Consistency and Causality of Interconnected Nonsignaling Resources

Abstract

This paper examines networks of $n$ measuring parties sharing $m$ nonsignaling resources that can be locally wired together: that is, each party follows a scheme to measure the resources in a cascaded fashion with inputs to later resources possibly depending on outputs of earlier-measured ones. A specific framework is provided for studying probability distributions arising in such networks, and this framework is used to directly prove some accepted, but often only implicitly invoked, facts: there is a uniquely determined and well-defined joint probability distribution for the outputs of all resources shared by the parties, and this joint distribution is nonsignaling. It is furthermore shown that is often sufficient to restrict consideration to only extremal nonsignaling resources when considering features and properties of such networks. Finally, the framework illustrates how the physical theory of nonsignaling boxes and local wirings is causal, supporting the applicability of the inflation technique to constrain such models. For an application, we probe the example of (3,2,2) inequalities that witness genuine three-party nonlocality according to the local-operations-shared-randomness definition, and show how all other examples can be derived from that of Mao et al. [Phys. Rev. Lett. 129:150401 (2022)]

31 pages, 4 figures. Minor revisions in V3; close to published version

References in corpus (22)

• Experimental loophole-free violation of a Bell inequality using entangled electron spins separated by 1.3 km
• Significant-loophole-free test of Bell's theorem with entangled photons
• A strong loophole-free test of local realism
• Informational derivation of Quantum Theory
• Non-local correlations as an information theoretic resource
• Event-Ready Bell Test Using Entangled Atoms Simultaneously Closing Detection and Locality Loopholes
• The definition of multipartite nonlocality
• Bell-type inequalities for partial separability in N-particle systems and quantum mechanical violations
• Popescu-Rohrlich correlations as a unit of nonlocality
• Experimentally Generated Randomness Certified by the Impossibility of Superluminal Signals
• Quantum nonlocality based on finite-speed causal influences leads to superluminal signaling
• The Inflation Technique for Causal Inference with Latent Variables
• Device-independent certification of entangled measurements
• Extremal correlations of the tripartite no-signaling polytope
• Constraints on nonlocality in networks from no-signaling and independence
• Dilation of states and processes in operational-probabilistic theories
• Test of Genuine Multipartite Nonlocality
• Experimental Demonstration that No Tripartite-Nonlocal Causal Theory Explains Nature's Correlations
• Experimental demonstration of genuine tripartite nonlocality under strict locality conditions
• Ruling out Bipartite Nonsignaling Nonlocal Models for Tripartite Correlations
• Generalizations of Boxworld
• A Hierarchy of Multipartite Nonlocality and Device-Independent Effect Witnesses