C.-H. Lai

The development of generalized synchronization on complex networks

In this paper, we numerically investigate the development of generalized synchronization (GS) on typical complex networks, such as scale-free networks, small-world networks, random networks, and modular networks. By adopting the auxiliary-system approach to networks, we observe that GS generally takes place in oscillator networks with both heterogeneous and homogeneous degree distributions, regardless of whether the coupled chaotic oscillators are identical or nonidentical. We show that several factors, such as the network topology, the local dynamics, and the specific coupling strategies, can affect the development of GS on complex networks.

Optimal resource allocation for efficient transport on complex networks

The problem of efficient transport on a complex network is studied in this paper. We find that there exists an optimal way to allocate resources for information processing on each node to achieve the best transport capacity of the network, or the largest input information rate which does not cause jamming in network traffic, provided that the network structure and routing strategy are given. More interestingly, this achievable network capacity limit is closely related to the topological structure of the network, and is actually inversely proportional to the average distance of the network, measured according to the same routing rule.

Detecting groups of similar components in complex networks

We study how to detect groups in a complex network each of which consists of component nodes sharing a similar connection pattern. Based on the mixture models and the exploratory analysis set up by Newman and Leicht (2007 Proc. Natl. Acad. Sci. USA 104 9564), we develop an algorithm that is applicable to a network with any degree distribution. The partition of a network suggested by this algorithm also applies to its complementary network. In general, groups of similar components are not necessarily identical with the communities in a community network; thus partitioning a network into groups of similar components provides additional information of the network structure. The proposed algorithm can also be used for community detection when the groups and the communities overlap. By introducing a tunable parameter that controls the involved effects of the heterogeneity, we can also investigate conveniently how the group structure can be coupled with the heterogeneity characteristics. In particular, an interesting example shows a group partition can evolve into a community partition in some situations when the involved heterogeneity effects are tuned. The extension of this algorithm to weighted networks is discussed as well.

Synchronizability of network ensembles with prescribed statistical properties

It has been shown that synchronizability of a network is determined by the local structure rather than the global properties. With the same global properties, networks may have very different synchronizability. In this paper, we numerically studied, through the spectral properties, the synchronizability of ensembles of networks with prescribed statistical properties. Given a degree sequence, it is found that the eigenvalues and eigenratios characterizing network synchronizability have well-defined distributions, and statistically, the networks with extremely poor synchronizability are rare. Moreover, we compared the synchronizability of three network ensembles that have the same nodes and average degree. Our work reveals that the synchronizability of a network can be significantly affected by the local pattern of connections, and the homogeneity of degree can greatly enhance network synchronizability for networks of a random nature.

Test of genuine multipartite nonlocality without inequalities.

In this Letter we propose a set of conditions on the joint probabilities as a test of genuine multipartite nonlocality without inequality. Our test is failed by all nonsignaling local models in which even nonlocal correlations among some observables (not all) are allowed as long as these correlations respect the nonsignaling principle. A pass of our test by a state therefore indicates that this state cannot be simulated by any nonsignaling local models; i.e., the state exhibits genuine multipartite nonlocality. It turns out that all entangled symmetric n-qubit (n≥3) states pass our test and therefore are n-way nonlocal. Also we construct two Bell-type inequalities from our proposed test whose violations indicate genuine multipartite nonlocal correlations.

Characterizing generalized synchronization in complex networks

Recently, it was shown that generalized synchronization (GS) can generally occur in systems of networked oscillators. In this paper, we further characterize the states of GS by both theoretical analysis and numerical experiments. We show that the entrainment of local dynamics in a network can be characterized by the conditional Lyapunov exponent of the local oscillator. Meanwhile, different types of states of GS can be identified by analyzing the Lyapunov exponent spectra of the coupled system. Most importantly, we further provide direct evidence demonstrating that node dynamics in a network in a chaotic GS state can indeed achieve functional relations, although they may not directly connect to each other in typical complex networks.

Complete condition for nonzero quantum correlation in continuous variable systems

Quantum correlation provides a promising measure beyond entanglement. Here, we propose a necessary and sufficient condition for nonzero quantum correlation in continuous variable systems, which is simple and easy to perform in terms of a marker Qr. In order to get this condition, we introduce continuous-variable local orthogonal bases of the operator space, which are generalized from the orthogonal basis sets in local operator space for discrete variables. Based on this, we obtain the marker Qr for all bipartite continuous variable states, and provide several examples including two-mode Gaussian and non-Gaussian states. Our result may provide a candidate for quantum correlation measures, and can be measured by designed quantum circuits.

Trapped Ion Quantum Computation by Adiabatic Passage

We propose a new universal quantum computation scheme for trapped ions in thermal motion via the technique of adiabatic passage, which incorporates the advantages of both the adiabatic passage and the model of trapped ions in thermal motion. Our scheme is immune from the decoherence due to spontaneous emission from excited states as the system in our scheme evolves along a dark state. In our scheme the vibrational degrees of freedom are not required to be cooled to their ground states because they are only virtually excited. It is shown that the fidelity of the resultant gate operation is still high even when the magnitude of the effective Rabi frequency moderately deviates from the desired value.

Quantum computation based on a quantum switch in cavity QED

A feasible scheme for constructing quantum logic gates is proposed on the basis of quantum switches in cavity QED. It is shown that the light field which is fed into the cavity due to the passage of an atom in a certain state can be used to manipulate the conditioned quantum logical gate. In our scheme, the quantum information is encoded in the states of Rydberg atoms and the cavity mode is not used as logical qubits or as a communicating “bus”; thus, the effect of atomic spontaneous emission can be neglected and the strict requirements for the cavity can be relaxed.