Weaker entanglement guarantees stronger entanglement
• Distillability and PPT entanglement of low-rank quantum states
• Entanglement and nonclassicality for multi-mode radiation field states
• Efficient distillation beyond qubits
• Bell inequalities and distillability in N-quantum-bit systems
• Generation and detection of bound entanglement
• Minimal and Maximal Operator Spaces and Operator Systems in Entanglement Theory
• Qubit-qudit states with positive partial transpose
• Distillation protocols: Output entanglement and local mutual information
• Entanglement under restricted operations: Analogy to mixed-state entanglement
• Analysing quantum systems with randomised measurements
• Rank three bipartite entangled states are distillable
• Non-positive-partial-transpose quantum states of rank four are distillable
• Quantum Entanglement: Separability, Measure, Fidelity of Teleportation and Distillation
• Non-full rank bound entangled states satisfying the range criterion
• Multipartite entanglement measures: a review
• Diagonal unitary and orthogonal symmetries in quantum theory
• New classes of n-copy undistillable quantum states with negative partial transposition
• Characterization of distillability of entanglement in terms of positive maps
• Entanglement and Symmetry: A Case Study in Superselection Rules, Reference Frames, and Beyond
• Generalized Circulant Densities and a Sufficient Condition for Separability
• Entanglement Theory and the Quantum Simulation of Many-Body Physics
• Activating Hidden Teleportation Power: Theory and Experiment
• Construction of noisy bound entangled states and the range criterion
• A simple class of bound entangled states based on the properties of the antisymmetric subspace
• Properties and construction of extreme bipartite states having positive partial transpose
• When only two thirds of the entanglement can be distilled
• Positive tensor products of qubit maps and n-tensor-stable positive qubit maps
• Five open problems in quantum information
• Bound entanglement in quantum phase transitions
• Violation of Bell's inequalities implies distillability for N qubits
• Entanglement Distillation; A Discourse on Bound Entanglement in Quantum Information Theory
• Various notions of positivity for bi-linear maps and applications to tri-partite entanglement
• Unextendible product bases, bound entangled states, and the range criterion
• Many body physics from a quantum information perspective
• Gaussian local unitary equivalence of $n$-mode Gaussian states and Gaussian transformations by local operations with classical communication
• Distillation Protocols that Involve Local Distinguishing: Composing Upper and Lower Bounds on Locally Accessible Information
• Inertias of entanglement witnesses
• Reducing Computational Complexity of Quantum Correlations
• Construction of genuine multipartite entangled states
• Norms and Cones in the Theory of Quantum Entanglement
• Beyond the standard entropic inequalities: stronger scalar separability criteria and their applications
• Correlated entanglement distillation and the structure of the set of undistillable states
• Orthogonal product bases of four qubits
• Entanglement monotones and transformations of symmetric bipartite states
• Characterizing entanglement with geometric entanglement witnesses
• Remarks on the equivalence of full additivity and monotonicity for the entanglement cost
• Detecting Quantum Entanglement
• On two-distillable Werner states
• A Decomposition of Separable Werner States
• Catalytic and asymptotic equivalence for quantum entanglement
• Annihilating Entanglement Between Cones
• Halos and undecidability of tensor stable positive maps
• Can entanglement hide behind triangle-free graphs?
• Strong quantum nonlocality: Unextendible biseparability beyond unextendible product basis
• Fidelity between a bipartite state and another one undergoing local unitary dynamics
• Non-distillable entanglement guarantees distillable entanglement
• A complete picture of the four-party linear inequalities in terms of the 0-entropy
• Construction of genuinely entangled multipartite subspaces from bipartite ones by reducing the total number of separated parties
• Witness Operator Provides Better Estimate of the Lower Bound of Concurrence of Bipartite Bound Entangled States in $d_1\otimes d_2$ Dimensional System
• Constructing all entanglement witnesses from density matrices
• Canonical Distillation of Entanglement
• Maximally-Disordered Distillable Quantum States
• On a matrix inequality related to the distillability problem
• Computable entanglement conversion witness that is better than the negativity
• A characterization of entangled two-qubit states via partial-transpose-moments
• Bipartite Bound Entanglement
• Symmetric extendibility of quantum states
• The Decompositions of Werner and Isotropic States
• Fully undistillable quantum states are separable
• Investigating bound entangled two-qutrit states via the best separable approximation
• Experimental single-copy distillation of quantumness from higher-dimensional entanglement
• Two-mode light states before and after delocalized single-photon addition
• Tripartite genuinely entangled states from entanglement-breaking subspaces
• Random covariant quantum channels
• Random private quantum states
• Birkhoff-James Orthogonality in the Trace Norm, with Applications to Quantum Resource Theories
• Retrodiction of measurement outcomes on a single quantum system reveals entanglement with its environment
• The Role of Entanglement in Quantum Communication, and Analysis of the Detection Loophole
• Does connected wedge imply distillable entanglement?
• Conical Designs and Categorical Jordan Algebraic Post-Quantum Theories
• Entanglement Breaking Channels
• Partial transpose of permutation matrices
• The detection power of real entanglement witnesses under local unitary equivalence
• Bound entanglement and distillability of multipartite quantum systems
• New Partial Trace Inequalities and Distillability of Werner States
• State-witness contraction
• Cones with a Mapping Cone Symmetry in the Finite-Dimensional Case
• Genuinely entangled subspaces beyond strongly nonlocal unextendible biseparable bases
• A matrix inequality related to the entanglement distillation problem
• Detection of $d_1\otimes d_2$ Dimensional Bipartite Entangled State: A Graph Theoretical Approach
• Creating two-qudit maximally entangled quantum link through bulk
• Maximal extension on converse monogamy of entanglement for tripartite pure states
• Detecting Entanglement by State Preparation and Local Measurements
• Unveiling NPT bound problem: From Distillability Sets to Inequalities and Multivariable Insights
• Broadcasting of NPT Entanglement in Two Qutrit Systems
• Generalized distillability conjecture and generalizations of Cauchy-Bunyakovsky-Schwarz inequality and Lagrange identity
• Entanglement distillation in terms of a conjectured matrix inequality
• Entanglement - A Queer In The World Of Quantum : Some Perspectives