Determination of Quantum Instrument Parameters for a Stern-Gerlach Non-ideal Device

TL;DR

This work addresses modeling non-ideal Stern-Gerlach measurements using operational quantum physics (OQP). It develops a two-outcome quantum instrument described by Kraus operators A_up and A_down, with effects F_up and F_down, and links experimental probabilities to instrument parameters through the probabilistic rule p(X) = Tr[I(X) rho_s]. In the small non-ideality regime, the authors derive linear, perturbative relations between angular fit coefficients (c0, c1, c2, c3) and the Kraus parameters, enabling practical parameter extraction from both single and successive rotated measurements. The method yields experimentally accessible quantities that test the OQP framework and can be extended to stronger non-ideality and longer sequences, providing a concrete pathway to characterize real SG devices. The key outcome is a tractable, perturbative bridge between observable measurement statistics and the underlying quantum instrument describing non-ideal spin filtering.

Abstract

In the Stern--Gerlach (SG) apparatus, when the filtering is not perfect, the fermion state transformation is done by non-ideal devices. Such an apparatus is described in quantum mechanics by quantum instruments. It will be shown how the parameters of this instrument can be expressed in terms of some experimentally accessible quantities. These relations are valid both for single and successive measurements. In the latter case, the measuring device is rotated with respect to the first one.