Causal orders, quantum circuits and spacetime: distinguishing between definite and superposed causal orders

TL;DR

This paper explores the differences between definite and superposed causal orders in quantum circuits and spacetime, showing that superpositions of causal orders are linked to superposed gravitational fields and proposing methods to distinguish them.

Contribution

It introduces a framework to differentiate between classical and quantum superpositions of causal orders in spacetime, including new observables for experimental distinction.

Findings

Current quantum switch experiments do not exhibit superpositions of causal orders.

Superpositions of causal orders are only possible with superposed gravitational fields.

Two observables can distinguish between classical and superposed causal order implementations.

Abstract

We study the notion of causal orders for the cases of (classical and quantum) circuits and spacetime events. We show that every circuit can be immersed into a classical spacetime, preserving the compatibility between the two causal structures. Using the process matrix formalism, we analyse the realisations of the quantum switch using 4 and 3 spacetime events in classical spacetimes with fixed causal orders, and the realisation of a gravitational switch with only 2 spacetime events that features superpositions of different gravitational field configurations and their respective causal orders. We show that the current quantum switch experimental implementations do not feature superpositions of causal orders between spacetime events, and that these superpositions can only occur in the context of superposed gravitational fields. We also discuss a recently introduced operational notion of an event, which does allow for superpositions of respective causal orders in flat spacetime quantum switch implementations. We construct two observables that can distinguish between the quantum switch realisations in classical spacetimes, and gravitational switch implementations in superposed spacetimes. Finally, we discuss our results in the light of the modern relational approach to physics.