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.

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]

References in corpus (9)

• A derivation of quantum theory from physical requirements
• Higher-order interference and single-system postulates characterizing quantum theory
• Generalised phase kick-back: the structure of computational algorithms from physical principles
• Quantum Theory, namely the pure and reversible theory of information
• Deriving Grover's lower bound from simple physical principles
• A toy model for quantum mechanics
• Bounds on the power of proofs and advice in general physical theories
• The complex and quaternionic quantum bit from relativity of simultaneity on an interferometer
• Quaternionic Computing

Cited by in corpus (13)

• General probabilistic theories: An introduction
• A no-go theorem on the nature of the gravitational field beyond quantum theory
• Accessible fragments of generalized probabilistic theories, cone equivalence, and applications to witnessing nonclassicality
• Quantum computation is the unique reversible circuit model for which bits are balls
• Post-quantum steering is a stronger-than-quantum resource for information processing
• Quantum Computing without Quantum Computers: Database Search and Data Processing Using Classical Wave Superposition
• On defining the Hamiltonian beyond quantum theory
• On the impossibility of coin-flipping in generalized probabilistic theories via discretizations of semi-infinite programs
• Correlations constrained by composite measurements
• Compositional resource theories of coherence
• Quantum Darwinism and the spreading of classical information in non-classical theories
• Simulating all multipartite non-signalling channels via quasiprobabilistic mixtures of local channels in generalised probabilistic theories
• Spacetime symmetries and the qubit Bloch ball: a physical derivation of finite dimensional quantum theory and the number of spatial dimensions