Purifying GHZ States Using Degenerate Quantum Codes

TL;DR

This paper demonstrates that degenerate quantum codes enable more noise-tolerant purification of depolarized GHZ states among multiple players, outperforming existing one-way schemes in quantum information processing.

Contribution

The study introduces three new purification schemes for GHZ states using degenerate quantum codes, showing improved noise tolerance over previous methods.

Findings

Schemes tolerate more noise than existing methods

Degenerate quantum codes are effective for GHZ state purification

Enhanced robustness in quantum information tasks

Abstract

Degenerate quantum codes are codes that do not reveal the complete error syndrome. Their ability to conceal the complete error syndrome makes them powerful resources in certain quantum information processing tasks. In particular, the most error-tolerant way to purify depolarized Bell states using one-way communication known to date involves degenerate quantum codes. Here we study three closely related purification schemes for depolarized GHZ states shared among $m \geq 3$ players by means of degenerate quantum codes and one-way classical communications. We find that our schemes tolerate more noise than all other one-way schemes known to date, further demonstrating the effectiveness of degenerate quantum codes in quantum information processing.