We investigate a two-body quantum system with hard-core interaction potential in a two-dimensional harmonic trap. We provide the exact analytical solution of the problem. The energy spectrum of this system as a function of the range of the interaction reveals level crossings which can be explained examining the potential and kinetic part of the energy, as well as the localization and oscillatory properties of the wavefunctions quantified by the Fisher information. The latter is sensitive to the wavefunction localization between nodes promoting this property as a resource of quantum correlations in interacting particle systems.
This study scrutinizes one-dimensional three-boson systems with on-site interactions, delving into perturbation theory, continuous-time quantum walks, and quantum Fisher information (QFI), among other areas. Notably, two critical on-site interaction strength points emerge. At these specific locations, the QFI reaches its zenith, exhibiting a proportionality to
t4. This substantively amplifies the precision in measuring both the Newtonian constant of gravitation and the E\"otv\"os parameter. The improvement surpasses models devoid of on-site interactions by 6 orders of magnitude. The methodology used to measure big
G can be adapted to quantify the Casimir energy of a many-particle system.
Abstract Quantum Fisher information (QFI) and skew information (SI) plays a key role in the quantum resource theory. Understanding these measures in the physical system has practical significance in the state parameter estimation and quantum metrology. In this article, we consider a pair of spin-1/2 particles coupled with dipolar and Dzyaloshinsky-Moriya (DM) interactions, serving as the physical carrier of quantum information. We examine the bipartite nonlocal correlations of pair of spin-1/2 particle system for the thermal equilibrium states, characterized by local quantum uncertainty (LQU) and local quantum Fisher information (lQFI). The effects of dipolar coupling constants on quantum correlation quantifiers are studied. The DM interaction greatly enhances the quantum correlation in the system whereas the temperature tends to annihilate the amount of quantum correlations.