General perturbation theory for local quantum uncertainty and its formulation in the linear-response regime

TL;DR

This paper develops a perturbation theory for local quantum uncertainty (LQU), enabling explicit calculations in the linear response regime and illustrating how external fields can modulate quantum discord independently of entanglement.

Contribution

It introduces a general perturbation framework for LQU applicable to arbitrary dimensions and specializes it to the linear response regime with explicit frequency dependence.

Findings

Derived a first-order expansion of the density matrix using gamma function integral representation.

Reduced LQU optimization to diagonalization of a specific matrix based on SU(d) generators.

Demonstrated external magnetic fields can resonantly enhance quantum discord without entanglement.

Abstract

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 $\mathrm{SU}(d_1)$ generators. The 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. We further specialize the theory to the quantum linear response regime, where the perturbation is generated by a time-dependent external field, and $w^1$ acquires explicit dependence on the driving frequency $\omega$, the eigenstates and occupation probabilities of the equilibrium Hamiltonian $H_0$, and the matrix elements of the coupling operator $\hat{A}$. As an illustration, we apply the formalism to the isotropic Heisenberg model of two coupled spins driven by a local periodic magnetic field, obtaining closed-form 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 field induces a resonantly enhanced quantum discord without generating entanglement, demonstrating that frequency acts as a tunable modulator of nonclassicality -- an effect of purely quantum-discord type inaccessible to entanglement-based quantifiers.