Evolutionary subgradient inclusions with nonlinear weakly continuous operators and applications

In this paper we consider the first order evolutionary inclusions with nonlinear weakly continuous operators and a multivalued term which involves the Clarke subgradient of a locally Lipschitz function. First, we provide a surjectivity result for stationary inclusion with weakly–weakly upper semicontinuous multifunction. Then, we use this result to prove the existence of solutions to the Rothe sequence and the evolutionary subgradient inclusion. Finally, we apply our results to the non-stationary Navier–Stokes equation with nonmonotone and multivalued frictional boundary conditions.     

A normed space of genetic operators with applications to scalability issues

We define an abstract normed vector space where the genetic operators are elements. This is used to define the disturbance of the generational operator G as the distance between the crossover and mutation operator (combined) and the identity. This quantity appears in a bound on the variance of fixed-point populations, and in a bound on the force //v - G(v)// that applies to the optimal population v. When analyzed for the case of fixed-length binary strings, a connection is shown between these measures and the size of the search space. Guides for parameter settings are given, if population convergence is required as the string length tends to infinity.     

Quantum state transfer with a two-dimensional Cooper-pair box qubit array

A theoretical scheme is proposed to transfer quantum state with a two-dimensional Cooper-pair box qubit array in circuit QED devices, in which coplanar transmission line resonators play the role of a quantum data bus. Based on the Raman transitions, the resonator-assisted quantum state transfer between any selected pair of qubits can be performed by addressing the local gate pulses. Thus the scheme may offer an effective route towards scalable quantum state transfer with superconducting qubits.     

Quantum teleportation between a single-rail single-photon qubit and a coherent-state qubit using hybrid entanglement under decoherence effects

We study quantum teleportation between two different types of optical qubits using hybrid entanglement as a quantum channel under decoherence effects. One type of qubit employs the vacuum and single-photon states for the basis, called a single-rail single-photon qubit, and the other utilizes coherent states of opposite phases. We find that teleportation from a single-rail single-photon qubit to a coherent-state qubit is better than the opposite direction in terms of fidelity and success probability. We compare our results with those using a different type of hybrid entanglement between a polarized single-photon qubit and a coherent state.     

Fixed-point theorems for discontinuous multivalued operators on ordered spaces with applications

In this paper, some fixed-point theorems for discontinuous multivalued operators on ordered spaces are proved. These theorems improve the earlier known fixed-point theorems of [1,2]. The main fixed-point theorems are applied to first-order discontinuous differential inclusions for proving the existence of extremal solutions under certain monotonicity conditions.     

A Faà di Bruno Hopf algebra for a group of Fliess operators with applications to feedback

A Faà di Bruno type Hopf algebra is developed for a group of integral operators known as Fliess operators, where operator composition is the group product. Such operators are normally written in terms of generating series over a noncommutative alphabet. Using a general series expansion for the antipode, an explicit formula for the generating series of the compositional inverse operator is derived. The result is applied to analytic nonlinear feedback systems to produce an explicit formula for the feedback product, that is, the generating series for the Fliess operator representation of the closed-loop system written in terms of the generating series of the Fliess operator component systems. This formula is employed to provide a proof that local convergence is preserved under feedback.     

The capacity of transmitting atomic qubit with light

The quantum information transfer between a single photon and a two-level atom is considered as a part of a quantum channel. The channel is a degradable channel even when there are decays of the atomic excited state and the single photon state, as far as the total excitation of the combined initial state does not exceed one. The single letter formula for quantum capacity is obtained.     

Bounding the slope of polynomial operators and some applications

We discuss several systematic possibilities for removing certain intervals when using an interval expression of the derivative in iterative methods. In general, the speed of convergence is accelerated in this way. Starting from a different point of view the same problem has been treated recently in [5].     

Coexistence of qubit effects

Two quantum events, represented by positive operators (effects), are coexistent if they can occur as possible outcomes in a single measurement scheme. Equivalently, the corresponding effects are coexistent if and only if they are contained in the ranges of a single (joint) observable. Here we give several equivalent characterizations of coexistent pairs of qubit effects. We also establish the equivalence between our results and those obtained independently by other authors. Our approach makes explicit use of the Minkowski space geometry inherent in the four-dimensional real vector space of selfadjoint operators in a two-dimensional complex Hilbert space.     

Geometric phase and entanglement for a single qubit interacting with deformed-states superposition

The geometric phase and quantum entanglement for a nonlinear field-atom system are described quantitatively in terms of different parameters. Specifically, considering a deformed Schrödinger cat interacting with a qubit and taking into account the time dependent of the system coupling. The results show that the initial state setting, atomic motion, photon number and deformation play important roles in the evolution of the system dynamics, nonlocal correlation and geometric phase. An interesting correlation between the entanglement and geometric phase is observed during the time evolution. The presented system is very useful to generate and maintain high amount of entanglement through controlling the phase variation of the system under consideration. We test this observation with experimentally accessible parameters and some new aspects are obtained.     

关于新的弱化缓冲算子的研究及其应用

在灰色系统理论缓冲算子公理体系下,构造出一类新的弱化缓冲算子.研究其一些特性和内在联系,可有效地解决冲击扰动数据序列在建模预测过程中经常出现的定量预测结果与定性分析结论不符的问题.实例分析结果表明,该类算子是有效而实用的.     

