# Order-invariant two-photon quantum correlations in PT-symmetric interferometers

## TL;DR

This paper discovers and experimentally verifies sequences of two-mode optical transformations in PT-symmetric interferometers where two-photon correlations remain unchanged when the order of transformations is reversed, revealing new ways to preserve quantum correlations.

## Contribution

It introduces order-invariant two-photon correlation sequences in PT-symmetric interferometers and experimentally demonstrates their behavior in complex optical networks.

## Key findings

- Two-photon correlations are invariant under reversal of concatenated transformations.
- Experimental verification in PT-symmetric interferometers confirms theoretical predictions.
- Quantum correlations can be preserved in non-Hermitian networks despite counterintuitive configurations.

## Abstract

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.