Relativistic Causality vs. No-Signaling as the limiting paradigm for correlations in physical theories

TL;DR

This paper investigates how relativistic causality constrains no-signaling conditions in multi-party quantum experiments, revealing that only subsets of these conditions are necessary for causality and exploring implications for cryptography and non-locality.

Contribution

It demonstrates that the usual no-signaling constraints are not always necessary for causality, introduces a new causal bilocal model, and redefines free-choice in multi-party Bell scenarios.

Findings

Causality imposes only a subset of no-signaling conditions depending on space-time coordinates.

Explicit attack shows security can be compromised under certain relativistic configurations.

New Svetlichny-type inequality distinguishes causal bilocal models from quantum correlations.

Abstract

The no-signaling constraints state that the probability distribution of the outputs of any subset of parties is independent of the inputs of the complementary set; here we re-examine these to see how they arise from relativistic causality. We show that while the usual no-signaling constraints are sufficient, in general they are not necessary to ensure that a theory does not violate causality. Depending on the exact space-time coordinates of the measurement events in a multi-party Bell experiment, causality only imposes a subset of the usual no-signaling conditions. After revisiting the derivation of the two-party no-signaling constraints, we consider the three-party Bell scenario and characterise a space-time region in which a subset of the no-signaling conditions is sufficient to preserve causality. Secondly, we examine the implications for device-independent cryptography against an eavesdropper constrained only by the laws of relativity. We show an explicit attack in certain measurement configurations on a family of protocols based on the n-party Mermin inequalities that were previously proven secure under the old no-signaling conditions. We then show that security of two-party protocols can also be compromised when the eavesdropper's measurement configuration is not constrained. The monogamy of non-local correlations that underpin their use in secrecy can also be broken in certain space-time configurations. Thirdly, we inspect the notion of free-choice and propose a definition of free-choice in the multi-party Bell experiment. We then re-examine the question whether quantum correlations may admit explanations by finite speed superluminal influences. Finally, we study genuine multiparty non-locality and present a new class of causal bilocal models. We propose a new Svetlichny-type inequality that is satisfied by the causal bilocal model and show its violation within quantum theory.