Fig. 3: The initial state \(\left\vert Sy{m}_{N.d}\right\rangle\) of dN bosons in N spatial modes.
From: Shortcut to multipartite entanglement generation: A graph approach to boson subtractions

Each spatial mode has d bosons, which have mutually orthogonal internal states \(\left\vert 0\right\rangle ,\left\vert 1\right\rangle ,\cdots \,,\left\vert d-1\right\rangle\).