Distillation of Greenberger-Horne-Zeilinger states by combinatorial methods

TL;DR

This paper establishes a lower bound on the rate at which GHZ states can be distilled from pure multipartite states using LOCC, employing combinatorial methods inspired by matrix multiplication algorithms, with a focus on asymptotically vanishing error.

Contribution

It introduces a novel combinatorial approach to GHZ state distillation that achieves asymptotically vanishing error, improving upon previous algebraic complexity methods.

Findings

Derived a lower bound on GHZ distillation rate

Developed a protocol with asymptotically vanishing error

Connected quantum information theory with combinatorial matrix methods

Abstract

We prove a lower bound on the rate of Greenberger-Horne-Zeilinger states distillable from pure multipartite states by local operations and classical communication (LOCC). Our proof is based on a modification of a combinatorial argument used in the fast matrix multiplication algorithm of Coppersmith and Winograd. Previous use of methods from algebraic complexity in quantum information theory concerned transformations with stochastic local operations and classical operation (SLOCC), resulting in an asymptotically vanishing success probability. In contrast, our new protocol works with asymptotically vanishing error.