Causality in a qubit-based quantum switch

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.