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Within photonic quantum computing, one of the ways to represent information is the dual-rail representation of single-photon states ($c_0|01\rangle \ + \ c_1|10\rangle$). Is it possible to utilize multi-photon states (for example, two optical cavities with total energy $2\hbar\omega$, using a state like $c_0|02\rangle \ + \ c_1|20\rangle \ + \ c_2|11\rangle$, where $|02\rangle$ represents two photons in one cavity, $|20\rangle$ represents two photons in the other cavity, and $|11\rangle$ represents one photon in each cavity?