Discord in relation to resource states for measurement-based quantum computation

TL;DR

This paper establishes minimal criteria for resource states in measurement-based quantum computation (MBQC), arguing discord-free states are not resources and clarifying misconceptions about their computational capabilities.

Contribution

It introduces minimal resource criteria for MBQC states and refutes claims that discord-free states can serve as resources, clarifying their limitations.

Findings

Discord-free states cannot be resources for MBQC according to the proposed criteria.

Arguments suggesting discord-free states can implement Shor's algorithm are invalid.

The paper clarifies the distinction between universal and non-universal resource states.

Abstract

We consider the issue of what should count as a resource for measurement-based quantum computation (MBQC). While a state that supports universal quantum computation clearly should be considered a resource, universality should not be necessary given the existence of interesting, but less computationally-powerful, classes of MBQCs. Here, we propose minimal criteria for a state to be considered a resource state for MBQC. Using these criteria, we explain why discord-free states cannot be resources for MBQC, contrary to recent claims [Hoban et al., arXiv:1304.2667v1]. Independently of our criteria, we also show that the arguments of Hoban et al., if correct, would imply that Shor's algorithm (for example) can be implemented by measuring discord-free states.