Optical soliton in a one-dimensional array of a metal nanoparticle-microcavity complex (2021 Commun. Theor. Phys. 73 115105)

During the production process an error was introduced into equation (14). The absolute value symbol was moved to the wrong place. Here, we give the correct version of equation (14) ：

ECONOMIZING NONLOCAL RESOURCE IN TWO-WAY REMOTE PREPARATIONS OF INEQUIVALENT QUANTUM STATES UNDER A COMMON CONTROL

A recently proposed protocol for two parties to securely and simultaneouslyexchange inequivalent quantum states under the same control of a third party[\textit{Int. J. Theor. Phys.} (2020);https://doi.org/10.1007/s10773-020-04657-0] is revisited. It is shown inthis paper that the required tasks are equally well accomplished with anonlocal resource which is greatly economized by rationally exploiting localresources. Furthermore, the economized nonlocal resource with appropriatelocal operations on local resources also allows exchanging inequivalentstates other than those previously considered.

Derived Equivalences for the Flops of Type C2 and ${A}_{4}^{G}$ via Mutation of Semiorthogonal Decomposition

We give a new proof of the derived equivalence of a pair of varieties connected by the flop of type C2 in the list of Kanemitsu (2018), which is originally due to Segal (Bull. Lond. Math. Soc., 48 (3) 533–538, 2016). We also prove the derived equivalence of a pair of varieties connected by the flop of type ${A}_{4}^{G}$ A 4 G in the same list. The latter proof follows that of the derived equivalence of Calabi–Yau 3-folds in Grassmannians Gr(2,5) and Gr(3,5) by Kapustka and Rampazzo (Commun. Num. Theor. Phys., 13 (4) 725–761 2019) closely.

An improved E-payment protocol based on quantum blind signature without entanglement

E-payment plays an important role in modern daily life, so the security problem of E-payment has been widely concerned by researchers. In a recent paper [Int. J. Theor. Phys. 57, 2657 (2018)], the authors presented a trusted third-party E-payment protocol based on quantum blind signature without entanglement. In this paper, we show that there is a serious security flaw in their E-payment protocol. That is, the partial keys will be disclosed by performing a simple attack strategy. Furthermore, we propose an improved E-payment protocol and analyze its security.

Optimizing the scheme of bidirectional controlled quantum teleportation with a genuine five-qubit entangled state

A bidirectional controlled quantum teleportation (BCQT) scheme was proposed by Yan Chen [Int. J. Theor. Phys. 53, 1454 (2014)] with a genuine five-qubit entangled state as quantum channel. In the scheme two remote participants have to perform some two-qubit joint operations to accomplish the BCQT task. Such joint operations are nonlocal and usually regarded as serious faults in some sense. To overcome them, in this paper we put forward an optimized version. Our scheme has the distinct advantages of degrading the necessary-operation complexity (i.e., both intensity and difficulty) and consuming fewer classical resources as well as owing higher intrinsic efficiency in contrast to Chen’s. Besides, it is feasible in experiment and applicable in the intending quantum network.

Bidirectional quantum-controlled teleportation using six-qubit cluster state without remote joint operation

Utilizing a six-qubit cluster state as quantum channel, a bidirectional controlled quantum teleportation (BCQT) scheme was put forward by Yan in [Int. J. Theor. Phys. 52, 3870 (2013)]. However, in order to accomplish the task, two agents must cooperate to perform a quantum controlled phase gate operation on their two qubits. In view of the present technique, such kind of remote joint operation is difficult to be realized. In this paper, based on the same cluster state, we propose a different BCQT scheme to avoid the remote joint operation. Besides, an unnecessary waste of classical messages in Yan’s scheme is point out.

Jacobi structures with background

Combining the twisted Jacobi structure [Twisted Jacobi manifolds, twisted Dirac–Jacobi structures and quasi-Jacobi bialgebroids, J. Phys. A: Math. Gen. 39(33) (2006) 10449–10475] with that of a Poisson structure with a 3-form background [Poisson geometry with a 3-form background, Prog. Theor. Phys. Suppl. 144 (2001) 145–154], alias twisted Poisson, we propose and analyze a new structure, called Jacobi structure with background. The background is a pair consisting of a [Formula: see text]-form and a [Formula: see text]-form. We describe their characteristic leaves. For twisted contact dual pairs, we show the correspondence of characteristic leaves of the two Jacobi manifolds with background.

Q2 dependence of the fractional momenta carried by small x quarks and gluons in models of proton structure function

Recently, we suggested two alternative analytical models of proton structure function [Formula: see text] and gluon distribution [Formula: see text] at small [Formula: see text] [L. Machahari and D. K. Choudhury, Eur. Phys. J. A 54, 69 (2018); Commun. Theor. Phys. 71, 56 (2019)] derived from the coupled DGLAP equations for quarks and gluons approximated by Taylor expansion. In this work, we compute the partial momentum fractions carried by quarks and gluons in limited small [Formula: see text] range: [Formula: see text] and compare them with few other models available in the current literature. The analysis leads to understand qualitatively the effects of notions like Froissart saturation and self-similarity in the proton at small [Formula: see text]. We also study if our results conform to the total momentum fractions as predicted in perturbative and lattice QCD.

Passive attack to the controlled secure direct communication with seven-qubit entangled states protocol

It is found that the controlled quantum secure direct communication (CQSDC) based on a seven-qubit entangled state protocol [S. K. Wang, X. W. Zha and H. Wu, Int. J. Theor. Phys. 57, 48 (2018)] can be passively attacked. That is to say, this protocol has the security loophole of information leakage. To be specific, the first bit of the sender’s two-bit message can be deduced by an attacker Eve according to the first and the third bits of Alice’s announcement and the first bit of the controller Charlie’s announcement. Then, a way to fix this loophole is discussed.

Charge–mass sum rules for unified spinor fields in extradimensions and the prediction for the existence of tachyon quarks and tachyon leptons

Within the framework of the mechanism proposed in our previous works [Duc and Giao, J. Mod. Phys. 5, 477 (2014); Duc et al., Int. J. Theor. Phys. 54, 1071 (2015); Duc and Giao, Int. J. Theor. Phys. 55, 959 (2016)] for mass and charge creation, we consider the charge and mass spectrum of spinor fields in extradimensions. It is shown that a single spinor field in spacetime with extradimensions corresponds to a set of effective spinor fields in ordinary four-dimensional spacetime with charges and masses obeying the sum rules dictated from some specific assumptions related to the compactification of extradimensions. The obtained results allow us to present an example for unifying six existing flavor quarks, as well as for unifying three existing lepton generators. On the base of the derived charge–mass sum rules, we would predict the existence of some hidden tachyon quarks with fractional charges, as well as some hidden tachyon leptons, neutral or negative charged.