Multiphoton correlations in linear photonic quantum networks are governed by matrix permanents. Yet, surprisingly few systematic properties of these crucial algebraic objects are known, while their calculation is a computationally hard task. As such, predicting the overall multiphoton behavior of a network from its individual building blocks typically defies intuition. In this work we identify sequences of concatenated two-mode linear optical transformations whose two-photon behavior is invariant under reversal of the order. We experimentally verify this systematic behavior in parity-time-symmetric complex interferometer arrangements of varying composition. Our results underline new ways in which quantum correlations may be preserved in counterintuitive ways even in small-scale non-Hermitian networks.
@article{arxiv.2302.11884,
title = {Order-invariant two-photon quantum correlations in PT-symmetric interferometers},
author = {Tom A. W. Wolterink and Matthias Heinrich and Stefan Scheel and Alexander Szameit},
journal= {arXiv preprint arXiv:2302.11884},
year = {2025}
}