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

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 $\mathcal{A}$ and $\mathcal{B}$ in a superposition of the two possible orders, $\mathcal{A}$ before $\mathcal{B}$ and $\mathcal{B}$ before $\mathcal{A}$. Experimental implementations of the quantum switch have been challenged by some on the grounds that the operations $\mathcal{A}$ and $\mathcal{B}$ 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.

arXiv commentUpdated version with a slightly modified abstract and conclusion emphasizing more on the exact assumptions and outcomes of the work. The Fig1 has a rewritten legend. Minor details were also added on various parts

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• Identification is Pointless: Quantum Coordinates, Localisation of Events, and the Quantum Hole Argument
• Higher-order Process Matrix Tomography of a passively-stable Quantum SWITCH
• Experimental superposition of time directions
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• Charging a quantum spin network towards Heisenberg-limited precision
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