Indefinite Causal Orders from Superpositions in Time

TL;DR

This paper introduces a scheme leveraging superpositions in time to realize indefinite causal orders, exemplified by the Quantum SWITCH, without requiring exotic quantum gravity effects, but using naturally fuzzy temporal phenomena.

Contribution

It presents a novel method to achieve indefinite causal order using superpositions in time based on a space-time-symmetric formalism, including a specific implementation.

Findings

Recovered the Quantum SWITCH as a special case

Demonstrated implementation using atomic decay phenomena

Showed no need for quantum gravity effects

Abstract

Treating the time of an event as a quantum variable, we derive a scheme in which superpositions in time are used to perform operations in an indefinite causal order. We use some aspects of a recently developed space-time-symmetric formalism of events. We propose a specific implementation of the scheme and recover the Quantum SWITCH, where quantum operations are performed in an order which is entangled with the state of a control qubit. Our scheme does not rely on any exotic quantum gravitational effect, but instead on phenomena which are naturally fuzzy in time, such as the decay of an excited atom.