Magic State Distillation from Entangled States

TL;DR

This paper explores how non-local magic states in many-body entangled systems can be distilled using existing protocols, revealing that entanglement and spin squeezing can enhance magic distillation beyond traditional assumptions.

Contribution

It demonstrates that non-local magic states are distillable, introduces spin squeezing as a method to convert non-distillable states, and highlights the importance of diverse entangled inputs for magic distillation.

Findings

Non-local magic states are distillable using Bravyi-Kitaev protocol.

Spin squeezing can convert non-distillable states into distillable ones.

Product input states are atypical among states with distillable magic.

Abstract

Magic can be distributed non-locally in many-body entangled states, such as the low energy states of condensed matter systems. Using the Bravyi-Kitaev magic state distillation protocol, we find that non-local magic is distillable and can improve the distillation outcome. We analyze a few explicit examples and show that spin squeezing can be used to convert non-distillable states into distillable ones. Our analysis also suggests that the conventional product input states assumed by magic distillation protocols are extremely atypical among general states with distillable magic. It further justifies the need for studying a diverse range of entangled inputs that yield magic states with high probability.