Information-Theoretic Analysis of a Mass-Dependent Minimal Length Quantum Harmonic Oscillator

Abstract

This work investigates the impact of a mass-dependent minimal length deformation on the information-theoretic properties of quantum systems, focusing on the ground state of a deformed harmonic oscillator. The deformation, tied to the particle’s Compton wavelength, modifies the canonical commutation relations and introduces a non-trivial momentum-space geometry. We derive exact analytical expressions for the ground-state Shannon entropy and Fisher information, demonstrating that the deformation reduces both quantities compared to the standard case. This reduction reflects a suppression of high-momentum contributions and a narrowing of the probability distribution, revealing the minimal length’s role as an informational regulator. A key feature of this framework is its relational character: the deformation strength depends explicitly on the particle’s mass, leading to distinct informational signatures. Our results provide new insights into how fundamental length scales reshape the uncertainty structure of quantum states.