Interconversion of Nonlocal Correlations

Abstract

In this paper we study the correlations that arise when two separated parties perform measurements on systems they hold locally. We restrict ourselves to those correlations with which arbitrarily fast transmission of information is impossible. These correlations are called nonsignaling. We allow the measurements to be chosen from sets of an arbitrary size, but promise that each measurement has only two possible outcomes. We find the structure of this convex set of nonsignaling correlations by characterizing its extreme points. Taking an information-theoretic view, we prove that all of these extreme correlations are interconvertible. This suggests that the simplest extremal nonlocal distribution (called a PR box) might be the basic unit of nonlocality. We also show that this unit of nonlocality is sufficient to simulate all quantum states when measured with two outcome measurements.

7 pages + appendix, single column

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 (60)

• Bell nonlocality
• Quantum Resource Theories
• The resource theory of quantum reference frames: manipulations and monotones
• Specker's Parable of the Over-protective Seer: A Road to Contextuality, Nonlocality and Complementarity (PLUS AN ERRATUM)
• Local orthogonality as a multipartite principle for quantum correlations
• Geometry of the set of quantum correlations
• Efficient quantum key distribution secure against no-signalling eavesdroppers
• On nonlocality as a resource theory and nonlocality measures
• Extremal correlations of the tripartite no-signaling polytope
• Limits on non-local correlations from the structure of the local state space
• Nonlocality in many-body quantum systems detected with two-body correlators
• Cloning and Broadcasting in Generic Probabilistic Theories
• The communication complexity of non-signaling distributions
• Identifying Nonconvexity in the Sets of Limited-Dimension Quantum Correlations
• Maximally nonlocal theories cannot be maximally random
• Entanglement and thermodynamics in general probabilistic theories
• Exploring the Local Orthogonality Principle
• Free randomness amplification using bipartite chain correlations
• Violations of locality and free choice are equivalent resources in Bell experiments
• Quantifying multipartite nonlocality via the size of the resource
• Contextuality and nonlocality in 'no signaling' theories
• Simulation of partial entanglement with nonsignaling resources
• Quantum Correlations and Quantum Non-locality: a review and a few new ideas
• Bell Inequalities From No-Signalling Distributions
• Strong monogamies of no-signaling violations for bipartite correlation Bell inequalities
• Information and communication in polygon theories
• Bipartite Units of Non-Locality
• Bell Inequalities with Communication Assistance
• Quantum Bell Inequalities from Macroscopic Locality
• Parts and Wholes. An Inquiry into Quantum and Classical Correlations
• Neither Contextuality nor Nonlocality Admits Catalysts
• A comonadic view of simulation and quantum resources
• Bell inequalities with one bit of communication
• Geometric Decompositions of Bell Polytopes with Practical Applications
• Simple conditions constraining the set of quantum correlations
• Non-Local Network Coding in Interference Channels
• Ruling out Bipartite Nonsignaling Nonlocal Models for Tripartite Correlations
• The local content of bipartite qubit correlations
• Bell-type inequalities for non-local resources
• Quantum Nonlocality: Multi-copy Resource Inter-convertibility & Their Asymptotic Inequivalence
• Amplifying the randomness of weak sources correlated with devices
• Neural Network Approach to the Simulation of Entangled States with One Bit of Communication
• Measurement uncertainty from no-signaling and non-locality
• Closing Bell: Boxing black box simulations in the resource theory of contextuality
• Device-independent characterizations of a shared quantum state independent of any Bell inequalities
• Device-independent and semi-device-independent entanglement certification in broadcast Bell scenarios
• Characterizing quantum correlations in the nonsignaling framework
• Nonlocal games, synchronous correlations, and Bell inequalities
• Limitations on device independent key secure against non signaling adversary via the squashed non-locality
• One-time Pad Encryption Model for Non-local Correlations
• Quantum value for a family of $I_{3322}$-like Bell functionals
• Certifying nonlocal properties of noisy quantum operations
• The Role of Entanglement in Quantum Communication, and Analysis of the Detection Loophole
• Asymptotically Optimal Adversarial Strategies for the Probability Estimation Framework
• Error-free interconversion of nonlocal boxes
• Bit Commitment from Weak Non-Locality
• The Binary-Outcome Detection Loophole
• The Hardy's nonlocality argument
• Investigation of quantum entanglement simulation by random variables theories augmented by either classical communication or nonlocal effects
• Chained Clauser-Horne-Shimony-Holt inequality for Hardy's ladder test of nonlocality