Quantum Nonlocality without Entanglement

Abstract

We exhibit an orthogonal set of product states of two three-state particles that nevertheless cannot be reliably distinguished by a pair of separated observers ignorant of which of the states has been presented to them, even if the observers are allowed any sequence of local operations and classical communication between the separate observers. It is proved that there is a finite gap between the mutual information obtainable by a joint measurement on these states and a measurement in which only local actions are permitted. This result implies the existence of separable superoperators that cannot be implemented locally. A set of states are found involving three two-state particles which also appear to be nonmeasurable locally. These and other multipartite states are classified according to the entropy and entanglement costs of preparing and measuring them by local operations.

27 pages, Latex, 6 ps figures. To be submitted to Phys. Rev. A. Version 2: 30 pages, many small revisions and extensions, author added. Version 3: Proof in Appendix D corrected, many small changes; final version for Phys. Rev. A Version 4: Report of Popescu conjecture modified

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• Mixed-state entanglement and distillation: is there a ``bound'' entanglement in nature?
• Unextendible Product Bases and Bound Entanglement
• No-cloning of Orthogonal States in Composite Systems

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• LOCC distinguishable orthogonal product states with least entanglement resource
• Vector Representations of Graphs and Distinguishing Quantum Product States with One-way LOCC
• Local indistinguishability and incompleteness of entangled orthogonal bases: Method to generate two-element locally indistinguishable ensembles
• Convolution algebra of superoperators and nonseparability witnesses for quantum operations
• Multi-system measurements in generalized probabilistic theories and their role in information processing
• All multipartite entanglements are quantum coherences in locally distinguishable bases
• Optimal estimation of a physical observable's expectation value for pure states
• Unambiguous discrimination of sequences of quantum states
• The Adaptive Classical Capacity of a Quantum Channel, or Information Capacities of Three Symmetric Pure States in Three Dimensions
• Quantifying entanglement from the geometric perspective
• A new entanglement measure based on the total concurrence
• Achieving the Multi-parameter Quantum Cramér-Rao Bound with Antiunitary Symmetry
• Quantum Discord and Logarithmic Negativity in the Generalized n-qubit Werner State
• Algebraic Probability-Theoretic Characterization of Quantum Correlations
• Detectors for local discrimination of sets of generalized Bell states
• Getting Information on Independently Prepared Quantum States -- When Are Individual Measurements as Powerful as Joint Measurements?
• On Quantum Statistical Inference, II
• Strongest quantum nonlocality in $N$-partite systems
• A consolidating review of Spekkens' toy theory
• Optimal supplier of single-error-type entanglement via coherent-state transmission
• Local cloning of genuine entangled states of three qubit
• Local approximation of multipartite quantum measurements
• Locality of Orthogonal Product States via Multiplied Copies
• Choi-Defined Resource Theories
• Quantifying the performance of bidirectional quantum teleportation
• One-Shot Static Entanglement Cost of Bipartite Quantum Channels
• Local Decoherence-free Macroscopic Quantum states
• Optimal discrimination of quantum states on a two-dimensional Hilbert space by local operations and classical communication
• Local Unambiguous Discrimination with Remaining Entanglement
• Comment on "Entanglement transformation between two-qubit mixed states by LOCC" [Phys. Lett. A 373 (2009) 3610]
• Self-testing composite measurements and bound entangled state in a single quantum network
• Information locking and its resource efficient extraction
• The causal structure of Minkowski space time: possibilities and impossibilities of secure positioning
• Unextendible product operator basis
• Time-extensive classical and quantum correlations in thermal machines
• Bound on optimal local discrimination of multipartite quantum states
• Continuous decomposition of quantum measurements via Hamiltonian feedback
• Remote extraction and destruction of spread qubit information
• One-way deficit of SU(2) invariant states
• Efficient Implementation and the Product State Representation of Numbers
• Strong nonlocal sets of UPB
• Witnessing nonseparability of bipartite quantum operations
• Impossibility Criterion for Obtaining Pure Entangled States From Mixed States By Purifying Protocols
• Bipartite quantum state discrimination and decomposable entanglement witness
• Special unextendible entangled bases with continuous integer cardinality
• Local simultaneous state discrimination
• Any four orthogonal ququad-ququad maximally entangled states are locally markable
• Exploration of nonlocalities in ensembles consisting of bipartite quantum states
• Entanglement witness and multipartite quantum state discrimination
• Multipartite Generalization of Geometric measure of Discord
• Correlations, Bell Inequality Violation & Quantum Entanglement
• Studies on the Role of Entanglement in Mixed-state Quantum Computation
• Identifying families of multipartite states with non-trivial local entanglement transformations
• Second Law of Entanglement Dynamics for the Non-Asymptotic Regime
• Interpolatability distinguishes LOCC from separable von Neumann measurements
• On the state space structure of tripartite quantum systems
• The Independence of Distinguishability and the Dimension of the System
• Quantum Coherence and Distinguishability as Complementary Resources: A Resource-Theoretic Perspective from Wave-Particle Duality
• Entanglement witness and nonlocality in confidence of measurement from multipartite quantum state discrimination
• Locally distinguishing a maximally entangled basis using shared entanglement
• Attainability of quantum state discrimination bounds with collective measurements on finite copies
• Bell Nonlocality and the Reality of Quantum Wavefunction
• Optimal discrimination of quantum sequences
• Global restrictions under local state discrimination
• Analyzing the free states of one quantum resource theory as resource states of another
