# Interferometric Computation Beyond Quantum Theory

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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.

## Keywords

Post-quantum computation Interference Deutsch–Jozsa algorithm Generalized probabilistic theories Mach–Zehnder interferometer Spekkens’ toy model## Notes

### Acknowledgements

The author is very grateful for illuminating discussions and correspondence with Felix Binder, Oscar Dahlsten, Daniela Frauchiger, Nana Liu, Markus Müller, Vlatko Vedral, and Benjamin Yadin. The author is grateful for financial support from the John Templeton Foundation and the Foundational Questions Institute. This research was undertaken whilst the author was funded by the Engineering and Physical Sciences Research Council (UK) at the University of Oxford. Some of concepts in this article have also appeared as part of the author’s DPhil thesis [31].

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