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arXiv · 1610.04349

Interferometric computation beyond quantum theory

Andrew J. P. Garner
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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.

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Andrew J. P. Garner. 2016-10-14. Interferometric computation beyond quantum theory. https://doi.org/10.1007/s10701-018-0142-7

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