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

Ämin Baumeler1,2,3, Amin Shiraz Gilani1,4, and Jibran Rashid5

1Institute for Quantum Optics and Quantum Information (IQOQI-Vienna), Austrian Academy of Sciences, 1090 Vienna, Austria
2Faculty of Physics, University of Vienna, 1090 Vienna, Austria
3Facoltà indipendente di Gandria, 6978 Gandria, Switzerland
4Department of Computer Science, University of Maryland, College Park, Maryland 20742, USA
5School of Mathematics and Computer Science, Institute of Business Administration, Karachi, Pakistan

### 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 $\textit{insufficient to limit the amount of "acausality"}$ of non-causal correlations. This leaves open the identification of a principle that forbids non-causal correlations. Our results exhibit $\textit{qualitative and quantitative parallels}$ with the non-local correlations due to Ardehali and Svetlichny.

It is generally assumed that events $A,B,C,\dots$ in space-time cannot influence each other in a cyclic way, i.e., if $A$ influences $B$ ($A$ is in the causal past of $B$), then $B$ cannot influence $A$. This logic, however, breaks down if one assumes quantum theory to hold locally without further assumptions on the causal order among the events: There exist processes where each party (event) influences every other but itself. In previous studies it has been shown that such processes comply with various desiderata: They are logically consistent without restricting free choice, they can be embedded in reversible dynamics, and they are computationally tame. This work reports that causal order is also not enforced by increasing the number of parties. Even more so, this work presents processes among any number of parties where causal order is violated by a larger degree the more parties are considered. Remarkably, these non-causal processes are constructed out of the Ardheali-Svetlichny functions that display the same qualitative and quantitative features for non-local correlations.

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### Cited by

[1] Ravi Kunjwal and Ämin Baumeler, "How quantum nonlocality without entanglement witnesses classical processes without causal order", arXiv:2202.00440.

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