Systems with stationary distribution of quantum correlations: open spin-1/2 chains with XY interaction

Although quantum correlations in a quantum system are characterized by the evolving quantities (which are entanglement and discord usually), we reveal such basis (i.e. the set of virtual particles) for the representation of the density matrix that the entanglement and/or discord between any two virtual particles in such representation are stationary. In particular, dealing with the nearest neighbor approximation, this system of virtual particles is represented by the $\beta $ -fermions of the Jordan–Wigner transformation. Such systems are important in quantum information devices because the evolution of quantum entanglement/discord leads to the problems of realization of quantum operations. The advantage of stationary entanglement/discord is that they are completely defined by the initial density matrix and by the Hamiltonian governing the quantum dynamics in the system under consideration. Moreover, using the special initial condition together with the special system’s geometry, we construct large cluster of virtual particles with the same pairwise entanglement/discord. In other words, the measure of quantum correlations is stationary in this system and correlations are uniformly “distributed” among all virtual particles. As examples, we use both homogeneous and non-homogeneous spin-1/2 open chains with XY-interaction although other types of interactions might be also of interest.     

On the impossibility of non-static quantum bit commitment between two parties

Recently, Choi et al. proposed an assumption on Mayers–Lo–Chau (MLC) no-go theorem that the state of the entire quantum system is invariable to both participants before the unveiling phase. This makes us suspect that the theorem is only applicable to static quantum bit commitment (QBC). This paper clarifies that the MLC no-go theorem can be applied to not only static QBC, but also non-static one. A non-static QBC protocol proposed by Choi et al. is briefly reviewed and analyzed to work as a supporting example. In addition, a novel way to prove the impossibility of the two kinds of QBC is given.     

Thermal entanglement of the mixed spin-1/2 and spin-5/2 Heisenberg model under an external magnetic field

We use the concept of negativity to study the entanglement of spin-1/2 and spin-5/2 antiferromagnetic Heisenberg model with an inhomogeneous magnetic field. Analytical conclusions of the model are acquired. It is found that the critical temperature \(T_\mathrm{c}\) goes up, as the increase of anisotropy parameter \(k\) . The temperature \(T_\mathrm{c}\) becomes bigger than the results of spin-1/2 and spin-3/2 Heisenberg XXZ chain for the same value of \(k\) . And we can gain more entanglement at higher temperature by coordinating the value of inhomogeneity \(b\) .     

Mediating and inducing quantum correlation between two separated qubits by one-dimensional plasmonic waveguide

We investigate the dynamics of quantum correlation between two separated qubits trapped in one-dimensional plasmonic waveguide. It is found that for a class of initial states, the quantum discord shows a sudden change phenomenon during the dynamical evolution. Furthermore, we demonstrate that the quantum discord can be enhanced if a proper product of the plasmon wave number and two qubits distance is chosen. Finally, we find that the non-zero quantum discord between two qubits can be created for the states without initial quantum discord during the time evolution of the system.     

Minimum-error discrimination between two sets of similarity-transformed quantum states

Using the equality form of the necessary and sufficient conditions introduced in Jafarizadeh (Phys Rev A 84:012102 (9 pp), 2011), minimum error discrimination between states of the two sets of equiprobable similarity transformed quantum qudit states is investigated. In the case that the unitary operators describing the similarity transformations are generating sets of two irreducible representations and the states fulfill a certain constraint, the optimal set of measurements and the corresponding maximum success probability of discrimination are determined in closed form. In the cases that they are generating sets of reducible representations, there exist no closed-form formula in general, but the procedure can be applied properly in each case provided that the states obey some constraints. Finally, we give the maximum success probability of discrimination and optimal measurement operators for some important examples of mixed quantum states, such as generalized Bloch sphere m-qubit states, qubit states and their three special cases.     

Localizable entanglement in antiferromagnetic and mixed Heisenberg chains: a quantum Monte Carlo study

We investigate entanglement formation in antiferromagnetic and mixed anisotropic, finite, one-dimensional Heisenberg chains with and without the presence of a uniform magnetic field. We explore the thermal entanglement created in terms of the bounds of the localizable entanglement and the possibility for quantum phase transitions in the zero field cases by means of standard quantum Monte Carlo method.     

