An ideal experiment to determine the 'past of a particle' in the nested Mach-Zehnder Interferometer

TL;DR

This paper proposes an ideal quantum experiment using standard quantum mechanics to determine the past path of a photon in a nested Mach-Zehnder interferometer, challenging previous claims based on two-state vector formalism.

Contribution

It introduces a novel experimental setup that clarifies the photon’s past in the nested MZI within standard quantum mechanics, refuting earlier interpretations.

Findings

Photon only follows the outer arm when detected

Photon leaves no trace in the inner MZI if it reaches the detector

Results contradict two-state vector formalism claims

Abstract

An ideal experiment is designed to determine the past of a particle in the nested Mach-Zehnder interferometer (MZI) by using standard quantum mechanics with quantum non-demolition measurements. We find that when the photon reaches the detector, it only follows one arm of the outer interferometer and leaves no trace in the inner MZI; while when it goes through the inner MZI, it cannot reach the detector. Our result obtained from the standard quantum mechanics is contradict to the statement based on two state vector formulism, "the photon did not enter the (inner) interferometer, the photon never left the interferometer, but it was there". Therefore, the statement and also the overlap claim are incorrect.