Reassessing thermodynamic advantage from indefinite causal order

TL;DR

This paper critically examines whether indefinite causal order offers genuine thermodynamic advantages, concluding that simple causally ordered processes often outperform more complex indefinite order schemes in thermodynamic tasks.

Contribution

The study demonstrates that indefinite causal order is not necessary for thermodynamic advantages, showing simpler processes can outperform quantum switches in relevant tasks.

Findings

Causally ordered processes can outperform quantum switches in thermodynamics

Non-Markovian interactions can replicate advantages without indefinite causal order

Extreme indefinite causal order scenarios do not provide additional benefits

Abstract

Indefinite causal order is a key feature involved in the study of quantum higher order transformations. Recently, intense research has been focused on possible advantages related to the lack of definite causal order of quantum processes. Quite often the quantum switch is claimed to provide advantages in information-theoretic and thermodynamic tasks. We address here the question whether indefinite causal order is a resource for quantum thermodynamics. Inspired by previous results in the literature, we show that indefinite causal order is not necessary for the reported increase in free energy and ergotropy. More specifically, we show that a simple causally ordered process, which replaces the system's state with a new one before the final measurement, outperforms the quantum switch in all thermodynamic tasks considered so far. We further show that a similar advantage can be also achieved without completely discarding system, if we allow for non-Markovian interactions between the system and an environment. We extend the analysis to more extreme examples of indefinite causal order, showing that they do not provide an advantage either. Finally, we discuss a possible way to study the advantages that may arise from indefinite causal order in a general scenario.