Pre- and post-selected spin measurements under one internal degree of freedom induced decoherence

Abstract

We investigate the quantum measurement dynamics of a spin-1/2 particle using Galapon's measurement model, focusing on the spin-z component. The particle interacts with a probe and pointer, both initialized in Gaussian wave packets. By varying the interaction time, we observe a transition from weak to strong measurement regimes. In the weak limit, our results reproduce Aharonov's anomalous weak values; in the strong limit, outcomes converge to the spin-z eigenvalues. This study highlights the transition of expectation values from weak to strong measurements within Galapon's framework.