Quantum information crossover in time-fractional Pauli channels: Analysis of quantum Fisher information and fidelity

We develop a time-fractional Lindblad master equation to describe the dynamics of open quantum systems with long-time environmental memory. The introduction of a fractional derivative gives rise to an intrinsic power-law memory kernel, providing a physically transparent extension of the standard Lindblad framework while preserving complete positivity. Within this framework, we systematically investigate Pauli channels, including bit-flip, phase damping, and depolarizing noise, and derive analytical expressions for both the quantum Fisher information and the average fidelity. We reveal a pronounced crossover behavior in their dynamics, where strong memory effects accelerate information loss at short times while significantly protecting quantum coherence and metrological precision at long times. Such a crossover, absent in conventional integer-order descriptions without ad hoc time-dependent modifications, constitutes a clear hallmark of fractional quantum dynamics. Our results provide new physical insight into non-Markovian evolution and offer practical guidance for optimizing quantum metrology and quantum-state preservation in realistic noisy environments.