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

Ämin Baumeler; Amin Shiraz Gilani; Jibran Rashid

doi:10.22331/q-2022-03-29-673

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

Ämin Baumeler^1,2,3, Amin Shiraz Gilani^1,4, 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

Published:	2022-03-29, volume 6, page 673
Eprint:	arXiv:2104.06234v3
Doi:	https://doi.org/10.22331/q-2022-03-29-673
Citation:	Quantum 6, 673 (2022).

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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.

Featured image: This figure shows various correlation sets for $n$ parties. Bi-causal inequalities bound the set of correlations that are obtained by partitioning the $n$ parties in two sets, and where only one set can influence the other. Correlations that lie outside this set are genuinely multi-party non-causal. The processes reported in this work establish the non-causal correlations $G_n$. The degree of violation of the respective bi-causal inequality increases with $n$. More so, the processes do not require any quantum-theoretic features, and are therefore obtained with classical processes.

Popular summary

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.

► BibTeX data

@article{Baumeler2022unlimitednoncausal,
  doi = {10.22331/q-2022-03-29-673},
  url = {https://doi.org/10.22331/q-2022-03-29-673},
  title = {Unlimited non-causal correlations and their relation to non-locality},
  author = {Baumeler, {\"{A}}min and Gilani, Amin Shiraz and Rashid, Jibran},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {6},
  pages = {673},
  month = mar,
  year = {2022}
}

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Cited by

[1] Ravi Kunjwal and Ämin Baumeler, "Trading Causal Order for Locality", Physical Review Letters 131 12, 120201 (2023).

[2] Alessandro Capurso, "The Universe as a Telecommunication Network", Journal of Physics: Conference Series 2533 1, 012045 (2023).

[3] Alessandro Capurso, "The Potential of a Thick Present through Undefined Causality and Non-Locality", Entropy 24 3, 410 (2022).

[4] Eleftherios-Ermis Tselentis and Ämin Baumeler, "Admissible Causal Structures and Correlations", PRX Quantum 4 4, 040307 (2023).

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