Strong entanglement distribution of quantum networks

TL;DR

This paper investigates the strong entanglement distribution in quantum networks, establishing new inequalities and theorems that deepen understanding of high-dimensional entanglement and network classification.

Contribution

It introduces a strong CKW monogamy inequality for generalized EPR and GHZ states, and applies this to derive a quantum max-flow min-cut theorem and classify network configurations.

Findings

Connected networks satisfy strong CKW monogamy inequality.

Derived quantum max-flow min-cut theorem using entanglement distribution.

Classified entangled networks based on local unitary operations.

Abstract

Large-scale quantum networks have been employed to overcome practical constraints of transmissions and storage for single entangled systems. Our goal in this article is to explore the strong entanglement distribution of quantum networks. We firstly show any connected network consisting of generalized EPR states and GHZ states satisfies strong CKW monogamy inequality in terms of bipartite entanglement measure. This reveals interesting feature of high-dimensional entanglement with local tensor decomposition going beyond qubit entanglement. We then apply the new entanglement distribution relation in entangled networks for getting quantum max-flow min-cut theorem in terms of von Neumann entropy and R\'{e}nyi-$\alpha$ entropy. We finally classify entangled quantum networks by distinguishing network configurations under local unitary operations. These results provide new insights into characterizing quantum networks in quantum information processing.