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arXiv:1606.08113 · Physical review. E

Quantum synchronization and quantum state sharing in an irregular complex network

Wenlin Li, Chong Li, He‐Shan Song

Published Feb 6, 2017• 72 citations
arXivHTMLPDF

Abstract

We investigate the quantum synchronization phenomenon of the complex network constituted by coupled optomechanical systems and prove that the unknown identical quantum states can be shared or distributed in the quantum network even though the topology is varying. Considering a channel constructed by quantum correlation, we show that quantum synchronization can sustain and maintain high levels in Markovian dissipation for a long time. We also analyze the state-sharing process between two typical complex networks, and the results predict that linked nodes can be directly synchronized, but the whole network will be synchronized only if some specific synchronization conditions are satisfied. Furthermore, we give the synchronization conditions analytically through analyzing network dynamics. This proposal paves the way for studying multi-interaction synchronization and achieving effective quantum information processing in a complex network.

DOI
10.1103/physreve.95.022204

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We investigate the quantum synchronization phenomenon of the complex network constituted by coupled optomechanical systems and prove that the unknown identical quantum states can be shared or distributed in the quantum network even though the topology is varying. Considering a channel constructed by quantum correlation, we show that quantum synchronization can sustain and maintain high levels in Markovian dissipation for a long time. We also analyze the state-sharing process between two typical complex networks, and the results predict that linked nodes can be directly synchronized, but the whole network will be synchronized only if some specific synchronization conditions are satisfied. Furthermore, we give the synchronization conditions analytically through analyzing network dynamics. This proposal paves the way for studying multi-interaction synchronization and achieving effective quantum information processing in a complex network.
Synchronization is one of the paradigmatic phenomena in the study of complex systems. It has been explored theoretically and experimentally mostly to understand natural phenomena, but also in view of technological applications. Although several mechanisms and conditions for synchronous behavior in spatially extended systems and networks have been identified, the emergence of this phenomenon has been largely unexplored in quantum systems until very recently. Here we discuss synchronization in quantum networks of different harmonic oscillators relaxing towards a stationary state, being essential the form of dissipation. By local tuning of one of the oscillators, we establish the conditions for synchronous dynamics, in the whole network or in a motif. Beyond the classical regime we show that synchronization between (even unlinked) nodes witnesses the presence of quantum correlations and entanglement. Furthermore, synchronization and entanglement can be induced between two different oscillators if properly linked to a random network.
We introduce the use of entanglement entropy as a tool for studying the amount of information shared between the nodes of quantum complex networks. By considering the ground state of a network of coupled quantum harmonic oscillators, we compute the information that each node has on the rest of the system. We show that the nodes storing the largest amount of information are not the ones with the highest connectivity, but those with intermediate connectivity, thus breaking down the usual hierarchical picture of classical networks. We show both numerically and analytically that the mutual information characterizes the network topology. As a by-product, our results point out that the amount of information available for an external node connecting to a quantum network allows one to determine the network topology.
We consider a network of quantum oscillators in which quantum states are distributed among connected nodes by means of unitary transformations. The distributed states interact with each local state according to a time-dependent interaction Hamiltonian, which is modeled by a Hermitian operator constructed in terms of the states themselves, thereby introducing nonlinear network interactions. For qubit nodes of differing natural frequencies, we show numerically that for a sufficiently large coupling constant, synchronization of quantum nodes occurs in which the spins of all qubits are mutually aligned with a common frequency of oscillation, following initial transient configurations. We discuss the significance of quantum synchronization as a means to create copies of unknown quantum states.
Quantum information science has altered the concept of the method of processing and transporting information through the laws of quantum mechanics. Quantum entanglement is one of its basic properties, which is instrumental to non-classical correlations between spatially separate particles. New quantum communication networks and quantum computing systems distributed are based on these interrelations. In this paper, quantum information flow dynamics of multi-particle entangled networks with particular emphasis to the processes governing information transmission, redistribution and maintenance of coupled quantum nodes are discussed. The paper discloses the way in which the entangled structures comprising multiple entities can help in facilitating the sharing of information beyond the capabilities of the classical communication systems. Complex entangled structures are analyzed in terms of the channels through which the flow of quantum information is analyzed in respect to the theoretical models of multi-qubit systems and networked quantum channels. The way the communication between the particles influences the coherence, strength of correlation, as well as the stability of the whole network in general, is given particular attention. The effect of environmental noise and decoherence which can cause a break of entanglement and the loss of efficiency in quantum information exchange is also considered in the analysis. Moreover, the article discusses the application of network topology in order to establish the behaviour of entangled systems. The impact of the structural changes on information transfer reliability and speed is determined by the evaluation of the various forms of quantum nodes and connections. These findings suggest that entangled networks structured appropriately will be able to enhance stability of quantum communication and assist in distributing quantum resources more efficiently. Overall, the present research can be deemed as part of the bigger initiative of scaling up quantum communication infrastructures. The research builds knowledge in the sense that it provides an insight into the behavior of information in multi-particle entangled networks with important considerations being made as to the advancement of robust quantum networks which can be used in future to support the realization of future applications in the area of secure communication, distributed computing and the future developments in information processing technologies.
Abstract Quantum synchronization and synchronization transmission among three mechanical oscillators are investigated in a coupled multimode optomechanical system. The system consists of three subsystems, each comprising an optical cavity and a mechanical oscillator. The tripartite synchronization among the oscillators can be visualized through the joint limit-cycle trajectories and Wigner functions. Quantum synchronization and anti-synchronization of two oscillators can be achieved simultaneously in the coupled multimode optomechanical system. For three coupled optomechanical systems, some parameter ranges for achieving synchronization are presented. Moreover, the synchronization transmission among mechanical oscillators is also investigated by manipulating the driving laser. In addition, the circular optomechanical configuration is also identified as an effective platform for studying quantum synchronization. The differences between the two optomechanical system configurations are analyzed and compared. These results provide a promising platform for studying quantum correlations and quantum information processing with mechanical oscillators based on controllable multimode optomechanical systems.
Abstract In this work, we investigate the quantum synchronization and ϕ synchronization of two mechanical oscillators of different frequencies in two optomechanical systems with asymmetric coupling interaction. The whole system can be modulated by cavity detuning or driving amplitudes. Under certain parameters, quantum ϕ synchronization can be enhanced by asymmetric coupling in optomechanical systems, and the phase difference ϕ has an inversion. Moreover, we show that with the introduction of Kerr nonlinear medium, nonlinearity is dominated in achieving synchronization within asymmetric coupled cavities and ϕ can be corrected. Apart from achieving quantum synchronization, quantum anti-synchronization can be observed depending on the asymmetric coupling and the asymmetric external driving field. Our findings could offer insights into other quantum effects and pave the way for studying quantum correlations in asymmetric coupled optomechanical systems.