Fig. 2: The initial state \(\left\vert Sy{m}_{N}\right\rangle\) of 2N bosons in N spatial modes.
From: Shortcut to multipartite entanglement generation: A graph approach to boson subtractions

Each spatial mode has two bosons, one in the internal state \(\left\vert 0\right\rangle\) and the other in \(\left\vert 1\right\rangle\).