Minimum uncertainty states of the conventional Heisenberg uncertainty relation have been extensively studied and are often regarded as the most classical quantum states from the perspective of uncertainty, providing valuable insight into the nature of quantumness and its potential applications. In this work, we investigate the minimum uncertainty states associated with an information-theoretic refinement of the Heisenberg uncertainty relation in general spin systems. Using two different approaches, the matrix formulation and the Wick symbol representation, we derive explicit expressions for the states that saturate the uncertainty bound. We show that spin coherent states indeed achieve minimum uncertainty, consistent with their conventional identification as the classical states of spin systems. Moreover, we also identify additional classes of minimum uncertainty states beyond the coherent family. Finally, we compare the spin-system results with the previously studied bosonic case and elucidate the origin of the differences between the two settings.Minimum uncertainty states of the conventional Heisenberg uncertainty relation have been extensively studied and are often regarded as the most classical quantum states from the perspective of uncertainty, providing valuable insight into the nature of quantumness and its potential applications. In this work, we investigate the minimum uncertainty states associated with an information-theoretic refinement of the Heisenberg uncertainty relation in general spin systems. Using two different approaches, the matrix formulation and the Wick symbol representation, we derive explicit expressions for the states that saturate the uncertainty bound. We show that spin coherent states indeed achieve minimum uncertainty, consistent with their conventional identification as the classical states of spin systems. Moreover, we also identify additional classes of minimum uncertainty states beyond the coherent family. Finally, we compare the spin-system results with the previously studied bosonic case and elucidate the origin of the differences between the two settings.

quant-pharXiv:2512.17307Journal of Physics A Mathematical and TheoreticalDec 22, 20250 citations

Minimum-uncertainty states and pseudoclassical dynamics

V. Canivell, Pere Seglar

All the minimum-uncertainty states $|z(\ensuremath{\alpha})〉$ are built as the eigenstates of generalized annihilation operators $a(\ensuremath{\alpha})$. We obtain the most general Hamiltonian which verfies the following property: Given an initial minimum-uncertainty state $|z(\ensuremath{\alpha})〉$ at $t = 0$ , the ${z}^{\ensuremath{'}}$ which corresponds to the minimum-uncertainty state that maximizes ${|〈{z}^{\ensuremath{'}}(\ensuremath{\alpha})|z(\ensuremath{\alpha}),t〉|}^{2}$ follows the classical trajectory in phase space. Finally, we comment on its relationship with the most general Hamiltonian which preserves minimality.All the minimum-uncertainty states $|z(\ensuremath{\alpha})〉$ are built as the eigenstates of generalized annihilation operators $a(\ensuremath{\alpha})$. We obtain the most general Hamiltonian which verfies the following property: Given an initial minimum-uncertainty state $|z(\ensuremath{\alpha})〉$ at $t = 0$, the ${z}^{\ensuremath{'}}$ which corresponds to the minimum-uncertainty state that maximizes ${|〈{z}^{\ensuremath{'}}(\ensuremath{\alpha})|z(\ensuremath{\alpha}),t〉|}^{2}$ follows the classical trajectory in phase space. Finally, we comment on its relationship with the most general Hamiltonian which preserves minimality.

Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fieldsFeb 15, 19778 citations

Dynamical symmetry, integrability of quantum systems, and general character of quantum regular motion

Gong-ou Xu, Yatian Yang, Xing Yong-Zhong

The notion of quantum-classical correspondence is carefully investigated in order to prepare firm grounds for studying the spatiotemporal evolution of quantum states in the same spirit as for corresponding classical cases. Three relevant problems, (1) the integrability of dynamical equations of quantum systems, (2) the initial minimum uncertainty states one-to-one correspondent to classical phase points, and (3) the effective Planck constants for systems having analogous dynamical properties but exhibiting different quantum effects, have been successfully resolved. Then the solution ${\ensuremath{\rho}}_{\ensuremath{\gamma}}(t)$ of the dynamical equation of a quantum integrable system is shown to be expressed as an analytical functional of the initial minimum uncertainty state ${\ensuremath{\rho}}_{\ensuremath{\gamma}}^{0}$ varying smoothly with $\ensuremath{\gamma}$ and t. Such a general character of the quantum regular motion serves as a reference for the study of quantum irregular motion under the action of perturbed Hamiltonian.The notion of quantum-classical correspondence is carefully investigated in order to prepare firm grounds for studying the spatiotemporal evolution of quantum states in the same spirit as for corresponding classical cases. Three relevant problems, (1) the integrability of dynamical equations of quantum systems, (2) the initial minimum uncertainty states one-to-one correspondent to classical phase points, and (3) the effective Planck constants for systems having analogous dynamical properties but exhibiting different quantum effects, have been successfully resolved. Then the solution ${\ensuremath{\rho}}_{\ensuremath{\gamma}}(t)$ of the dynamical equation of a quantum integrable system is shown to be expressed as an analytical functional of the initial minimum uncertainty state ${\ensuremath{\rho}}_{\ensuremath{\gamma}}^{0}$ varying smoothly with $\ensuremath{\gamma}$ and t. Such a general character of the quantum regular motion serves as a reference for the study of quantum irregular motion under the action of perturbed Hamiltonian.

Physical Review AMar 17, 20004 citations

Uncertainty relations in the theory of open quantum systems

Аурелиан Исар

Romanian Journal of PhysicsJan 1, 20030 citations

t = 0

, the ${z}^{\ensuremath{'}}$ which corresponds to the minimum-uncertainty state that maximizes ${|〈{z}^{\ensuremath{'}}(\ensuremath{\alpha})|z(\ensuremath{\alpha}),t〉|}^{2}$ follows the classical trajectory in phase space. Finally, we comment on its relationship with the most general Hamiltonian which preserves minimality.