Interferometric computation beyond quantum theory
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.
Cite
@article{arxiv.1610.04349,
title = {Interferometric computation beyond quantum theory},
author = {Andrew J. P. Garner},
journal= {arXiv preprint arXiv:1610.04349},
year = {2018}
}
Comments
AAM, appearing in special issue on the Foundational Aspects of Quantum Information in Foundations of Physics. Some of the concepts presented here are also in the author's DPhil thesis [University of Oxford, Hilary 2015]