One-state vector formalism for the evolution of a quantum state through nested Mach-Zehnder interferometers

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 contraintuitive results. To circumvent this issue, we establish a more reliable which-path witness and show that it yields well-expected outcomes of the experiment.

Figure 1

Drawing of the experimental setup with two nested Mach-Zender interferometers. (a) Power spectrum on detector D shows all frequencies of mirror oscillations for the phase $\phi =\pi$, (b) power spectra for $\phi =0$, and (c) power spectrum for phase $\phi =0$ and the lower path $\widehat{c}$ blocked, as predicted by our approach.