In quantum mechanics, it is not easy to answer the question where a photon has been. On the one hand, If we try to measure the accurate "position" of a photon, then the interaction between the photon and the measurement devices will generally be strong enough to destroy the quantum state of the photon (e.g., the photon is absorbed by a photon detector.), and the propagation of the photon will be blocked. On the other hand, if the interaction between the photon and the measurement devices is too weak to destroy the quantum state of the photon, the accurate "position" of the photon could not be measured.

However, if we make the propagating photon interact with the environment slightly and limit the interaction to be very weak, the quantum state of the photon is not destroyed while some subtle "traces" of the photon-environment interaction is produced. By measuring these "traces", it is possible to collect the information about where the photon has been. These techniques of measurement are called "weak measurement", and the "traces" are called "weak traces". The presence of weak trace is often considered to be the criterion of where the photon has been.

The nested Mach-Zehnder interferometer (NMZI) can be used for such weak measurements. In such experiments, the mirrors in the NMZI vibrate slightly in different frequencies, and when a photon reflects off on a certain mirror, the photon will obtain a tiny transverse momentum relating to the vibration frequency of the mirror and cause a little shift of the light spot on the detector. By measuring the shift, the vibration frequency of the mirror can be recognized and one can determine that if the photon has been reflected by the certain mirror.

Dr. Qizhang Yuan and Prof. Xunli Feng from Shanghai Normal University introduced the absence of the weak traces under some conditions in Chinese Optics Letters, Vol. 19, No. 1, 2021 (Qizhang Yuan, Xunli Feng. Photons can hide where they have been [J]. Chinese Optics Letters, 2021, 19(1): 012701).

With Dove prisms, the weak trace relating to mirror E can be erased by destructive interference, while the photon actually has reflected off on the mirror

By placing Dove prisms in the arms of NMZI and properly adjusting the interference conditions of the interferometer, one can erase the weak trace relating to a certain mirror making used of destructive interference although the photon actually have reflected on the mirror.

This study shows that the presence of weak traces is a sufficient condition for photons having gone to some places, but it is not a necessary condition. If the weak trace relating to a certain location is not observed, it does not mean that the photon definitely has not passed through the corresponding location.

The study explains the quantum non-locality phenomena observed in NMZI experiments with a clear and simple physical picture, deepens the understanding of weak traces, and helps to further understand the non-local properties of photons.