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We study the ability of a quantum channel to generate quantum coherence when it applies to incoherent states. We define the measure of coherence generating power (CGP) for a generic quantum channel to be the average coherence generated by the quantum channel acting on a uniform ensemble of incoherent states based on the skew information-based coherence measure. We present explicitly the analytical formulae of the CGP for any arbitrary finite dimensional unitary channels. We derive the mean value of the CGP over the unitary groups and investigate the typicality of the normalized CGP. Furthermore, we give an upper bound of the CGP for the convex combinations of unitary channels. Detailed examples are provided to calculate exactly the values of the CGP for the unitary channels related to specific quantum gates and for some qubit channels., Comment: 21pages. arXiv admin note: text overlap with arXiv:2101.07427

We study the degree to which the coherence of quantum states is affected by noise. We give the definition of the $n$-th decay rate and investigate the coherence of Bell-diagonal states under $n$ iterations of channels. We derive explicit formulas of the $n$-th decay rates based on $l_1$ norm of coherence, relative entropy of coherence and skew information-based coherence. It is found that the larger $n$ is, the faster the $n$-th decay rate decreases as the parameter $p$ of Bell-diagonal states increases. Moreover, for any fixed $n$, with the increase of $p$, Bell-diagonal states can be completely incoherent under generalized amplitude damping (GAD) channels, depolarization (DEP) channels and phase flip (PF) channels, while this is not the case for bit flip (BF) channels and bit-phase flip (BPF) channels. We also investigate the geometry of the relative entropy of coherence and skew information-based coherence of Bell-diagonal states under different channels when the $n$-th decay rate is one, i.e., the coherence is frozen. It is shown that compared with BF and BPF channels, when $n$ is large enough, the coherence of Bell-diagonal states will not be frozen under GAD, DEP and PF channels. For skew information-based coherence, similar properties of coherence freezing are found.

Quantifying the quantumness of ensembles is a vital and practical task in quantum information theory. In this paper, we quantify the quantumness of quantum ensembles based on a quantifier of the coherence of ensembles via generalized α-z-relative Renyi entropy. It is shown that this measure satisfies the intuitive and desirable properties which are required by a measure of quantumness, such as positivity, unitary invariance, monotonicity under any commutativity preserving operations and so on. The relationship between our measure and some existing measures for quantumness of quantum ensembles is discussed. Detailed examples are presented to some important ensembles to illustrate the quantumness given by our measure.

Uncertainty relation is a core issue in quantum mechanics and quantum information theory. We introduce modified generalized Wigner-Yanase-Dyson (MGWYD) skew information and modified weighted generalizedWigner-Yanase-Dyson (MWGWYD) skew information, and establish new uncertainty relations in terms of the MGWYD skew information and MWGWYD skew information., 16 pages

We introduce modified generalized Wigner-Yanase-Dyson (MGWYD) skew information and modified weighted generalized Wigner-Yanase-Dyson (MWGWYD) skew information. By revisiting state-channel interaction based on MGWYD skew information, a family of coherence measures with respect to quantum channels is proposed. Furthermore, explicit analytical expressions of these coherence measures of qubit states are derived with respect to different quantum channels. Moreover, complementarity relations based on MGWYD skew information and MWGWYD skew information are also presented. Specifically, the conservation relations are investigated, while two interpretations of them including symmetry-asymmetry complementarity and wave-particle duality have been proposed., 20pages

In this paper, we introduce the concepts of cyclic $$\varphi $$ -contractions in Menger PM-spaces and cyclic weak $$\phi $$ -contractions in generalized Menger PM-spaces. Based on these concepts, some fixed point results for cyclic $$\varphi $$ -contractions in Menger PM-spaces are obtained. Furthermore, some fixed point theorems for cyclic weak $$\phi $$ -contractions and cyclic $$\varphi $$ -contractions in generalized Menger PM-spaces are obtained by assuming that the number of cyclic sets is odd. An example is also given to show the validity of our main results.

In this paper, we propose some new coupled coincidence point and fixed point theorems for the mappings F and g. Our results are obtained by exploring the corresponding initial value problems for the mapping F and weakening the involved contractive conditions. As an application, we study the existence and uniqueness of solution to integro-differential equations.

In this paper, the new concepts of \(\alpha \)-admissible mappings with respect to \(\eta \) in single-valued case and \(\alpha _{*}\)-admissible mappings with respect to \(\eta _{*}\) in set-valued case in Menger PM-spaces are introduced, and some new fixed point results for both single-valued and set-valued mappings under certain contractive conditions are studied, which extend and generalize some results in corresponding literatures. Some examples are provided to illustrate the validity of our main results, and an application is also given to discuss the existence of solution for Volterra type integral equations.

This paper presents an innovative bolt model suitable for the three dimensional finite element analysis (FEA) of the semirigid beam-to-column bolted connections. The model is particularly useful for the moment-rotation relationship of beam-tocolumn connections, especially in cases where the connectors such as endplates, angles, T-stubs, are not particularly thin. In this paper, the bolt tensile behavior is firstly discussed by using a refined finite element model, in which the complex geometries of both external and internal threads were modeled. Then, the bolt behavior predicted by the commonly used models was compared with that of the refined FEA to appraise the accuracy of these models. The comparison shows most of the models commonly used can not predict accurately the axial stiffness, carrying capacity and ductility of bolt simultaneously. Afterwards, an innovative bolt model was proposed and the model accorded with the refined FEA for single bolts. Finally, the proposed model was applied to analyze the moment-rotation behavior of several experimented and well documented connections with different configurations. The results indicate that the proposed model is feasible and efficient.

In this work, we introduce a new φ-contractive mapping; following that, we obtain some multipled common fixed point theorems for a pair of mappings $T: \underbrace{X \times X \times\cdots\times X}_{m\text{-times}}\rightarrow X$ and $A: X\rightarrow X$ . The main results of this paper are generalization of the main results of Kutbi et al. (Fixed Point Theory Appl. 2015(1):32, 2015). As an illustration, we give an example to demonstrate the validity of the obtained results.

In this paper, we generalize the algebraic sum ⊕ of Fang. Based on this concept, we prove some common fixed point theorems for three pairs of self-mappings satisfying the common $(E.A)$ property in Menger $PGM$ -spaces. Finally, an example is given to exemplify our main results.

In this paper, we introduce a new concept of generalized cyclic (κh, ϕL)S-weak contraction mappings and establish some coincidence point results for such mappings in complete partially ordered Menger PM-spaces. Our results generalize the main results of Nashine (Nonlinear Anal. 75:6160-6169, 2012) and Gopal et al. (Appl. Math. Comput. 233:955-967, 2014). We also obtain the corresponding coincidence point theorems for generalized cyclic (κh, ϕL)S-weak contractions in partially ordered metric spaces. MSC: 47H10; 54H25

In this paper, the new concepts of generalized Menger probabilistic metric spaces and tripled common fixed point for a pair of mappings T : X × X × X → X and A : X → X are introduced. Utilizing the properties of the pseudo-metric and the triangular norm, some tripled common fixed point problems of hybrid probabilistic contractions with a gauge function φ are studied. The obtained results generalize some coupled common fixed point theorems in the corresponding literature. Finally, an example is given to illustrate our main results. MSC:47H10, 46S50.

In this paper, some Banach spaces are introduced. Based on these spaces and the coincidence degree theory, a 2m-point boundary value problem for a coupled system of impulsive fractional differential equations at resonance is considered, and the new criterion on existence is obtained. Finally, an example is also given to illustrate the availability of our main results. MSC:34A08, 34B10, 34B37.