Non-Markovian refrigeration and heat flow in the quantum switch

The quantum switch has seen multiple applications in quantum information and thermodynamical tasks. As it is constructed by placing two quantum channels in a coherent superposition of alternating causal orders, a composition known as indefinite causal order, these enhancements are often attributed to this indefinite causality and coherent superposition. However, as recent works have shown that the quantum switch also features non-Markovian effects that can contribute to the enhancement of communication capacities and work extraction, we attempt to show in this work that these non-Markovian effects can also enhance heat extraction tasks. In particular, we compare the quantum switch to the superposition of independent channels where two quantum channels are placed in a superposition, which have no non-Markovian effects, and show that the quantum switch can only outperform the superposition of independent channels in the prethermalization regimes, which also depends on the presence and amount of non-Markovianity. Our work reveals that positive heat extraction is still possible even when the working body is at a higher temperature than the interacting baths, allowing us to construct a refrigeration cycle utilizing this feature.