@inproceedings{5f00bfb5521d436ab8d662c6049b0cde,
title = "Quantum network reduced-state synchronization part I-convergence under directed 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. This part of the paper focuses on convergence conditions. We show that reduced-state synchronization is achieved if and only if the quantum permutations form a strongly connected union graph. The proof is based on an algebraic analysis making use of the Perron-Frobenius theorem for non-negative matrices. The convergence rate and the limiting orbit are explicitly characterized. Numerical examples are provided illustrating the obtained results.",
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.2015.7170716",
language = "English",
series = "Proceedings of the American Control Conference",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
pages = "86--91",
booktitle = "ACC 2015 - 2015 American Control Conference",
address = "United States",
}