Singlet Generation in Mixed State Quantum Networks

TL;DR

This paper investigates how to generate singlet states in quantum networks with mixed entangled states, establishing conditions for success and developing protocols to optimize entanglement distribution.

Contribution

It extends entanglement percolation methods to mixed states, introduces new distillation and preprocessing protocols, and demonstrates their integration into complex quantum network architectures.

Findings

Singlets can be generated if initial states have a specific form.

Generalized entanglement percolation protocols are effective for mixed states.

Preprocessing strategies improve success probabilities of entanglement distribution.

Abstract

We study the generation of singlets in quantum networks with nodes initially sharing a finite number of partially entangled bipartite mixed states. We prove that singlets between arbitrary nodes in such networks can be created if and only if the initial states connecting the nodes have a particular form. We then generalize the method of entanglement percolation, previously developed for pure states, to mixed states of this form. As part of this, we find and compare different distillation protocols necessary to convert groups of mixed states shared between neighboring nodes of the network into singlets. In addition, we discuss protocols that only rely on local rules for the efficient connection of two remote nodes in the network via entanglement swapping. Further improvements of the success probability of singlet generation are developed by using particular forms of `quantum preprocessing' on the network. This includes generalized forms of entanglement swapping and we show how such strategies can be embedded in regular and hierarchical quantum networks.