Dynamics simulation of multibody chains on a transputer system

The paper describes the implementation on a transputer system of a novel parallel algorithm for dynamics simulation of a multibody chain. The algorithm is formulated at a level of parallelism which is natural for the problem but is essentially unavailable to other simulation dynamics algorithms. The experimental results demonstrate that one can improve efficiency of computation by exploiting this level of parallelism. However, analysis of the performance shows that the serial component of the resulting parallel algorithm grows to be a large fraction of the total parallel execution time and therefore limits the speedup that can be achieved with this approach.     

Dynamical behavior of quantum correlations between two qubits coupled to an external environment

We investigate the dynamics of quantum correlations of a two-qubit system coupled to an external environment. We have considered both cases: a spin environment and a bosonic environment. In all cases, we have chosen the Bell-diagonal state as the initial state and computed the evolution of quantum correlations in terms of entanglement, quantum discord and trace distance geometric quantum discord. Special attention is paid to the singular quantum phenomena, such as entanglement sudden death, sudden transition and double sudden transitions from classical to quantum decoherence, which all depend on the initial state and the parameters related to the system and the environment. We find the trace distance geometric quantum discord has a good robustness in resisting the spin and bosonic environmental noise.     

TC-VGC: a tumor classification system using variations in genes' correlation

Classification analysis of microarray data is widely used to reveal biological features and to diagnose various diseases, including cancers. Most existing approaches improve the performance of learning models by removing most irrelevant and redundant genes from the data. They select the marker genes which are expressed differently in normal and tumor tissues. These techniques ignore the importance of the complex functional-dependencies between genes. In this paper, we propose a new method for cancer classification which uses distinguished variations of gene–gene correlation in two sample groups. The cancer specific genetic network composed of these gene pairs contains many literature-curated prostate cancer genes, and we were successful in identifying new candidate prostate cancer genes inferred by them. Furthermore, this method achieved a high accuracy with a small number of genes in cancer classification.     

Control oriented system identification: a worst-case/deterministicapproach in H∞

The authors formulate and solve two related control-oriented system identification problems for stable linear shift-invariant distributed parameter plants. In each of these problems the assumed a priori information is minimal, consisting only of a lower bound on the relative stability of the plant, an upper bound on a certain gain associated with the plant, and an upper bound on the noise level. The first of these problems involves identification of a point sample of the plant frequency response from a noisy, finite, output time series obtained in response to an applied sinusoidal input with frequency corresponding to the frequency point of interest. This problem leads naturally to the second problem, which involves identification of the plant transfer function in H_∞ from a finite number of noisy point samples of the plant frequency response. Concrete plans for identification algorithms are provided for each of these two problems     

Feedback control of quantum entanglement in a two-spin system

A pair of spins is the most simple quantum system that can exhibit entanglement: a nonclassical property that plays an essential role in quantum information technologies. In this paper, feedback control problems of a symmetric two-spin system conditioned on a continuous measurement are investigated. In order to make some useful formulas in stochastic control theory directly applicable, we first derive a two-dimensional representation of the system. We then prove that a feedback controller stabilizes an entangled state of the two spins almost globally with probability one. Furthermore, it is demonstrated that some entangled states, which correspond to nonequilibrium points of the dynamics, are globally stabilized via feedback in the sense that the mean distance from a target can be reduced to an arbitrarily small value.     

1-optimality of static BSP computations: scheduling independent chains as a case study

The aim of this work is to study a specific scheduling problem under the machine-independent model BSP. The problem of scheduling a set of independent chains in this context is shown to be a difficult optimization problem, but it can be easily approximated in practice. Efficient heuristics taking into account communications are proposed and analyzed in this paper. We particularly focus on the influence of synchronization between consecutive supersteps. A family of algorithms is proposed with the best possible load-balancing. Then, a strategy for determining a good compromise between the two opposite criteria of minimizing the number of supersteps and a good balance of the load is derived. Finally, a heuristic which considers the influence of the latency is presented. Simulations of a large number of instances have been carried out to complement the theoretical worst case analysis. They confirm the very good behavior of the algorithms on the average cases.     

