Graph Picture of Linear Quantum Networks and Entanglement

TL;DR

This paper introduces a graph-based framework for analyzing and designing linear quantum networks (LQNs) to generate multipartite entanglement, providing new tools and criteria for entanglement analysis and network construction.

Contribution

It presents a novel mapping of LQNs to graphs and introduces the perfect matching diagram (PM diagram) for analyzing and designing entangled quantum networks.

Findings

PM diagrams include all entanglement information

Rigorous criteria for LQN entanglement are established

LQNs for fundamental N-partite entangled states are constructed

Abstract

The indistinguishability of quantum particles is widely used as a resource for the generation of entanglement. Linear quantum networks (LQNs), in which identical particles linearly evolve to arrive at multimode detectors, exploit the indistinguishability to generate various multipartite entangled states by the proper control of transformation operators. However, it is challenging to devise a suitable LQN that carries a specific entangled state or compute the possible entangled state in a given LQN as the particle and mode number increase. This research presents a mapping process of arbitrary LQNs to graphs, which provides a powerful tool for analyzing and designing LQNs to generate multipartite entanglement. We also introduce the perfect matching diagram (PM diagram), which is a refined directed graph that includes all the essential information on the entanglement generation by an LQN. The PM diagram furnishes rigorous criteria for the entanglement of an LQN and solid guidelines for designing suitable LQNs for the genuine entanglement. Based on the structure of PM diagrams, we compose LQNs for fundamental $N$-partite genuinely entangled states.