Abstract

Quantum correlations in linear optical networks are a crucial resource for quantum information processing. Correlations between multiple photons are described by the permanent of the transmission matrix of the optical network [1]. Yet, despite their central role, very few properties of permanents are known to exist and the calculation of matrix permanents remains a computationally hard problem, which, at large scale, has sparked the field of boson sampling. However, the lack of tangible properties also affects small-scale networks, as it hinders intuitive prediction of the behavior of composite systems from their components. This especially holds for non-Hermitian systems that incorporate losses, which are known to drastically alter quantum correlations even in networks of just two modes, such as a lossy beam splitter [2,3]. Here, we systematically identify sequences of two-mode systems that perform distinct transformations, whereas their permanents remain invariant under reversal of the entire sequence’s order. We experimentally verify this property by probing the two-photon correlations in parity-time (PT)-symmetric interferometers of wildly different composition.

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