• Classifying locally distinguishable sets: No activation across bipartitions
• Unextendible and strongly uncompletable product bases
• Limits on the Observable Dynamics of Mixed States
• Multi-partite subspaces containing no locally inaccessible information
• Quantum Reactivity: A Measure of Quantum Correlation
• The construction of sets with strong quantum nonlocality using fewer states
• Gaussian multipartite quantum discord from classical mutual information
• Theoretical investigations of quantum correlations in NMR multiple-pulse spin-locking experiments
• Quantum Correlations in NMR systems
• Statistics of leading digits leads to unification of quantum correlations
• Extended necessary condition for local operations and classical communication: Tight bound for all measurements
• On the Physical Explanation for Quantum Computational Speedup
• Topics in Estimation of Quantum Channels
• Coherence measure of ensembles with nonlocality without entanglement
• Entanglement of Assistance as a measure of multiparty entanglement
• Power of unentangled measurements on two antiparallel spins
• Quantum change point and entanglement distillation
• Entanglement cost hierarchies in quantum fragmented mixed states
• Local cloning of CAT states
• Genuinely entangled subspaces beyond strongly nonlocal unextendible biseparable bases
• Certifying the dimensionality of any quantum channel with minimal assumptions
• Max- Relative Entropy of Entanglement, alias Log Robustness
• Circuit cutting with classical side information
• The existence of distinguishable bases in three-dimensional subspaces of qutrit-qudit systems under one-way local operations and classical communication
• Witness to detect quantum correlation of bipartite states in arbitrary dimension
• Approximate and ensemble local entanglement transformations for multipartite states
• Tractable measure of nonclassical correlation using density matrix truncations
• Dynamics of quantum discord in the purification process
• A Measure of Stregth of an Unextendible Product Basis
• A note on quantum Bell nonlocality and quantum entanglement for high dimensional quantum systems
• Constructing unextendible product bases from multiqubit ones
• Limitation for linear maps in a class for detection and quantification of bipartite nonclassical correlation
• The construction and local distinguishability of multiqubit unextendible product bases
• Remotely prepared entanglement: a quantum web page
• Quantum non-locality co-exists with locality
• Small sets of locally indistinguishable orthogonal maximally entangled states
• Minimal-error quantum state discrimination versus robustness of entanglement:More indistinguishability with less entanglement
• Stochastic approximate state conversion for entanglement and general quantum resource theories
• Mathematical framework for detection and quantification of nonclassical correlation
• Orthogonality Broadcasting and Quantum Position Verification
• Annihilating and creating nonlocality without entanglement by postmeasurement information
• Multipartite Monogamy of Entanglement for Three Qubit States
• On Classical Teleportation and Classical Nonlocality
• Novel methods to construct nonlocal sets of orthogonal product states in arbitrary bipartite high-dimensional system
• Few-body entanglement manipulation
• Information acquisition, scrambling, and sensitivity to errors in quantum chaos
• The Local Orthogonality between Quantum States and Entanglement Decomposition
• Classical-to-quantum non-signalling boxes
• Entanglement - A Queer In The World Of Quantum : Some Perspectives
• A thorough introduction to non-relativistic matrix mechanics in multi-qudit systems with a study on quantum entanglement and quantum quantifiers
• Genuine network quantum nonlocality and self-testing
• Reinforcement Learning with Neural Networks for Quantum Multiple Hypothesis Testing
• Non-Bilocal Measurement via Entangled State
• On the Implication of Bell's Probability Distribution and Proposed Experiments of Quantum Measurement
• Application of Ramsey theory to localization of set of product states via multicopies
• Quantifying measurement-induced nonbilocal correlation
• Trade-off between Information Gain and Disturbance in Local Discrimination of Entangled Quantum States
• Maximal Holevo quantity based on weak measurements
• One-Way LOCC Indistinguishable Lattice States via Operator Structures
• A Non-Convex Optimization Strategy for Computing Convex-Roof Entanglement
• Conditions for local transformations between sets of quantum states
• Conclusive Local State Marking: More Nonlocality With No Entanglement
• Strong quantum nonlocality for multipartite entangled states
• Locking and unlocking of quantum nonlocality without entanglement in local discrimination of quantum states
• Parallel repetition of local simultaneous state discrimination
• Purification and time-reversal deny entanglement in LOCC-distinguishable orthonormal bases
• Progress in the study of the (non)existence of genuinely unextendible product bases
• Global versus Local Discrimination of Locally Implementable Multipartite Unitaries
• Single-shot antidistinguishability of unitary operations
• Structure of quantum measurements implementable with one round of classical communication
• Entanglement Superactivation in Multiphoton Distillation Networks
• Gleason's Theorem for a Qubit as Part of a Composite System
• Thermodynamics of bipartite entanglement
• Graph theoretic quantum contextuality and unextendible Product Bases
• The entangling power of non-entangling channels
• Activate genuine nonlocality from distinguishable sets in tripartite systems
• Useful variants and perturbations of completely entangled subspaces and spans of unextendible product bases
• Nonlocal sets of orthogonal multipartite product states with less members
• Approaching the Multiparameter Quantum Cramér-Rao Bound via Classical Correlation and Entangling Measurements
• Graph connectivity based strong quantum nonlocality with genuine entanglement
• Some Entanglement Survives Most Measurements
• General Classes of Impossible Operations through the Existence of Incomparable States
• Geometric Measure of Entanglement and Schmidt Decomposition of Multipartite Systems
• Online identification of symmetric pure states
• NMR Quantum Information Processing and Entanglement
• Multi-player quantum data hiding by nonlocal quantum state ensembles