Structural Vulnerability Of Quantum Networks

Structural vulnerability of a network can be studied via two key notions in graph theory: articulation points (APs) and bridges, representing nodes and edges whose removal will disconnect the network, respectively. Fundamental properties of APs and bridges in classical random networks have been studied recently. Yet, it is unknown if those properties still hold in quantum networks. Quantum networks allow for the transmission of quantum information between physically separated quantum systems. They play a very important role in quantum computing, quantum communication, and quantum sensing. Here we offer an analytical framework to study the structural vulnerability of quantum networks in terms of APs and bridges. In particular, we analytically calculate the fraction of APs and bridges for quantum networks with arbitrary degree distribution and entangled qubits in pure states. We find that quantum networks with swap operations have lower fractions of APs and bridges than their classical counterparts. Moreover, we find that quantum networks under low-degree swap operations are substantially more robust against AP attacks than their classical counterparts. These results help us better understand the structural vulnerability of quantum networks and shed light on the design of more robust quantum networks.