Nonlocality Without Entanglement: Quantum Theory and Beyond

Abstract

Quantum nonlocality without entanglement (Q-NWE) encapsulates nonlocal behavior of multipartite product states as they may entail global operation for optimal decoding of the classical information encoded within. Here we show that the phenomena of NWE is not specific to quantum theory only, rather a class of generalized probabilistic theories can exhibit such behavior. In fact several manifestations of NWE, e.g., asymmetric local discrimination, suboptimal local discrimination, notion of separable but locally unimplementable measurement arise generically in operational theories other than quantum theory. We propose a framework to compare the strength of NWE in different theories and show that such behavior in quantum theory is limited, suggesting a specific topological feature of quantum theory, namely, the continuity of state space structure. Our work adds profound foundational appeal to the study of NWE phenomena along with its information theoretic relevance.

arXiv comment5+6 pages, Comments are welcome

References in corpus (46)

• Bell nonlocality
• Quantum Nonlocality without Entanglement
• Hidden Variables and the Two Theorems of John Bell
• On the reality of the quantum state
• Information Causality as a Physical Principle
• Informational derivation of Quantum Theory
• Graph States for Quantum Secret Sharing
• Probabilistic theories with purification
• Everything You Always Wanted to Know About LOCC (But Were Afraid to Ask)
• A limit on nonlocality in any world in which communication complexity is not trivial
• The uncertainty principle determines the non-locality of quantum mechanics
• A derivation of quantum theory from physical requirements
• A generalized no-broadcasting theorem
• Nonlocality, Asymmetry, and Distinguishing Bipartite States
• Hiding bits in Bell states
• A glance beyond the quantum model
• Local orthogonality as a multipartite principle for quantum correlations
• No quantum advantage for nonlocal computation
• A Combinatorial Approach to Nonlocality and Contextuality
• Hiding classical data in multi-partite quantum states
• Simple explanation of the quantum violation of a fundamental inequality
• Distinguishability of quantum states under restricted families of measurements with an application to quantum data hiding
• Strong Quantum Nonlocality without Entanglement
• Quantum secret sharing based on local distinguishability
• Limited Holism and Real-Vector-Space Quantum Theory
• Limits on non-local correlations from the structure of the local state space
• The structure of reversible computation determines the self-duality of quantum theory
• Generalized Probabilistic Theories Without the No-Restriction Hypothesis
• Degree of Complementarity Determines the Nonlocality in Quantum Mechanics
• Genuinely Nonlocal Product Bases: Classification and Entanglement Assisted Discrimination
• Nonlocal variables with product states eigenstates
• Nonlocality of the Aharonov-Bohm Effect
• A Return to the Optimal Detection of Quantum Information
• Classical information storage in an $n$-level quantum system
• No-hypersignaling principle
• Steering, incompatibility, and Bell inequality violations in a class of probabilistic theories
• Difficulty of distinguishing product states locally
• Limited preparation contextuality in quantum theory and its relation to the Cirel'son bound
• Bounding quantum contextuality with lack of third-order intereference
• Almost quantum correlations violate the no-restriction hypothesis
• Information and communication in polygon theories
• Reversibility and the structure of the local state space
• Perfect Discrimination of Non-Orthogonal Separable Pure States on Bipartite System in General Probabilistic Theory
• The principle of information symmetry constrains the state-space in any physical theory
• On affine maps on non-compact convex sets and some characterizations of finite-dimensional solid ellipsoids
• Several foundational and information theoretic implications of Bell's theorem

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• Mutually Unbiased Balanced Functions & Generalized Random Access Codes
• Self-testing nonlocality without entanglement
• Activating Strongest Possible Nonlocality from Local Sets: An Elimination Paradigm
• Multiphoton Bell-type inequality: a tool to unearth nonlocality of continuous variable quantum optical systems
• Local Quantum State Marking
• Classical analogue of quantum superdense coding and communication advantage of a single quantum system
• Quantum nonlocality without entanglement depending on nonzero prior probabilities in optimal unambiguous discrimination
• Timelike correlations and quantum tensor product structure
• Multi-system measurements in generalized probabilistic theories and their role in information processing
• Quantum Advantage: A Single Qubit's Experimental Edge in Classical Data Storage
• Bell Nonlocality and the Reality of Quantum Wavefunction
• On the state space structure of tripartite quantum systems
• Annihilating and creating nonlocality without entanglement by postmeasurement information
• Online identification of symmetric pure states
• Conclusive Local State Marking: More Nonlocality With No Entanglement
• Bipartite polygon models: entanglement classes and their nonlocal behaviour
• Locking and unlocking of quantum nonlocality without entanglement in local discrimination of quantum states
• Global versus Local Discrimination of Locally Implementable Multipartite Unitaries
• Graph connectivity based strong quantum nonlocality with genuine entanglement