  Non-Hermitian systems with parity-time ($\mathcal{PT}$) symmetry give rise to
exceptional points (EPs) with exceptional properties that arise due to the
coalescence of eigenvectors. Such systems have been extensively explored in the
classical domain, where second or higher order EPs have been proposed or
realized. In contrast, quantum information studies of $\mathcal{PT}$-symmetric
systems have been confined to systems with a two-dimensional Hilbert space.
Here by using a single-photon interferometry setup, we simulate quantum
dynamics of a four-dimensional $\mathcal{PT}$-symmetric system across a
fourth-order exceptional point. By tracking the coherent, non-unitary evolution
of the density matrix of the system in $\mathcal{PT}$-symmetry unbroken and
broken regions, we observe the entropy dynamics for both the entire system, and
the gain and loss subsystems. Our setup is scalable to the higher-dimensional
$\mathcal{PT}$-symmetric systems, and our results point towards the rich
dynamics and critical properties.
