title: Qutrit Magic State Distillation Tight in Some Directions.
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 nonstablizer in a specific sense.
authors.affiliation: Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada.|Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada.
authors.forename: Hillary
authors.initials: H
authors.lastname: Dawkins
authors.affiliation: Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada.|Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada.
authors.forename: Mark
authors.initials: M
authors.lastname: Howard