Temporal nonlocality from indefinite causal orders

TL;DR

This paper investigates the possibility of temporal nonlocality using indefinite causal orders, proposing a test that avoids common assumptions and exploring retrocausal interpretations to understand nonlocal correlations in time.

Contribution

It introduces a novel, assumption-free protocol to test temporal nonlocality via indefinite causal orders and discusses its physical interpretation through retrocausality.

Findings

The proposed test can detect temporal nonlocal correlations without problematic assumptions.

Indefinite causal orders can violate temporal locality principles.

Retrocausal influences provide a plausible explanation for observed correlations.

Abstract

A temporal counterpart to Bell nonlocality would intuitively refer to the presence of non-classical correlations between timelike-separated events. The hypothesis of temporal nonlocality has received recent support in the literature, and its existence would likely influence the future development of physical theories. This paper shows how Adlam's principle of temporal locality can be violated within a protocol involving indefinite causal orders. While the derivations of Leggett-Garg inequalities or the temporal CHSH inequality are said to involve problematic assumptions preventing a targeted probing of a well-defined notion of temporal nonlocality, the present test is free from such worries. However, it is shown that the test, in its current formulation, fails to be fully model-independent. We provide several considerations regarding the physicality of ICOs that could help alleviate this drawback. In the present work, a specific physical interpretation of ICOs in terms of retrocausal influences would explain the presence of temporally nonlocal correlations. It is argued that, as the physical underpinnings of temporal nonlocality might also account for standard Bell nonlocality, focusing on the former as a consequence of ICOs might support under-explored strategies to make sense of the latter.