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• W1807458715 abstract "We establish a thorough treatment of reduced-state synchronization for 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. We show that reduced-state synchronization is achieved if and only if the quantum interaction graphs corresponding to the permutation operators 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. Further, we 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. We show that the quantum synchronization equation is by nature equivalent to several parallel cut-balanced consensus processes, and a necessary and sufficient condition is obtained for quantum reduced-state synchronization under switching interactions applying recent work of Hendrickx and Tsitsiklis." @default.
• W1807458715 created "2016-06-24" @default.
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• W1807458715 date "2014-10-22" @default.
• W1807458715 modified "2023-09-23" @default.
• W1807458715 title "Reduced-State Synchronization of Quantum Networks: Convergence, Graphical Information Hierarchy, and the Missing Symmetry" @default.
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• W1807458715 hasPublicationYear "2014" @default.
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