Which-path information of path-polarization hybrid state in polarization-based nested Mach-Zehnder interferometer

The two-state vector formalism (TSVF) describes a quantum system between two measurements, with a pre- and post-selected states evolving forward and backward in time, respectively. In this paper, we investigate the which-path information and the TSVF analysis considering the polarization and path states in a polarization-based nested Mach-Zehnder interferometer (NMZI). By adjusting photon polarization in the multipath via polarization optics, we can investigate the which-path information of the photons after the polarization beam splitter in the polarization-based NMZI under conditions of constructive or destructive interference conditions. Considering the incomplete polarization states of photons in the NMZI, the interpretation of our experimental results does not contradict the TSVF analysis.