Genuinely Nonlocal Product Bases: Classification and Entanglement Assisted Discrimination

Abstract

An orthogonal product basis of a composite Hilbert space is genuinely nonlocal if the basis states are locally indistinguishable across every bipartition. From an operational point of view such a basis corresponds to a separable measurement that cannot be implemented by local operations and classical communication (LOCC) unless all the parties come together in a single location. In this work we classify genuinely nonlocal product bases into different categories. Our classification is based on state elimination property of the set via orthogonality-preserving measurements when all the parties are spatially separated or different subsets of the parties come together. We then study local state discrimination protocols for several such bases with additional entangled resources shared among the parties. Apart from consuming less entanglement than teleportation based schemes our protocols indicate operational significance of the proposed classification and exhibit nontrivial use of genuine entanglement in local state discrimination problem.

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References in corpus (49)

• Bell nonlocality
• Quantum Nonlocality without Entanglement
• Unextendible Product Bases and Bound Entanglement
• Local Distinguishability of Multipartite Orthogonal Quantum States
• Graph States for Quantum Secret Sharing
• Exact and Asymptotic Measures of Multipartite Pure State Entanglement
• Everything You Always Wanted to Know About LOCC (But Were Afraid to Ask)
• Unextendible Product Bases, Uncompletable Product Bases and Bound Entanglement
• Multipartite Nonlocality without Entanglement in Many Dimensions
• Nonlocality, Asymmetry, and Distinguishing Bipartite States
• Distinguishability of the Bell states
• Hiding bits in Bell states
• Impossibility of deleting an unknown quantum state
• Distinguishability and indistinguishability by LOCC
• Local indistinguishability and LOCC monotones
• Local indistinguishability: more nonlocality with less entanglement
• Hiding classical data in multi-partite quantum states
• Optimal local discrimination of two multipartite pure states
• Distinguishing Bipartitite Orthogonal States using LOCC: Best and Worst Cases
• Strong Quantum Nonlocality without Entanglement
• Quantum secret sharing based on local distinguishability
• Distinguishability of maximally entangled states
• Four Locally Indistinguishable Ququad-Ququad Orthogonal Maximally Entangled States
• Bipartite subspaces having no LOCC-distinguishable bases
• Distinguishing Arbitrary Multipartite Basis Unambiguously Using Local Operations and Classical Communication
• Nonlocality of orthogonal product basis quantum states
• A framework for bounding nonlocality of state discrimination
• Distinguishability of complete and unextendible product bases
• Understanding entanglement as resource: locally distinguishing unextendible product bases
• Several nonlocal sets of multipartite pure orthogonal product states
• Local indistinguishability of orthogonal product states
• Limitations on separable measurements by convex optimization
• Distinguishability of Quantum States by Positive Operator-Valued Measures with Positive Partial Transpose
• Nonlocal variables with product states eigenstates
• Entanglement as a resource for local state discrimination in multipartite systems
• The Minimum Size of Unextendible Product Bases in the Bipartite Case (and Some Multipartite Cases)
• Constructing locally indistinguishable orthogonal product bases in an $m\otimes n$ system
• Genuinely entangled subspace with all-encompassing distillable entanglement across every bipartition
• Entanglement Cost of Nonlocal Measurements
• Local Distinguishability of Any Three Quantum States
• Family of bound entangled states on the boundary of Peres set
• Optimal resource states for local state discrimination
• Detecting the local indistinguishability of maximally entangled states
• Entanglement cost of two-qubit orthogonal measurements
• Difficulty of distinguishing product states locally
• Local Distinguishability of Orthogonal Quantum States and Generators of SU(N)
• Constructing unextendible product bases from the old ones
• Local distinguishability of quantum states in multipartite System
• Local distinguishability of quantum states in bipartite systems

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• Nonlocal sets of orthogonal product states in arbitrary multipartite quantum system
• Strong quantum nonlocality with entanglement
• Strongly nonlocal unextendible product bases do exist
• Strong quantum nonlocality in $N$-partite systems
• Thermodynamic Signatures of Genuinely Multipartite Entanglement
• Nonlocality Without Entanglement: Quantum Theory and Beyond
• Nonlocality without entanglement in general multipartite quantum systems
• Multiparty orthogonal product states with minimal genuine nonlocality
• Strong quantum nonlocality for unextendible product bases in heterogeneous systems
• Distinguishability classes, resource sharing, and bound entanglement distribution
• Locally distinguish unextendible product bases by efficiently using entanglement resource
• Multi-copy adaptive local discrimination: Strongest possible two-qubit nonlocal bases
• Local distinguishability based genuinely quantum nonlocality without entanglement
• Bounds on the smallest sets of quantum states with special quantum nonlocality
• Strong quantum nonlocality without entanglement in $n$-partite system with even $n$
• Locally stable sets with minimum cardinality
• Locally distinguishing quantum states with limited classical communication
• Orthogonal product sets with strong quantum nonlocality on plane structure
• Nonlocality of tripartite orthogonal product states
• Activating Strongest Possible Nonlocality from Local Sets: An Elimination Paradigm
• Nonlocality without entanglement: Party asymmetric case
• Strong quantum nonlocality with genuine entanglement in an $N$-qutrit system
• Small set of orthogonal product states with nonlocality
• Local Quantum State Marking
• Entanglement resource theory of quantum channel
• Strong quantum nonlocality: Unextendible biseparability beyond unextendible product basis
• Strong quantum nonlocality from hypercubes
• Genuinely nonlocal sets without entanglement in multipartite systems
• Genuine Activation of Quantum Nonlocality: Stronger Than Local Indistinguishability
• Locally unidentifiable subset of quantum states and its resourcefulness in secret password distribution
• Exploring strong locality : Quantum state discrimination regime and beyond
• Strong quantum nonlocality without entanglement in every $(n-1)$-partition
• Information locking and its resource efficient extraction
• Multi-partite subspaces containing no locally inaccessible information
• On the state space structure of tripartite quantum systems
• Classifying locally distinguishable sets: No activation across bipartitions
• Genuinely entangled subspaces beyond strongly nonlocal unextendible biseparable bases
• Activate genuine nonlocality from distinguishable sets in tripartite systems
• Conclusive Local State Marking: More Nonlocality With No Entanglement
• Strong quantum nonlocality for multipartite entangled states
• Graph connectivity based strong quantum nonlocality with genuine entanglement