Interferometric computation beyond quantum theory

TL;DR

This paper generalizes interferometric computation beyond quantum theory, exploring how alternative theories like quaternionic quantum theory can perform distributed calculations, contrasting with classical and other non-quantum models.

Contribution

It introduces a generalized interferometric framework for computation applicable to theories beyond quantum mechanics, identifying quaternionic quantum theory as a viable candidate.

Findings

Quaternionic quantum theory supports interferometric computation.

Classical hidden variable models can perform similar computations under certain restrictions.

Box-world does not support this type of interferometric computation.

Abstract

There are quantum solutions for computational problems that make use of interference at some stage in the algorithm. These stages can be mapped into the physical setting of a single particle travelling through a many-armed interferometer. There has been recent foundational interest in theories beyond quantum theory. Here, we present a generalized formulation of computation in the context of a many-armed interferometer, and explore how theories can differ from quantum theory and still perform distributed calculations in this set-up. We shall see that quaternionic quantum theory proves a suitable candidate, whereas box-world does not. We also find that a classical hidden variable model first presented by Spekkens [Phys. Rev. A, 75:3:32100, 2007] can also be used for this type of computation due to the epistemic restriction placed on the hidden variable.