Dynamical geometric signatures of quantum channels: a geometric framework for analysing channel-induced dynamics
摘要
We present a geometric framework for quantum channels based on Bures–Fisher–Rao information geometry. Rather than modifying the underlying geometry, quantum channels induce trajectories in the space of quantum states whose properties encode information about noise and decoherence from a geometric perspective. Building on this viewpoint, we introduce a family of dynamical geometric descriptors that characterise how channel-induced evolutions explore the state space, providing descriptive indicators of aspects such as efficiency, alignment, anisotropy, and cumulative behaviour. These quantities define a unified geometric framework that complements conventional scalar diagnostics, such as fidelity or purity, by incorporating trajectory-level information. Numerical analysis of canonical single-qubit noise channels (dephasing, depolarisation, and amplitude damping) reveals consistent geometric patterns associated with each mechanism, reflecting differences in trajectory structure, curvature exposure, and directional behaviour within state space. A case study of fibre-induced dephasing illustrates the behaviour of the framework in a physically motivated setting, showing that the proposed descriptors reproduce expected decoherence trends as a function of transmission distance. The proposed dynamical geometric descriptors provide a complementary perspective on quantum noise by characterising trajectory-level aspects of channel-induced dynamics, including geodesic deviation, alignment, anisotropy, and cumulative geometric behaviour, beyond standard endpoint-based metrics.