Computation in a general physical setting

TL;DR

This paper explores the computational capabilities of various physical theories within the generalized probabilistic framework, comparing quantum theory to others and establishing bounds and conjectures about their computational power.

Contribution

It derives new bounds on computational abilities of theories with n-local tomography and generalised superpositions, and refines a conjecture on quantum simulation of other theories.

Findings

New bounds on computational power for theories with n-local tomography

Refined conjecture on quantum simulation of generalized probabilistic theories

Established links between computational conjectures and delegated computation

Abstract

The computational abilities of theories within the generalised probabilistic theory framework has been the subject of much recent study. Such investigations aim to gain an understanding of the possible connections between physical principles and computation. Moreover, comparing and contrasting the computational properties of quantum theory with other operationally-sensible theories could shed light on the strengths and limitations of quantum computation. This paper reviews and extends some of these results, deriving new bounds on the computational ability of theories satisfying n-local tomography, and theories in which states are represented as generalised superpositions. It moreover provides a refined version of the conjecture that a quantum computer can simulate the computation in any theory within a certain sub-class of generalised probabilistic theories with at most polynomial overhead. The paper ends by describing an important relation between this conjecture and delegated computation, similar to the relation between quantum non-locality and device-independent cryptography.