Modern Physics Letters A

Lots of ready quantum private comparison (QPC) protocols usually only judge whether two users’ data are equal, whereas the quantum private magnitude comparison (QPMC) protocol can compare the magnitude of two numbers, whose results are greater than, equal and less than. It is by announcing a comparison result of two bits in two data that the existent QPMC protocols determine the size relationships of the whole data. Although the announcement leaks no information to outside attackers, yet it alerts two participants to know each other’s value of a certain bit. This is termed as bit leakage in this paper. In order to remedy this shortage, the paper proposes a novel QPMC protocol using a type of Bell state. The protocol is thoroughly analyzed, correct and secure. Also, it proves free of bit leakage. Additionally, because it is easier to implement because of the usage of a type of Bell state, it counts as a better alternative for QPMC.

The very early stage of the coalescence of two nuclei is studied and used to estimate the nuclear viscosity. The time evolution of the neck region has been simulated by the unified Langevin equation method, which is used in the analysis of heavy-ion collisions from the approaching stage to the fusion-fission stage. It is found that the transition from viscous to inertial coalescence that appeared in the neck growth of macroscopic drops can also be seen in the present simulation in nucleus–nucleus collisions. The dynamics of neck growth is analyzed in terms of the hydrodynamical formula and the viscosity coefficient of nuclear matter is estimated using the analogy of macroscopic drops.

Oscillating and dissipative energy exchange between the electromagnetic and axion fields is investigated in an effective electro-magneto dynamical (EEMD) model theory, implying the coexistence of axions with hypothetic magnetic charges. An exact formula is presented for the energy transfer between the electromagnetic and axionic sectors. In a first example, we compute analytically the homogeneously oscillating electric and magnetic field configurations generated by the combined action of a constant static magnetic field and a periodically oscillating axion condensate. In the second example, the electromagnetic radiative energy loss of a gravitationally bound axion configuration is computed in the EEMD model. As a result, an asymptotic $\sim t^{1/5}$ temporal increase of the clump size is found also in EEMD.

This paper investigates the static spherically symmetric vacuum solutions of Brans–Dicke Theory of Gravity. In this paper, we systematically derive the static spherically symmetric solutions by starting with the general static spherically symmetric anzats, discovering the nonzero Christoffel symbols, nonzero Ricci tensor components and the Ricci Scalar. These results allow us to rewrite the four Brans–Dicke gravitational field equations explicitly in terms of the metric components, the scalar field and its scalar potential. This paper systematically explains and shows how to modify these linear second-order ordinary differential equations in order to be able to find the solution of the scalar field, the metric components and the scalar potential analytically. We successfully find the most general solution of the static spherically symmetric vacuum solutions of Brans–Dicke gravity and the well-known Schwarzschild solution is recovered as the simplest solution.

The thermal quantum correlations of a three-qubit spin chain of XY type under an in-homogeneous magnetic field have been investigated, where by considering magnetic fields with different magnitudes ${ℬ}-b$, ${ℬ}$ and ${ℬ}+b$ for each spin, the quantum correlations between the adjacent and the non-adjacent qubits (spins) have been studied. For this purpose, the concurrence as an entanglement quantifier and the trace distance discord as a discord-like quantifier have been computed for the corresponding bipartite subsystems with the reduced density matrices ${\rho }^{(12)}$, ${\rho }^{(23)}$ and ${\rho }^{(13)}$. The differences between the concurrence and the trace distance discord, are explained in detail. Their dependence on the parameters of the uniform magnetic field ${ℬ}$, the temperature $T$, and the in-homogeneity parameter $b$ is discussed so that the thermal correlation decreases by increasing the mentioned parameters. Also, the results show that by changing and controlling the parameters ${ℬ}$, $T$ and $b$, especially the in-homogeneous magnetic field $b$, it is possible that the correlation value between non-adjacent spins, i.e. $c({\rho }^{(13)})$ can be reached to a greater value than the thermal correlations between adjacent spins, i.e. $c({\rho }^{(12)})$ and $c({\rho }^{(23)})$. Moreover, it is shown that the trace distance $D_T^{(13)}(\rho )$ between the non-adjacent spins has always a lower value than those of the adjacent spins $D_T^{(12)}(\rho )$ and $D_T^{(23)}(\rho )$. Finally, the results show that in-homogeneous magnetic field b can be effective for improving thermal quantum correlation.

The hydrodynamical form of Wigner–Dunkl quantum mechanics has been formulated. The main step to get such formulation was to derive a pair of Madelung-like equations (called Madelung–Wigner–Dunkl equations) from the Schrödinger equation appearing in Wigner–Dunkl quantum mechanics. Some aspects of both equations contained in the pair, i.e. the inhomogeneous continuity equation and the quantum Hamilton–Jacobi equation, have been investigated and discussed. With certain assumption, the relation between the expectation value of the quantum potential appearing in the quantum Hamilton–Jacobi equation and the so-called Fisher information has been derived. Then an uncertainty relation between momentum and position which may be tighter than the standard uncertainty relation has been derived by using Cramér–Rao inequality and Fisher information.

Based on Jin et al.’s hierarchical remote preparation scheme of an arbitrary $m$-qudit state with three agents, we propose one scheme for multiple agents by utilizing the symmetry of cluster states. To save entanglement resource, we then put forward the other improved scheme. There exists a hierarchy among the agents in terms of their abilities which are quantified by nonconditioned fidelity. The upper-grade agent needs the assistance of all the remaining upper-grade agents and any one of the lower-grade agents to recover the target state, while the lower-grade agent requires all the other agents’ collaboration. It is important to emphasize that the recovery operation is derived by a general expression clearly revealing the relationship with the measurement results.

In this paper, we investigate a new class of $\eta$-deformed $Ad{S}_5\times T^{1,1}$ backgrounds produced by classical $r$-matrices that satisfy the modified classical Yang–Baxter equation [JHEP 03, 094 (2022)]. We consider the string sigma model on $\eta$-deformed $Ad{S}_5\times T^{1,1}$ background. We numerically examined the classical phase space dynamics of these (semi)classical strings over this deformed background and computed several chaos indicators. These involve figuring out the Poincaré section and computing the Lyapunov exponents. In the (semi)classical limit, we discover evidence that supports a non-integrable phase space dynamics.