Lorentz-covariant,unitary evolution of a relativistic Majorana qubit

Quantum Information Processing - Unconditional security of the quantum key distribution protocol has been proved, but the practical quantum key distribution system may be attacked by utilizing...     

一类新的弱化缓冲算子的构造及其应用

利用灰色系统理论,在对缓冲算子和已有弱化缓冲算子研究的基础上,构造一类新的弱化缓冲算子,并研究其一些特性及内在关系,有效解决了冲击扰动数据序列在建模预测过程中经常出现的定量预测结果与定性分析结论不符的问题.实例分析结果表明,这类新的弱化缓冲算子能显著提高数据预测模型的预测精度.     

灰色预测中缓冲算子的组合性质及应用

通过研究同性缓冲算子作用样本数据序列所得灰色预测模型的预测精度问题, 发现同类缓冲算子对于相同样本数据序列的预测值一致, 对于具体预测问题, 某个缓冲算子在此类问题中有效, 用到另一类问题上可能失效. 为此, 提出一种同性缓冲算子的组合方法, 通过对同性缓冲算子的有效组合可以得到一种新的缓冲算子, 该缓冲算子不但能够提高模型的预测精度, 而且可以扩大缓冲算子的适用范围. 实例验证表明, 所提出的组合方法是有价值的.

     

Anistropic creep modeling based on elastic projection operators with applications to CMSX-4 superalloy

This paper presents a unified framework for creep modeling of anisotropic materials, which is specified in more detail to the cases of isotropy, cubic symmetry and transverse isotropy. To this end an additive decomposition of the elastic and inelastic strain tensors into dilational and isochoric Kelvin modes is assumed. Each of these modes is obtained from fourth-order projection operators, resulting from solution of the eigenvalue problem for the anisotropic fourth-order elasticity tensor. The amount of strain rate for each mode is modeled with a Norton-type ansatz in terms of an equivalent stress. The formulation for the equivalent stress in terms of quadratic forms with aid of the projection operators is compared with polynomial expressions from the literature. The experimental phenomenon of primary creep is taken into account by a back stress tensor of Armstrong–Frederick type, which is also decomposed into Kelvin modes. As a consequence of the mode decomposition the classical radial-return method of isotropic elasto-plasticity is generalized to the different cases of anisotropy. Furthermore the implications on parameter identification are addressed. Two numerical examples are concerned with a superalloy CMSX-4.     

Quantum dynamics of superconducting nano-circuits: phase qubit, charge qubit and rhombi chains

We have studied different quantum dynamics of superconducting nano-circuits with Josephson junctions. A dc SQUID, when it is strongly decoupled from the environment, demonstrates two-level and multilevel dynamics. We have realized a two qubits coupled circuit based on a dc SQUID in parallel with an asymmetric Cooper pair transistor (ACPT). The ACPT behaves as a charge qubit. Its asymmetry produces a strong tunable coupling with the dc SQUID which is used to realize entangled states between the two qubits and new read-out of the charge qubit based on adiabatic quantum transfer. We have measured the current–phase relations of different rhombi chains in the presence or absence of quantum fluctuations which confirm theoretical predictions.     

Quantum correlations in a family of bipartite separable qubit states

Quantum correlations (QCs) in some separable states have been proposed as a key resource for certain quantum communication tasks and quantum computational models without entanglement. In this paper, a family of nine-parameter separable states, obtained from arbitrary mixture of two sets of bi-qubit product pure states, is considered. QCs in these separable states are studied analytically or numerically using four QC quantifiers, i.e., measurement-induced disturbance (Luo in Phys Rev A77:022301, 2008), ameliorated MID (Girolami et al. in J Phys A Math Theor 44:352002, 2011),quantum dissonance (DN) (Modi et al. in Phys Rev Lett 104:080501, 2010), and new quantum dissonance (Rulli in Phys Rev A 84:042109, 2011), respectively. First, an inherent symmetry in the concerned separable states is revealed, that is, any nine-parameter separable states concerned in this paper can be transformed to a three-parameter kernel state via some certain local unitary operation. Then, four different QC expressions are concretely derived with the four QC quantifiers. Furthermore, some comparative studies of the QCs are presented, discussed and analyzed, and some distinct features about them are exposed. We find that, in the framework of all the four QC quantifiers, the more mixed the original two pure product states, the bigger QCs the separable states own. Our results reveal some intrinsic features of QCs in separable systems in quantum information.     

Entanglement evolution in a five qubit error correction code

In this paper I explore the entanglement evolution of qubits that are part of a five qubit quantum error correction code subject to various decohering environments. Specifically, I look for possible parallels between the entanglement degradation and the fidelity of the logical qubit of quantum information stored in the physical qubits. In addition, I note the possible exhibition of entanglement sudden death (ESD) due to decoherence and question whether ESD is actually a roadblock to successful quantum computation.     

Progress in the development of a single Cooper-pair box qubit

We describe in this review progress in techniques for measuring the quantum states of the single Cooper-pair box (SCB) at the Jet Propulsion Laboratory, and the use of these techniques to characterize their performance as quantum bits. Initially, the Radio-Frequency-Single-Electron Transistor was used to measure conventional and differential versions of the SCB. To overcome some of the difficulties associated with the radio-frequency single-electron transistor, a transition was made to readout based on the quantum capacitance technique. Using this method, entanglement between two SCBs was demonstrated spectroscopically and with ground state characterization.