Dynamics of quantum Fisher and Wigner-Yanase skew information following a noisy quench

TL;DR

This work investigates how noise affects the dynamical generation of quantum coherence during quenches across a quantum critical point in the transverse-field Ising model. By analyzing the two-spin reduced density matrix, it evaluates the quantum Fisher information (QFI) and the Wigner–Yanase skew information (WYSI) under both noiseless and noisy linear ramps, with noise modeled as Gaussian white fluctuations of strength $\xi$ in the control field. In the noiseless case, both $F$ and WYSI grow with the ramp time scale $\tau$ and saturate at adiabatic values, while in the presence of noise they decay exponentially with $\tau$ and exhibit an intermediate-\tau maximum at $\tau_m(\xi)$, with $\tau_m(\xi) \\propto (\xi^2)^{-\delta}$ and $\delta \approx 2/3$. The identical scaling exponent for QFI and WYSI across neighbor separations suggests a common mechanism linking defect production and dephasing under noisy driving, with potential implications for optimizing ramps in noisy quantum annealing and precision metrology.

Abstract

We study the effect of noise on the dynamics of the transverse-field Ising model quenched across a quantum critical point. To quantify two-spin correlations, we employ the quantum Fisher information (QFI) and the Wigner-Yanase skew information (WYSI) as measures of quantum coherence. In the noiseless case, in contrast to the dynamics of entanglement in anisotropic XY chains, both QFI and WYSI increase monotonically with the ramp quench time, approaching their adiabatic limits without exhibiting any Kibble-Zurek type scaling with quench duration. In contrast, when noise is added to the quench protocol, the coherence dynamics change qualitatively: QFI and WYSI both decay exponentially with the time scale of a ramp quench, with an exponent determined by the noise intensity. Furthermore, the maximum ramp time, at which either of these measures reach their maximum, scales linearly with the noise variance, featuring the same exponent that determines the optimal annealing time for minimizing defect production in noisy quantum annealing.

Figures (5)

• Figure 1: Quantum Fisher information for nearest‐neighbour $F_{\ell,\ell+1}$ (a), and next‐nearest‐neighbour $F_{\ell,\ell+2}$ (b) as a function of the instantaneous field $h(t)$ during a linear ramp from $h_i=-30$ to $h_f$, in the absence of noise. Insets zoom into the critical region $-2<h(t)<2$. The lower panel show the Quantum Fisher information $F_{\ell,\ell+1}$ (c) and $F_{\ell,\ell+2}$ (d) versus ramp duration $\tau$ for a full quench from $h_i=-30$ to $h_f=30$.
• Figure 2: The variation of (a) $\ln(F_{l,l+1})$ and (b) $\ln(F_{l,l+1})$ as a function of $\tau$ for the noisy quench from $h_i=-30$ to $h_f=30$ for different values of noise intensity $\xi$, reveals the linear scaling of logarithm of quantum Fisher information versus $\tau$. (c) The optimal time of $F_{\ell,\ell+1}$ and $F_{\ell,\ell+2}$ are shown to have power-law scaling with square of the strength of noise $\xi^2$ with exponent $\delta=0.66\pm0.02$.
• Figure 3: (a)-(c) Wigner–Yanase skew information between nearest‐neighbour spins ${\rm LQC}^{\alpha}_{\ell,\ell+1}$ for $\alpha=\{x,y,z\}$ as a function of the instantaneous field $h(t)$ during a noiseless ramp from $h_i=-30$ to $h(t)$. (d)-(f) Wigner–Yanase skew information for next‐nearest‐neighbour spins ${\rm LQC}^{\alpha}_{\ell,\ell+2}$ under the same ramp protocol and noiseless conditions. Insets zoom into the critical region $-2<h(t)<2$.
• Figure 4: Wigner–Yanase skew information versus ramp duration $\tau$ for a quench from $h_i=-30$ to $h_f=30$: (a) ${\rm LQC}^{x}_{l,l+1}$, (b) ${\rm LQC}^{y}_{l,l+1}$, (c) ${\rm LQC}^{x}_{l,l+2}$, and (d) ${\rm LQC}^{y}_{l,l+2}$.
• Figure 5: Logarithm of Wigner–Yanase skew information versus ramp duration $\tau$ for a noisy quench from $h_i=-30$ to $h_f=30$ at various noise intensities $\xi$: (a) $\ln({\rm LQC}^{x}_{l,l+1})$, (b) $\ln({\rm LQC}^{y}_{l,l+1})$, (c) $\ln({\rm LQC}^{x}_{l,l+2})$, (d) $\ln({\rm LQC}^{y}_{l,l+2})$, demonstrating a linear scaling. (e) The $\tau$ that maximises ${\rm LQC}^{\alpha}_{\ell,\ell+1}$ and ${\rm LQC}^{\alpha}_{\ell,\ell+2}$, $\tau_m$, shows power-law scaling with respect to the square of the noise strength $\xi^2$, with the exponent $\delta = 0.66 \pm 0.02 \approx 2/3$.