Experimental entanglement of temporal order

TL;DR

This paper demonstrates experimentally that certain correlations in nature cannot be explained by theories assuming definite causal order, using entangled temporal order and a Bell-like inequality.

Contribution

It presents the first experimental violation of a Bell-like inequality for indefinite temporal order outside of quantum formalism, challenging classical causal assumptions.

Findings

Experimental outcomes violate the Bell-like inequality.

Indefinite temporal order is demonstrated beyond quantum formalism.

Correlations incompatible with locality and definite causal order are observed.

Abstract

The study of causal relations has recently been applied to the quantum realm, leading to the discovery that not all physical processes have a definite causal structure. While indefinite causal processes have previously been experimentally shown, these proofs relied on the quantum description of the experiments. Yet, the same experimental data could also be compatible with definite causal structures within different descriptions. Here, we present the first demonstration of indefinite temporal order outside of quantum formalism. We show that our experimental outcomes are incompatible with a class of generalised probabilistic theories satisfying the assumptions of locality and definite temporal order. To this end, we derive physical constraints (in the form of a Bell-like inequality) on experimental outcomes within such a class of theories. We then experimentally invalidate these theories by violating the inequality using entangled temporal order. This provides experimental evidence that there exist correlations in nature which are incompatible with the assumptions of locality and definite temporal order.