Quantum Classical Correspondence Using Coherent State Measurements and Husimi Q Probability Distributions

Abstract

We propose and simulate a protocol to evolve a quantum particle forward in time such that its trajectory closely matches that of the particle's Newtonian counterpart. Using short bursts of Schr\"odinger time-evolution interleaved with positive operator-valued measurements (POVMs) in the coherent basis, we demonstrate quantum-classical convergence for durations far beyond Schr\"odinger time-evolution alone. We examine the impact of the time between measurements $\Delta t$ and the reduced Planck's constant $\hbar$ on divergence time. Results indicate that for appropriate values of $\Delta t$, smaller values of $\hbar$ lead to longer divergence times. This method suggests a elegant, intuitive bridge to recover classical motion from quantum postulates.