  Linear-optical interferometers play a key role in designing circuits for
quantum information processing and quantum communications. Even though nested
Mach-Zehnder interferometers appear easy to describe, there are occasions when
they provide unintuitive results. This paper explains the results of a highly
discussed experiment performed by Danan et al. [Phys. Rev. Lett. 111, 240402
(2013)] using a standard approach. We provide a simple and intuitive one-state
vector formalism capable of interpreting their experiment. Additionally, we
cross-checked our model with a classical-physics based approach and found that
both models are in complete agreement. We argue that the quantity used in the
mentioned experiment is not a suitable which-path witness producing seemingly
contra-intuitive results. To circumvent this issue, we establish a more
reliable which-path witness and show that it yields well expected outcomes of
the experiment.
