We strengthen the connection between Information Theory and quantum-mechanical systems using a recently developed dequantization procedure whereby quantum fluctuations latent in the quantum momentum are suppressed. The dequantization procedure results in a decomposition of the quantum kinetic energy as the sum of a classical term and a purely quantum term. The purely quantum term, which results from the quantum fluctuations, is essentially identical to the Fisher information. The classical term is complementary to the Fisher information and, in this sense, it plays a role analogous to that of the Shannon entropy. We demonstrate the kinetic energy decomposition for both stationary and nonstationary states and employ it to shed light on the nature of kinetic-energy functionals.
Universidad Internacional Menéndez Pelayo（门德斯·佩拉约国际大学）；Department of Physics and Astronomy, University College London（伦敦大学学院物理与天文系）；Quantum AI Lab, Fractal Analytics（分形分析量子人工智能实验室）；CSIRO（联邦科学与工业研究组织）；School of Science, Engineering and Digital Technologies, University of Southern Queensland（昆士兰南部大学科学、工程与技术学院）；Imperial College London（帝国理工学院）；Technical University of Munich（慕尼黑工业大学）
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 correlation…
The interacting model describing the Rabi transition is essential in studying atom-photon interactions, where the kinetic energy term is often neglected for the convenience of analysis. We first study the approximation through the fidelity approach and verify its valid region in the parameter space of detuning and momentum. We find that as the radiation field's momentum and the absolute value of detuning decrease, the approximation becomes valid. We further discover that the omission of the kinetic energy term will overestimate the measuring accuracy of the Rabi frequency in some parameter reg…
In this work, we analyze a particle with position-dependent mass, with solitonic mass distribution in a stationary quantum system, for the particular case of the BenDaniel-Duke ordering, in a hyperbolic barrier potential. The kinetic energy ordering of BenDaniel-Duke guarantees the hermiticity of the Hamiltonian operator. We find the analytical solutions of the Schrödinger equation and their respective quantized energies. In addition, we calculate the Shannon entropy and Fisher information for the solutions in the case of the lowest energy states of the system.
Finite-frequency fluctuation-response bounds for open quantum systems
Chengdu Academy of Educational Sciences（成都教育科学研究院）；School of Science, Key Laboratory of High Performance Scientific Computation, Xihua University（西华大学理学院高性能科学计算重点实验室）
