Characterizing non-classical correlations between multiple systems from two points of view: resource cost and additivity

Abstract

Non-classical correlations between multiple systems lie at the heart of notable features of quantum systems, especially in application to quantum information processing. However, their structures and properties are not yet well understood because of the complexity of multipartite quantum systems. In this thesis, we look into non-classical correlations between multiple systems from two points of view, with the aim to deepen the understanding of multipartite non-classical correlation. In the first point of view, multipartite nonclassical correlations are considered as a resource, which cannot be generated by a restricted set of operations, local operations and classical communication (LOCC). Then, we ask how much amount of multipartite entanglement is required to prepare a given multipartite state by LOCC. In other words, we define the Greenberger-Horne-Zeilinger (GHZ) entanglement cost as a generalization of the entanglement cost to the multipartite setting. We provide a LOCC procedure for preparing an arbitrary pure multipartite state from GHZ states, and show that the conversion rate of this procedure is given by multipartite quantum discord of the state to be prepared, which means that multipartite quantum discord is an upper bound for the GHZ entanglement cost. In the second point of view, bipartite correlations of pairs of subsystems are summed to yield the multipartite correlation of the total system. In this sense, we seek to find general relations between multipartite correlations and bipartite correlations of pairs of subsystems. We provide a general concept of the additivity relations, which is derived in terms of total correlation, and examine them for entanglement and discord.