Qutrit Magic State Distillation Tight in Some Directions

TL;DR

This paper introduces new four-qutrit magic state distillation protocols that expand the distillable region and are tight to the boundary of undistillable states, advancing understanding of quantum universality and non-stabilizer states.

Contribution

It presents novel four-qutrit distillation schemes that improve the known distillable region and identify states enabling universality linked to contextuality.

Findings

Distillation protocols tight to the boundary of undistillable states for some classes.

Identification of a state with maximal sum-negativity as a fixed point.

Establishment of a connection between state distillability and quantum contextuality.

Abstract

Magic state distillation is a crucial component in the leading approaches to implementing universal fault tolerant quantum computation, with existing protocols for both qubit and higher dimensional systems. Early work focused on determining the region of distillable states for qubit protocols, yet comparatively little is known about which states can be distilled and with what distillable region for d>2. Here we focus on d=3 and present new four-qutrit distillation schemes that improve upon the known distillable region, and achieve distillation tight to the boundary of undistillable states for some classes of state. As a consequence of recent results, this implies that there is a family of quantum states that enable universality if and only if they exhibit contextuality with respect to stabilizer measurements. We also identify a new routine whose fixed point is a magic state with maximal sum-negativity i.e., it is maximally non-stabilizer in a specific sense.