Three Party Quantum Networks Created by Quantum Cloning

TL;DR

This paper explores the creation of three-party quantum networks via quantum cloning, analyzing their properties, distinguishability from other networks, and quantifying their correlations using advanced inequalities and entanglement measures.

Contribution

It introduces methods to generate and analyze three-party quantum networks through cloning, extending Finner inequalities and applying mutual information and squashed entanglement for characterization.

Findings

Certain states in cloned networks cannot be distinguished by standard Finner inequalities.

Extended Finner inequalities with more observers improve distinguishability.

Tripartite mutual information and squashed entanglement effectively quantify network correlations.

Abstract

With progress in quantum technologies, the field of quantum networks has emerged as an important area of research. In the last few years, there has been substantial progress in understanding the correlations present in quantum networks. In this article, we study cloning as a prospective method to generate three party quantum networks which can be further used to create larger networks. We analyze various quantum network topologies that can be created using cloning transformations. This would be useful in the situations wherever the availability of entangled pairs is limited. In addition to that we focus on the problem of distinguishing networks created by cloning from those which are created by distributing independently generated entangled pairs. We find that there are several states which cannot be distinguished using the Finner inequalities in the standard way. For such states, we propose an extension to the existing Finner inequality for triangle networks by further increasing the number of observers from three to four or six depending on the network topology. This takes into account the additional correlations that exist in the case of cloned networks. In the last part of the article we have used tripartite mutual information to distinguish cloned networks from networks created by independent sources and have further used squashed entanglement as a measure to quantify the amount of dependence in the cloned networks.