Topological Quantum Teleportation and Superdense Coding -- Without Braiding

Abstract

We present the teleportation and superdense coding protocols for a family of anyon theories coming from Tambara-Yamagami categories, of which the lowest rank theories describe Ising anyons. In contrast to the usual approach to anyonic computation, we relax the requirement that we should be able to braid anyons. This is motivated by the goal of designing basic protocols that require less control over quasiparticles, and which may therefore be amenable to realisation in near-term systems. Since these implementations are braid-free, they are also compatible with Majorana modes on a 1d quantum wire.