Optimal thermalization under indefinite causal order with identical and asymmetric baths
Phys. Rev. A 113, 052445 – Published 20 May, 2026
DOI: https://doi.org/10.1103/zbgc-wdrk
Abstract
Indefinite causal order (ICO), in which the order of quantum operations is placed in a coherent superposition, has been demonstrated to enhance various information-processing tasks. Here we investigate its impact on the thermodynamic processes generated by thermalizing quantum channels. We consider a two-level system interacting with two thermal baths under a quantum SWITCH, with the channel order controlled coherently by an ancillary qubit. We derive closed-form expressions for the effective inverse temperature of the postselected system state for both identical and distinct bath temperatures, and identify the control-qubit parameters that maximize heating or cooling. Our analysis reveals how the diagonal and coherent components of the control-qubit state contribute separately to the temperature shift, and how their interplay enables departures from the thermal response attainable under protocols with a definite causal order within the thermodynamic setting considered here. Bath asymmetry enhances these effects, while reduced purity of the control qubit state suppresses them. These results provide a systematic framework for assessing SWITCH-based thermalization in the setting of indefinite causal order, and identify control-qubit coherence as a tunable resource.
