Unlimited non-causal correlations and their relation to non-locality

TL;DR

This paper explores non-causal correlations that lack a definite causal order, demonstrating that certain natural conditions do not restrict the extent of acausality, thus challenging the identification of principles to limit such correlations.

Contribution

It constructs processes with widespread influence among regions that satisfy natural desiderata but still exhibit unlimited non-causal correlations, highlighting the need for new principles.

Findings

Natural conditions do not limit non-causal correlations

Processes with arbitrary influence among regions can be logically consistent

Results parallel non-local correlations like Ardehali and Svetlichny

Abstract

Non-causal correlations certify the lack of a definite causal order among localized space-time regions. In stark contrast to scenarios where a single region influences its own causal past, some processes that distribute non-causal correlations satisfy a series of natural desiderata: logical consistency, linear and reversible dynamics, and computational tameness. Here, we present such processes among arbitrary many regions where each region influences every other but itself, and show that the above desiderata are altogether insufficient to limit the amount of "acausality" of non-causal correlations. This leaves open the identification of a principle that forbids non-causal correlations. Our results exhibit qualitative and quantitative parallels with the non-local correlations due to Ardehali and Svetlichny.