Non-adaptive Measurement-based Quantum Computation and Multi-party Bell Inequalities

TL;DR

This paper investigates a non-adaptive version of measurement-based quantum computation, revealing its connection to multipartite Bell inequalities and demonstrating how quantum correlations enable certain computational tasks without adaptivity.

Contribution

It introduces a non-adaptive MQC model, links it to non-classical correlations, and constructs new multipartite Bell inequalities with unique properties.

Findings

Non-adaptive MQC retains certain computational powers.

Explicit links between quantum correlations and computation are established.

New families of multipartite Bell inequalities are derived.

Abstract

Quantum correlations exhibit behaviour that cannot be resolved with a local hidden variable picture of the world. In quantum information, they are also used as resources for information processing tasks, such as Measurement-based Quantum Computation (MQC). In MQC, universal quantum computation can be achieved via adaptive measurements on a suitable entangled resource state. In this paper, we look at a version of MQC in which we remove the adaptivity of measurements and aim to understand what computational abilities still remain in the resource. We show that there are explicit connections between this model of computation and the question of non-classicality in quantum correlations. We demonstrate this by focussing on deterministic computation of Boolean functions, in which natural generalisations of the Greenberger-Horne-Zeilinger (GHZ) paradox emerge; we then explore probabilistic computation, via which multipartite Bell Inequalities can be defined. We use this correspondence to define families of multi-party Bell inequalities, which we show to have a number of interesting contrasting properties.