We develop a general perturbation theory for the local quantum uncertainty (LQU), a discord-type quantifier of nonclassicality based on the Wigner-Yanase skew information. Starting from a perturbed density matrix $\rho ={\rho }_0+\epsilon {\rho }_1$, we derive an explicit first-order expansion of ${\rho }^{1/2}$ using an integral representation based on the gamma function, and reduce the LQU optimization to the diagonalization of a $(d_1^2-1)\times (d_1^2-1)$ matrix $w=w^0+w^1$ defined in terms of the generators of $\mathrm{SU}\left(d_1\right)$. The resulting framework is valid for composite systems of arbitrary dimension $d_1\times d_2$ and provides a direct computational route to the LQU from the spectral decomposition of the unperturbed state ${\rho }_0$. We further specialize the theory to the quantum linear-response regime, where the perturbation ${\rho }_1$ is generated by a time-dependent external field coupled to the system through an operator $\widehat{A}$. In this regime, $w^1$ acquires an explicit dependence on the driving frequency $\omega$, the eigenstates and occupation probabilities of the equilibrium Hamiltonian $H_0$, and the matrix elements of $\widehat{A}$, establishing a direct link between the LQU and the spectral and dynamical structure of the system. The formalism is applicable to a broad class of physical models, including quantum spin arrays with anisotropic and spin-orbit interactions, atoms coupled to cavity fields, and optomechanical systems. To illustrate the approach, we apply the theory to the isotropic Heisenberg model of two coupled spins subject to a local periodic magnetic field, deriving closed-form analytical expressions for the LQU as a function of temperature $T$ and frequency $\omega$. Comparison with the concurrence shows that, above the entanglement critical temperature $T_c$, the external perturbation induces a resonantly enhanced quantum discord without generating entanglement. This demonstrates that frequency acts as a tunable modulator of nonclassicality in the linear-response regime, an effect that is purely of quantum-discord type and a property inaccessible to entanglement-based quantifiers.

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• Quantum correlations in quantum information
• Quantum information theory