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arXiv:2507.09659 · Physical review. B./Physical review. B

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

J. Naji, Rouhollah Jafari, Alireza Akbari, Mehdi Abdi

Published Oct 6, 2025• 2 citations
arXivHTMLPDF

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 timescale of a ramp quench, with an exponent determined by the noise intensity. Furthermore, the maximum ramp time, at which either of these measures reaches its 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.

DOI
10.1103/1btj-tnkr

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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 timescale of a ramp quench, with an exponent determined by the noise intensity. Furthermore, the maximum ramp time, at which either of these measures reaches its 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.
We study the impact of noise on the dynamics of entanglement in the transverse-field Ising chain, with the field quenched linearly across one or both of the quantum critical points of the model. Taking concurrence as a measure of entanglement, we find that a quench generates entanglement between nearest- and next-nearest-neighbor spins, with noise reducing the amount of entanglement. Focusing on the next-nearest-neighbor concurrence, known to exhibit Kibble-Zurek scaling with the square root of the quench rate in the noiseless case, we find a different result when noise is present: The concurrence now scales logarithmically with the quench rate, with a noise-dependent amplitude. This is also different from the “anti-Kibble-Zurek” scaling of defect density with quench rate when noise is present, suggesting that noisy entanglement generation is largely independent of the rate of defect formation. Intriguingly, the critical timescale beyond which no entanglement is produced by a noisy quench scales as a power law with the strength of noise, with the same exponent as that which governs the optimal quench time for which defect formation is at a minimum in a standard quantum annealing scheme.
The dynamics of relative entropy and l1{l}_{1}l1​ norm of coherence, as well as, the Wigner-Yanase skew and quantum Fisher information are studied in the one-dimensional XYXYXY spin chain in the presence of a time-dependent transverse magnetic field. We show that, independent of the initial state of the system and while the relative entropy of coherence, the l1{l}_{1}l1​ norm of coherence, and quantum Fisher information are incapable, surprisingly, the Wigner-Yanase skew information dynamic can truly spotlight the equilibrium critical point. We also observe that, when the system is quenched to the critical point, these quantities show suppressions and revivals. Moreover, the first suppression (revival) time scales linearly with the system size and its scaling ratio is unique for all quenches independent of the initial phase of the system. This is the promised universality of the first suppression (revival) time.
We study the dynamics of a transverse-field XY\mathrm{XY}XY chain driven across quantum critical points by noisy control fields. We characterize the defect density as a function of the quench time and the noise strength and demonstrate that the defect productions for three quench protocols with different scaling exponents exhibit the anti-Kibble-Zurek behavior, whereby slower driving results in more defects. The protocols are quenching through the boundary line between paramagnetic and ferromagnetic phases, quenching across the isolated multicritical point, and quenching along the gapless line, respectively. We also show that the optimal quench time to minimize defects scales as a universal power law of the noise strength in all three cases. Furthermore, by using quantum simulation of the quench dynamics in the spin system with well-designed Landau-Zener crossings in pseudomomentum space, we propose an experimentally feasible scheme to test the predicted anti-Kibble-Zurek behavior of this noisy transverse-field XY\mathrm{XY}XY chain with two-level systems under controllable fluctuations.
In the nonadiabatic dynamics across a quantum phase transition, the Kibble-Zurek paradigm describes that the average number of topological defects is suppressed as a universal power law with the quench time scale. A conflicting observation, termed anti-Kibble-Zurek dynamics, has been reported in several studies, specifically in the driven systems with an uncorrelated stochastic (white) noise. Here, we study the defect generation in the driven transverse field/anisotropy quantum XY model in the presence of a correlated (colored) Gaussian noise. We propose a generic conjecture that properly captures the noise-induced excitation features, which shows good agreement with the numerical simulations. We show that the dynamical features of defect density are modified by varying the noise correlation time. Our numerical simulations confirm that, for fast noises, the dynamics of the defect density is the same as that of the uncorrelated (white) noise, as is expected. However, the larger ratio of noise correlation time to the annealing time results in larger defect density formation and reforms the universal dynamical features. Our finding reveals that the noise-induced defects scale linearly with the annealing time for fast noises, while in the presence of slow noises the noise-induced defects scale linearly with the square of the annealing time. The numerical simulations confirm that the optimal annealing time, at which the defect density is minimum, scales linearly in logarithmic scale with the total noise power having different exponents for fast and slow noises.
Dynamical quantum phase transitions (DQPTs) have been studied in the extended X Y model under both noiseless and noisy linear driven staggered field cases. In the time-independent staggered field case, the model exhibits a single critical point where the transition occurs from the spin-liquid phase to the antiferromagnetic phase. In the noiseless ramp case, unlike the transverse field X Y model where DQPT always occurs for a quench crossing the single critical point, there is a critical sweep velocity above which the kinks corresponding to a DQPT are completely removed. Furthermore, in this case there are only two critical modes whose excitation probability is one-half. In the presence of a Gaussian white noise, we find that this critical sweep velocity decreases by increasing the noise strength, and scales linearly with the square of the noise intensity. A surprising result occurs when the noise intensity and sweep velocity are about the same order of magnitude: The number of critical modes is significantly increased, signaling a region with multiple critical modes. Furthermore, our findings indicate that the scaling of the dynamical free energy near the DQPT time is the same for both noiseless and noisy ramp quenches.
Understanding how noise influences nonequilibrium quantum critical dynamics is essential for both fundamental physics and the development of practical quantum technologies. While the quantum Kibble-Zurek (QKZ) mechanism predicts universal scaling during quenches across a critical point, real quantum systems exhibit complex decoherence that can substantially modify these behaviors, ranging from altering critical scaling to completely suppressing it. By considering a specific case of nondemolishing noise, we first show how decoherence can reshape universal scaling and verify these theoretical predictions using numerical simulations of spin chains across a wide range of noise strengths. Then, we study linear quenches in the transverse-field Ising model on IBM superconducting processors where the noise model is unknown. Using large system sizes of 80-120 qubits, we measure equal-time connected correlations, defect densities, and excess energies across various quench times. Surprisingly, unlike earlier observations where noise-induced defect production masked universal behavior at long times, we observe clear scaling relations, pointing towards persistent universal structure shaped by decoherence. The extracted scaling exponents differ from both ideal QKZ predictions and analytic results for simplified noise models, suggesting the emergence of a distinct noise-influenced universality regime. Our results, therefore, point toward the possibility of using universal dynamical scaling as a high-level descriptor of quantum hardware, complementary to conventional gate-level performance metrics.