@inproceedings{76dfc54849e140b5ba7ac98202e853d4,
title = "Quantum network reduced-state synchronization part II-the missing symmetry and switching interactions",
abstract = "We consider reduced-state synchronization of qubit networks with the aim of driving the qubits' reduced states to a common trajectory. The evolution of the quantum network's state is described by a master equation, where the network Hamiltonian is either a direct sum or a tensor product of identical qubit Hamiltonians, and the coupling terms are given by a set of permutation operators over the network. The permutations introduce naturally quantum directed interactions. Part I of the paper establishes synchronization conditions for fixed quantum interactions. In this part of the paper, we further investigate the missing symmetry in the reduced-state synchronization from a graphical point of view. The information-flow hierarchy in quantum permutation operators is characterized by different layers of information-induced graphs, based on which a clear bridge between quantum and classical consensus dynamics is built. We show that the quantum synchronization equation is by nature equivalent to a cut-balanced consensus process. Then a necessary and sufficient condition is obtained for reaching quantum reduced-state synchronization in light of recent work by Hendrickx and Tsitsiklis [19].",
keywords = "Master equations, Quantum networks, Reduced-state synchronization",
author = "Guodong Shi and Shuangshuang Fu and Petersen, {Ian R.}",
note = "Publisher Copyright: {\textcopyright} 2015 American Automatic Control Council.; 2015 American Control Conference, ACC 2015 ; Conference date: 01-07-2015 Through 03-07-2015",
year = "2015",
month = jul,
day = "28",
doi = "10.1109/ACC.2015.7170717",
language = "English",
series = "Proceedings of the American Control Conference",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
pages = "92--97",
booktitle = "ACC 2015 - 2015 American Control Conference",
address = "United States",
}