Circulating Genuine Multiparty Entanglement in Quantum Network

TL;DR

This paper introduces a deterministic method for generating genuine multiparty entangled states in quantum networks of arbitrary size through entanglement circulation, optimizing over unitary operators and initial resource states.

Contribution

It presents a novel entanglement circulation scheme that optimizes unitary operations and resource states to generate multipartite entanglement in quantum networks of any size.

Findings

GGM of the output state equals the minimum GGM of initial resources.

Optimal creation of six-qubit entangled states based on resource availability.

Ordered systems show periodic GGM variation; disordered systems maintain low, constant entanglement.

Abstract

We propose a deterministic scheme of generating genuine multiparty entangled states in quantum networks of arbitrary size having various geometric structures -- we refer to it as entanglement circulation. The procedure involves optimization over a set of two-qubit arbitrary unitary operators and the entanglement of the initial resource state. We report that the set of unitary operators that maximize the genuine multipartite entanglement quantified via generalized geometric measure (GGM) is not unique. We prove that the GGM of the resulting state of arbitrary qubits coincides with the minimum GGM of the initial resource states. By fixing the output state as the six-qubit one, we find the optimal way to create such states according to the available resource. Moreover, we show that the method proposed here can be implemented by using logic gates, or by using the time dynamics of realizable spin Hamiltonians. In case of an ordered system, GGM varies periodically with time while the evolution via disordered models lead to a low but constant multipartite entanglement in outputs at a critical time, which decreases exponentially with the increase of the strength of the disorder.