Phase estimation for a single-mode photon influenced by completely thermalizing channels with indefinite causal order

Abstract

Phase estimation for a single-mode photon is investigated when the photon is influenced by two completely thermalizing channels with indefinite causal order, where a phase shift takes place between the two channels. Accuracy of the phase estimation is evaluated in terms of the quantum Fisher information. It is shown that although the channels completely destruct the phase information of the photon, the phase estimation is possible with the assistance of the indefinite causal order.