On the sensitivity of the purity and entropy of mixed quantum states on variations of Planck’s constant

Abstract We explore the sensitivity of quantum state characteristics, specifically purity and entropy, to variations in the chosen value of Planck’s constant. This investigation begins with a novel examination of the Wigner function, framed through the displacement operator, providing fresh insights into quantum phase space analysis. Emphasizing Gaussian states, we systematically evaluate how changes in Planck’s constant influence the mixedness of quantum states. By leveraging the Narcowich–Wigner spectrum, we derive key behaviors of purity and entropy under these variations. Finally, our findings are interpreted through the lens of symplectic capacity, offering a robust theoretical framework that unifies quantum state dynamics and phase-space geometry.