  Exceptional points (EPs) are degeneracies of non-Hermitian operators where,
in addition to the eigenvalues, corresponding eigenmodes become degenerate.
Classical and quantum photonic systems with EPs have attracted tremendous
attention due to their unusual properties, topological features, and an
enhanced sensitivity that depends on the order of the EP, i.e. the number of
degenerate eigenmodes. Yet, experimentally engineering higher-order EPs in
classical or quantum domains remains an open challenge due to the stringent
symmetry constraints that are required for the coalescence of multiple
eigenmodes. Here we analytically show that the number-resolved dynamics of a
single, lossy, waveguide beamsplitter, excited by $N$ indistinguishable photons
and post-selected to the $N$-photon subspace, will exhibit an EP of order
$N+1$. By using the well-established mapping between a beamsplitter Hamiltonian
and the perfect state transfer model in the photon-number space, we
analytically obtain the time evolution of a general $N$-photon state, and
numerically simulate the system's evolution in the post-selected manifold. Our
results pave the way towards realizing robust, arbitrary-order EPs on demand in
a single device.
