Entanglement Purification of Hypergraph States

TL;DR

This paper develops optimized entanglement purification protocols for hypergraph states, enhancing efficiency and adaptability, which are crucial for quantum information processing involving complex multi-qubit entanglement.

Contribution

The paper introduces systematic graphical reformulation and optimization of hypergraph state purification protocols, including adaptive schemes and efficiency improvements.

Findings

Protocols are optimized for ordering of parties.

Adaptive measurement schemes improve purification success.

Fewer noisy state copies are needed for target fidelity.

Abstract

Entanglement purification describes a primitive in quantum information processing, where several copies of noisy quantum states are distilled into few copies of nearly-pure states of high quality via local operations and classical communication. Especially in the multiparticle case, the task of entanglement purification is complicated, as many inequivalent forms of pure state entanglement exist and purification protocols need to be tailored for different target states. In this paper we present optimized protocols for the purification of hypergraph states, which form a family of multi-qubit states that are relevant from several perspectives. We start by reformulating an existing purification protocol in a graphical language. This allows for systematical optimization and we present improvements in three directions. First, one can optimize the sequences of the protocol with respect to the ordering of the parties. Second, one can use adaptive schemes, where the measurement results obtained within the protocol are used to modify the protocols. Finally, one can improve the protocol with respect to the efficiency, requiring fewer copies of noisy states to reach a certain target state.