Unified Framework for Correlations in Terms of Local Quantum Observables

Abstract

We provide a unified framework for nonsignalling quantum and classical multipartite correlations, allowing all to be written as the trace of some local (quantum) measurements multiplied by an operator. The properties of this operator define the corresponding set of correlations.We then show that if the theory is such that all local quantum measurements are possible, one obtains the correlations corresponding to the extension of Gleason's Theorem to multipartite systems. Such correlations coincide with the quantum ones for one and two parties, but we prove the existence of a gap for three or more parties.

4 pages, final version

References in corpus (6)

• Information Causality as a Physical Principle
• A convergent hierarchy of semidefinite programs characterizing the set of quantum correlations
• Bounding the set of quantum correlations
• A generalized no-broadcasting theorem
• A glance beyond the quantum model
• Non-locality distillation and post-quantum theories with trivial communication complexity

Cited by in corpus (53)

• Bell nonlocality
• Quantum correlations with no causal order
• Specker's Parable of the Over-protective Seer: A Road to Contextuality, Nonlocality and Complementarity (PLUS AN ERRATUM)
• Entanglement witnesses: construction, analysis and classification
• Generalized Probability Theories: What determines the structure of quantum theory?
• Limits on non-local correlations from the structure of the local state space
• Quantifying Bell: the Resource Theory of Nonclassicality of Common-Cause Boxes
• Deriving quantum theory from its local structure and reversibility
• A physical approach to Tsirelson's problem
• Bell inequalities with no quantum violation and unextendible product bases
• No-signaling Principle Can Determine Optimal Quantum State Discrimination
• Tight Bell inequalities with no quantum violation from qubit unextendible product bases
• Information Causality and Extremal Tripartite Correlations
• Simulating all non-signalling correlations via classical or quantum theory with negative probabilities
• Dimension of physical systems, information processing, and thermodynamics
• Quantum correlations are stronger than all nonsignaling correlations produced by n-outcome measurements
• Quantifying non-classical and beyond-quantum correlations in the unified operator formalism
• Witnessing nonclassical multipartite states
• Memory cost of temporal correlations
• A formalism for steering with local quantum measurements
• Post-quantum steering is a stronger-than-quantum resource for information processing
• Unlimited non-causal correlations and their relation to non-locality
• Information Content of Systems as a Physical Principle
• Constructions of genuinely entangled multipartite states with applications to local hidden variables (LHV) and states (LHS) models
• Testing quantum theory by generalizing noncontextuality
• Typical local measurements in generalised probabilistic theories: emergence of quantum bipartite correlations
• The principle of information symmetry constrains the state-space in any physical theory
• Correlation Measure Equivalence in Dynamic Causal Structures of Quantum Gravity
• Towards correlation self-testing of quantum theory in the adaptive Clauser-Horne-Shimony-Holt game
• Bounding the persistency of the nonlocality of W states
• Probabilistic models on contextuality scenarios
• Evaluation of two different entanglement measures on a bound entangled state
• Theory of Quantum Gravity Information Processing
• Generalizations of Boxworld
• Bell measurement rules out supraquantum correlations
• Timelike correlations and quantum tensor product structure
• The relation between Hardy's non-locality and violation of Bell inequality
• On characterising assemblages in Einstein-Podolsky-Rosen scenarios
• Algebraic Probability-Theoretic Characterization of Quantum Correlations
• Postquantum steering
• Smallest state spaces for which bipartite entangled quantum states are separable
• Smooth Entropy Transfer of Quantum Gravity Information Processing
• Spin-bounded correlations: rotation boxes within and beyond quantum theory
• The incompatibility of quantum channels in general probabilistic theories
• Classification of no-signaling correlations and the guess your neighbor's input game
• Semi-device-independent information processing with spatiotemporal degrees of freedom
• Joint system quantum descriptions arising from local quantumness
• Quantum correlations cannot be reproduced with a finite number of measurements in any no-signaling theory
• Spacetime symmetries and the qubit Bloch ball: a physical derivation of finite dimensional quantum theory and the number of spatial dimensions
• Limitations imposed by complementarity
• Quantum information transfer using weak measurements and any non-product resource state
• Violation of no signaling in higher order quantum measure theories
• Hybrid no-signaling-quantum correlations