A Diagnostic Framework for Quantum Noise Channels in Single-Qubit Cyber-Physical Systems

Abstract

Single-qubit channels provide a controlled setting for comparing how different noise mechanisms change a quantum state. Using density matrices and Kraus operators, this paper compares bit-flip, phase-flip, depolarising, amplitudedamping, and phase-damping channels under the same set of input states and diagnostic metrics. The channels are tested on selected initial states to compare their effects on computational basis and superposition states. For each noisy state, purity, fidelity, von Neumann entropy, Bloch-vector norm, and quantum Fisher information (QFI) for $\boldsymbol{Z}$-axis phase encoding are calculated. The procedure is implemented in the Maple computing environment and used to perform parameter sweeps, generate two- and three-dimensional visualisations, and identify changes in metric behaviour. An engineering degradation index is introduced to combine the individual metrics and distinguish working, degraded, and critical parameter ranges. The calculations show that the $\vert+\rangle$ state is unchanged by bit-flip noise, whereas phase-flip noise produces maximum mixedness at $\boldsymbol{p}=\mathbf{0. 5}$, and phase damping progressively removes coherence and $\boldsymbol{Z}$-axis phase sensitivity. The Maple implementation returns metric curves and degradation-score crossings for all channels considered, along with state-angle surfaces for amplitude and phase damping.