Protocols for creating and distilling multipartite GHZ states with Bell pairs

TL;DR

This paper presents a heuristic dynamic programming approach to optimize protocols for creating and distilling high-quality GHZ states from imperfect Bell pairs in quantum networks, improving performance over previous methods.

Contribution

It introduces a flexible, optimized framework for GHZ state creation and purification using non-local stabilizer measurements, applicable to any number of parties and entangled pairs.

Findings

Protocols outperform previous methods without decoherence and noise.

The algorithms are adaptable to any number of parties and entangled pairs.

Enhanced GHZ state quality for quantum communication and computation.

Abstract

The distribution of high-quality Greenberger-Horne-Zeilinger (GHZ) states is at the heart of many quantum communication tasks, ranging from extending the baseline of telescopes to secret sharing. They also play an important role in error-correction architectures for distributed quantum computation, where Bell pairs can be leveraged to create an entangled network of quantum computers. We investigate the creation and distillation of GHZ states out of non-perfect Bell pairs over quantum networks. In particular, we introduce a heuristic dynamic programming algorithm to optimize over a large class of protocols that create and purify GHZ states. All protocols considered use a common framework based on measurements of non-local stabilizer operators of the target state (i.e., the GHZ state), where each non-local measurement consumes another (non-perfect) entangled state as a resource. The new protocols outperform previous proposals for scenarios without decoherence and local gate noise. Furthermore, the algorithms can be applied for finding protocols for any number of parties and any number of entangled pairs involved.