Erasure-Biased Noise from Angular Momentum Diffusion: An OAM Analog of Cat-Qubit Protection

Abstract

Description This technical note introduces a theoretical architecture for real-time Quantum Non-Demolition (QND) monitoring of Orbital Angular Momentum (OAM) Cat-Qubits using a synthetic frequency dimension. The proposed approach enables continuous estimation of channel hopping, erasure probability, and qubit health without modifying the logical populations encoded in the OAM basis. A complete Lindblad master-equation model is developed to evaluate the monitoring strategy under realistic quantum noise. Four numerical scenarios compare operation with and without QND monitoring during idle periods and coherent gate execution. The simulations confirm two important theoretical predictions: • QND monitoring preserves population dynamics and logical error statistics.• Continuous monitoring during coherent gates rapidly destroys off-diagonal coherence through measurement-induced dephasing. These results suggest that duty-cycled monitoring, enabled only during idle intervals, could provide a practical quantum telemetry layer for future photonic quantum processors while maintaining computational fidelity. This work is intended as a theoretical contribution and a numerical validation framework for future experimental implementations.