  In the context of the measurement problem, we propose to model the
interaction between a quantum particle and an "apparatus" through a
non-Hermitian Hamiltonian term. We simulate the time evolution of a normalized
quantum state split into two spin components (via a Stern-Gerlach experiment)
and that undergoes a wave-function collapse driven by a non-Hermitian
Hatano-Nelson Hamiltonian. We further analyze how the strength and other
parameters of the non-Hermitian perturbation influence the time-to-collapse of
the wave function obtained under a Schr\"{o}dinger-type evolution. We finally
discuss a thought experiment where manipulation of the apparatus could
challenge standard quantum mechanics predictions.
