Experimental entanglement of temporal order

Giulia Rubino1,2, Lee A. Rozema1, Francesco Massa1, Mateus Araújo1,3, Magdalena Zych4, Časlav Brukner1,3, and Philip Walther1

1Vienna Center for Quantum Science and Technology (VCQ), Faculty of Physics, University of Vienna, Boltzmanngasse 5, Vienna A-1090, Austria
2Quantum Engineering Technology Labs, H. H. Wills Physics Laboratory and Department of Electrical & Electronic Engineering, University of Bristol, Bristol BS8 1FD, United Kingdom
3Institute for Quantum Optics & Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, Vienna A-1090, Austria
4Centre for Engineered Quantum Systems, School of Mathematics and Physics, The University of Queensland, St Lucia, QLD 4072, Australia

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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.

In all standard physical theories, causal relations among events are inferred from a background temporal order, which is assumed as fixed. This assumption requires rigorous experimental tests which should be independent of the particular theory under study. Conversely, it was recently discovered that quantum mechanics permits the existence of processes without a predefined temporal order. Thus far, experimental evidence for this effect relied on the quantum description of the experiments. In this work we go beyond previous results by experimentally violating a Bell inequality for temporal order, which is fulfilled by a large class of theories in which a condition on locality and a predefined order of events are assumed. We thus provide the first proof of the indefiniteness of the temporal order without presupposing the quantum description of the experiment. Furthermore, within quantum theory, our results demonstrate for the first time quantum entanglement between two causal processes.

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