Popescu-Rohrlich correlations as a unit of nonlocality

Abstract

A set of nonlocal correlations that have come to be known as a PR box suggest themselves as a natural unit of nonlocality, much as a singlet is a natural unit of entanglement. We present two results relevant to this idea. One is that a wide class of multipartite correlations can be simulated using local operations on PR boxes only. We show this with an explicit scheme, which has the interesting feature that the number of PR boxes required is related to the computational resources necessary to represent a function defining the multipartite box. The second result is that there are quantum multipartite correlations, arising from measurements on a cluster state, that cannot be simulated with n PR boxes, for any n.

5 pages, no figures. v2: minor modifications

References in corpus (3)

• No Signalling and Quantum Key Distribution
• Non-local correlations as an information theoretic resource
• Quantum entanglement can be simulated without communication

Cited by in corpus (90)

• Bell nonlocality
• From Bell's Theorem to Secure Quantum Key Distribution
• Probabilistic theories with purification
• The resource theory of quantum reference frames: manipulations and monotones
• General properties of Nonsignaling Theories
• Quantum-Bayesian Coherence: The No-Nonsense Version
• Local orthogonality as a multipartite principle for quantum correlations
• A Combinatorial Approach to Nonlocality and Contextuality
• Quantum from principles
• Quasi-quantization: classical statistical theories with an epistemic restriction
• Introduction to the book "Quantum Theory: Informational Foundations and Foils"
• The completeness of quantum theory for predicting measurement outcomes
• Geometry of the set of quantum correlations
• Efficient quantum key distribution secure against no-signalling eavesdroppers
• The Inflation Technique for Causal Inference with Latent Variables
• On nonlocality as a resource theory and nonlocality measures
• Extremal correlations of the tripartite no-signaling polytope
• Observation of tunable Popescu-Rohrlich correlations through post-selection of a gaussian state
• Limits on non-local correlations from the structure of the local state space
• Quantifying Bell: the Resource Theory of Nonclassicality of Common-Cause Boxes
• Quantum Mechanical Realization of a Popescu-Rohrlich Box
• Cloning and Broadcasting in Generic Probabilistic Theories
• The communication complexity of non-signaling distributions
• Identifying Nonconvexity in the Sets of Limited-Dimension Quantum Correlations
• Quantifying the nonlocality of GHZ quantum correlations by a bounded communication simulation protocol
• Maximally nonlocal theories cannot be maximally random
• Bound non-locality and activation
• Exploring the Local Orthogonality Principle
• The local content of all pure two-qubit states
• Information Causality and Extremal Tripartite Correlations
• Violations of locality and free choice are equivalent resources in Bell experiments
• Quantifying multipartite nonlocality via the size of the resource
• Quantum-Bayesian Coherence
• Simulation of partial entanglement with nonsignaling resources
• Bounds for Non-Locality Distillation Protocols
• Quantum Correlations and Quantum Non-locality: a review and a few new ideas
• Information and communication in polygon theories
• Bipartite Units of Non-Locality
• Quantum Bell Inequalities from Macroscopic Locality
• Bounds on the power of proofs and advice in general physical theories
• Neither Contextuality nor Nonlocality Admits Catalysts
• A comonadic view of simulation and quantum resources
• Beating no-go theorems by engineering defects in quantum spin models
• Extendability in the Sheaf-theoretic Approach: Construction of Bell Models from Kochen-Specker Models
• Bell inequalities with one bit of communication
• No nonlocal box is universal
• Information-based measure of nonlocality
• Quantum bounds on multiplayer linear games and device-independent witness of genuine tripartite entanglement
• Contextuality in multipartite pseudo-telepathy graph games
• The local content of bipartite qubit correlations
• Ruling out Bipartite Nonsignaling Nonlocal Models for Tripartite Correlations
• Complementarity of genuine multipartite non-locality
• Simulation of equatorial von Neumann measurements on GHZ states using nonlocal resources
• Bell-type inequalities for non-local resources
• Categories of Empirical Models
• Bounding quantum theory with the exclusivity principle in a two-city experiment
• Quantum Nonlocality: Multi-copy Resource Inter-convertibility & Their Asymptotic Inequivalence
• Test to separate quantum theory from non-signaling theories
• Is Communication Complexity Physical?
• Distillation of Multi-Party Non-Locality With and Without Partial Communication
• PR-box correlations have no classical limit
• Continuous-variable supraquantum nonlocality
• Multi-User Non-Locality Amplification
• Closing Bell: Boxing black box simulations in the resource theory of contextuality
• Quantum value for a family of $I_{3322}$-like Bell functionals
• One-time Pad Encryption Model for Non-local Correlations
• Asymptotically Optimal Adversarial Strategies for the Probability Estimation Framework
• Algebra of Nonlocal Boxes and the Collapse of Communication Complexity
• Non-Local Box Complexity and Secure Function Evaluation
• Generalized Tsirelson Inequalities, Commuting-Operator Provers, and Multi-Prover Interactive Proof Systems
• Stabilizer states and local realism
• Trading Permutation Invariance for Communication in Multi-Party Non-Locality Distillation
• Quantum and Superquantum Nonlocal Correlations
• Uncertainty principle as post-quantum nonlocality witness for continuous variable multi-mode scenario
• Pseudo-telepathy games and genuine NS k-way nonlocality using graph states
• The Hardy's nonlocality argument
• Classical communication cost of a bipartite quantum channel assisted by non-signalling correlations
• Single trusted qubit is necessary and sufficient for quantum realisation of extremal no-signaling correlations
• Investigation of quantum entanglement simulation by random variables theories augmented by either classical communication or nonlocal effects
• Universal Bell Correlations Do Not Exist
• High-performance parallel classical scheme for simulating shallow quantum circuits
• Operational nonlocality
• Computational Perspectives on Bell Inequalities and Many-body Quantum Correlations
• Hybrid no-signaling-quantum correlations
• Non-Locality Distillation is Impossible for Isotropic Quantum Systems
• Consistency and Causality of Interconnected Nonsignaling Resources
• Quantum inputs in the prepare-and-measure scenario and stochastic teleportation
• Quantitative and Optimal Device-Independent Lower Bounds on Detection Efficiency
• No nonlocal box with uniform outputs is universal
• Indefinite global time