Quantum-to-Classical Transition via Single-Shot Generalized Measurements

Abstract: Quantum-to-classical transition for finite-dimensional systems is widely considered to occur continuously, yet the mechanism underlying the intermediate stage remains unclear. In this work, we address this challenge by adopting an operational framework to bridge discrete generalized coherent state positive-operator-valued measurements and continuous isotropic depolarizing channels. Our unified treatment reveals how dimensionality and decoherence rate collectively govern the quantum-to-classical transition. Notably, we demonstrate that a single-shot generalized measurement can eliminate most negative quasi-probabilities in phase space for finite-dimensional systems. Furthermore, we propose quantum circuit implementations achievable with current state-of-the-art quantum technologies.