Causality in a qubit-based quantum switch

TL;DR

This paper introduces a qubit-based quantum switch demonstrating that even with indefinite causal order, a clear notion of causality persists, showing independence of atom excitation probabilities under certain conditions.

Contribution

It presents a novel qubit-based quantum switch model that clarifies the concept of causality in superpositions of causal orders.

Findings

Excitation probabilities are independent at short times.

The model clarifies causality in indefinite causal order scenarios.

Photon exchange does not influence excitation probabilities under specific conditions.

Abstract

We introduce a qubit-based version of the quantum switch, consisting in a variation of the Fermi problem. Two qubits start in a superposition state where one qubit is excited and the other in the ground state, but it is undefined which is the excited qubit. Then, after some time, if a photon is detected, we know that it must have experienced an emission by one atom and then an absorption and re-emission by the other one, but the ordering of the emission events by both qubits is undefined. While it is tempting to refer to this scenario as one with indefinite causality or a superposition of causal orders, we show that there is still a precise notion of causality: the probability of excitation of each atom is totally independent of the other one when the times are short enough to prevent photon exchange.