Entropy maximization and NT vacation M/G/1 model with a startup and unreliable server: comparative analysis on the first two moments of system size

We consider the control policy of an M/G/1 queueing system with a startup and unreliable server, in which the length of the vacation period is controlled either by the number of arrivals during the idle period, or by a timer. After all the customers have been served in the queue, the server immediately takes a vacation and operates an NT vacation policy: the server reactivates as soon as the number of arrivals in the queue reaches a predetermined threshold N or when the waiting time of the leading customer reaches T units. In such a variant vacation system, the steady-state probabilities cannot be obtained explicitly. Thus, the maximum entropy principle is used to derive the approximate formulas for the steady-state probability distributions of the queue length. A comparitive analysis of two approximation approaches, using the first and the second moments of system size, is studied. Both solutions are compared with the exact results under several service time distributions with specific parameter values. Our numerical investigations demonstrate that the use of the second moment of system size for the available information is, in general, sufficient to obtain more accurate estimations than that of the first moment.     

磺胺类药物正辛醇/水分配系数与分子价键连接性指数相关性研究

研究了磺胺类药物的分子价键连接性指数(MCI)与其正辛醇/水分配系数(Kow)间的相互关系,通过13种磺胺类药物MCI与其logKow间的线性回归分析,建立了磺胺类药物正辛醇/水分配系数(Kow)的相关定量模型.结果表明,零阶P型价键连接指数0xvp是影响磺胺类药物正辛醇/水分配系数(Kow)的主要因素,六阶PC型价键连接指数6xvpc为次要因素,较佳线性回归方程的相关系数为r=0.8324,平均残差为0.145个对数单位.     

The robust H2 control problem: a worst-casedesign

The worst-case effect of a disturbance system on the H ₂ norm of the system is analyzed. An explicit expression is given for the worst-case H₂ norm when the disturbance system is allowed to vary over all nonlinear, time-varying and possibly noncausal systems with bounded L₂-induced operator norm. An upper bound for this measure, which is equal to the worst-case H₂ norm if the exogeneous input is scalar, is defined. Some further analysis of this upper bound is done, and a method to design controllers which minimize this upper bound over all robustly stabilizing controllers is given. The latter is done by relating this upper bound to a parameterized version of the auxiliary cost function studied in the literature     

Unitary invariant discord as a measures of bipartite quantum correlations in an N-qubit quantum system

We introduce a measure of quantum correlations in the N-qubit quantum system which is invariant with respect to the SU(2 ^N ) group of transformations of this system. This measure is a modification of the quantum discord introduced earlier and is referred to as the unitary or SU(2 ^N )-invariant discord. Since the evolution of a quantum system is equivalent to the proper unitary transformation, the introduced measure is an integral of motion and is completely defined by eigenvalues of the density matrix. As far as the calculation of the unitary invariant discord is rather complicated computational problem, we propose its modification which may be found in a simpler way. The case N?=?2 is considered in details. In particular, it is shown that the modified SU(4)-invariant discord reaches the maximum value for a pure state. A geometric measure of the unitary invariant discord of an N-qubit state is introduced and a simple formula for this measure is derived, which allows one to consider this measure as a witness of quantum correlations. The relation of the unitary invariant discord with the quantum state transfer along the spin chain is considered. We also compare the modified SU(4)-invariant discord with the geometric measure of SU(4)-invariant discord of the two-qubit systems in the thermal equilibrium states governed by the different Hamiltonians.     

Mixed H2/H∞ control:a convex optimization approach

The problem of finding an internally stabilizing controller that minimizes a mixed H₂/H_∞ performance measure subject to an inequality constraint on the H_∞ norm of another closed-loop transfer function is considered. This problem can be interpreted and motivated as a problem of optimal nominal performance subject to a robust stability constraint. Both the state-feedback and output-feedback problems are considered. It is shown that in the state-feedback case one can come arbitrarily close to the optimal (even over full information controllers) mixed H₂/H_∞ performance measure using constant gain state feedback. Moreover, the state-feedback problem can be converted into a convex optimization problem over a bounded subset of (n×n and n ×q, where n and q are, respectively, the state and input dimensions) real matrices. Using the central H_∞ estimator, it is shown that the output feedback problem can be reduced to a state-feedback problem. In this case, the dimension of the resulting controller does not exceed the dimension of the generalized plant