Correlations in Quantum Network Topologies Created with Cloning

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 will help us to create larger networks. We analyze various quantum network topologies that can be created using cloning transformations. This would be useful in 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 that are created by distributing independently generated entangled pairs. We find that there are several states that 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 use tripartite mutual information to distinguish cloned networks from networks created by independent sources and further use squashed entanglement as a measure to quantify the amount of dependence in the cloned networks.