A framework for bounding nonlocality of state discrimination

Abstract

We consider the class of protocols that can be implemented by local quantum operations and classical communication (LOCC) between two parties. In particular, we focus on the task of discriminating a known set of quantum states by LOCC. Building on the work in the paper "Quantum nonlocality without entanglement" [BDF+99], we provide a framework for bounding the amount of nonlocality in a given set of bipartite quantum states in terms of a lower bound on the probability of error in any LOCC discrimination protocol. We apply our framework to an orthonormal product basis known as the domino states and obtain an alternative and simplified proof that quantifies its nonlocality. We generalize this result for similar bases in larger dimensions, as well as the "rotated" domino states, resolving a long-standing open question [BDF+99].

33 pages, 7 figures, 1 table

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Cited by in corpus (62)

• Strong Quantum Nonlocality without Entanglement
• Nonlocality of orthogonal product basis quantum states
• Several nonlocal sets of multipartite pure orthogonal product states
• Local indistinguishability of orthogonal product states
• Limitations on separable measurements by convex optimization
• Genuinely Nonlocal Product Bases: Classification and Entanglement Assisted Discrimination
• Strong Quantum Nonlocality without Entanglement in Multipartite Quantum Systems
• Constructing locally indistinguishable orthogonal product bases in an $m\otimes n$ system
• Genuinely entangled subspace with all-encompassing distillable entanglement across every bipartition
• Practical distributed quantum information processing with LOCCNet
• Difficulty of distinguishing product states locally
• Distinguishability classes, resource sharing, and bound entanglement distribution
• Locally distinguish unextendible product bases by efficiently using entanglement resource
• Non-commutativity and Local Indistinguishability of Quantum States
• Relation between Quantum Coherence and Quantum Entanglement in Quantum Measurements
• Asymptotic State Discrimination and a Strict Hierarchy in Distinguishability Norms
• Optimal sequential measurements for bi-partite state discrimination
• Locally distinguishing quantum states with limited classical communication
• Genuine activation of nonlocality: From locally available to locally hidden information
• Genuine hidden nonlocality without entanglement: from the perspective of local discrimination
• Self-testing nonlocality without entanglement
• Building one-time memories from isolated qubits
• Activating Strongest Possible Nonlocality from Local Sets: An Elimination Paradigm
• Dense Coding with Locality Restriction for Decoder: Quantum Encoders vs. Super-Quantum Encoders
• Tight asymptotic bounds on local hypothesis testing between a pure bipartite state and the white noise state
• General approach to quantum channel impossibility by local operations and classical communication
• Distinguishing multipartite orthogonal product states by LOCC with entanglement as a resource
• Privacy Amplification in the Isolated Qubits Model
• Local discrimination of generalized Bell states via commutativity
• Limitations of Classically-Simulable Measurements for Quantum State Discrimination
• Separability and entanglement in superpositions of quantum states
• Local approximation for perfect discrimination of quantum states
• Single-shot security for one-time memories in the isolated qubits model
• Multiple-copy state discrimination of noisy qubits
• When asymptotic LOCC offers no advantage over finite LOCC
• Unextendible entangled bases and more nonlocality with less entanglement
• Incompatibility of local measurements provide advantage in local quantum state discrimination
• Nonlocal quantum state ensembles and quantum data hiding
• Necessary condition for local quantum operations and classical communication with extensive violation by separable operations
• Locally unidentifiable subset of quantum states and its resourcefulness in secret password distribution
• Local distinguishability of quantum states in multipartite System
• Bipartite discrimination of independently prepared quantum states as a counterexample to a parallel repetition conjecture
• Multi-system measurements in generalized probabilistic theories and their role in information processing
• Devising local protocols for multipartite quantum measurements
• The Round Complexity of Local Operations and Classical Communication (LOCC) in Random-Party Entanglement Distillation
• Bipartite quantum state discrimination and decomposable entanglement witness
• Algebraic and algorithmic frameworks for optimized quantum measurements
• Local approximation of multipartite quantum measurements
• Multi-partite subspaces containing no locally inaccessible information
• Quantum Coherence and Distinguishability as Complementary Resources: A Resource-Theoretic Perspective from Wave-Particle Duality
• Local simultaneous state discrimination
• Entanglement witness and nonlocality in confidence of measurement from multipartite quantum state discrimination
• Interpolatability distinguishes LOCC from separable von Neumann measurements
• Extended necessary condition for local operations and classical communication: Tight bound for all measurements
• Small sets of locally indistinguishable orthogonal maximally entangled states
• Circuit cutting with classical side information
• Orthogonality Broadcasting and Quantum Position Verification
• Local certification of unitary operations
• Strong quantum nonlocality for multipartite entangled states
• Conclusive Local State Marking: More Nonlocality With No Entanglement
• Parallel repetition of local simultaneous state discrimination
• Multi-player quantum data hiding by nonlocal quantum state ensembles