Comparing the quantum switch and its simulations with energetically-constrained operations

TL;DR

This paper investigates the quantum switch's ability to outperform its simulations under energy constraints, highlighting potential energetic advantages of quantum causal superpositions in physical implementations.

Contribution

It introduces an energetic model for the quantum switch, demonstrating its superiority over simulated versions when energy is limited, and explores implications for quantum causality and energy efficiency.

Findings

Quantum switch outperforms simulations at fixed energy levels.

Energy constraints reveal distinguishability between processes.

Potential energetic benefits of quantum causal superpositions are identified.

Abstract

Quantum mechanics allows processes to be superposed, leading to a genuinely quantum lack of causal structure. For example, the process known as the quantum switch applies two operations ${\cal A}$ and ${\cal B}$ in a superposition of the two possible orders, ${\cal A}$ before ${\cal B}$ and ${\cal B}$ before ${\cal A}$. Experimental implementations of the quantum switch have been challenged by some on the grounds that the operations ${\cal A}$ and ${\cal B}$ were implemented more than once, thereby simulating indefinite causal order rather than actually implementing it. Motivated by this debate, we consider a situation in which the quantum operations are physically described by a light-matter interaction model. While for our model the two processes are indistinguishable in the infinite energy regime, restricting the energy available for the implementation of the operations introduces imperfections, which allow one to distinguish processes using different number of operations. We consider such an energetically-constrained scenario and compare the quantum switch to one of its natural simulations, where each operation is implemented twice. Considering a commuting-vs-anticommuting unitary discrimination task, we find that within our model the quantum switch performs better, for some fixed amount of energy, than its simulation. In addition to the known computational or communication advantages of causal superpositions, our work raises new questions about their potential energetic advantages.