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The original KLM paper says:

The basic states of a bosonic qubit encoded in modes $l_1$ and $l_2$ are $|0\rangle\mapsto|0\rangle_{l_1}|1\rangle_{l_2}$ and $|1\rangle\mapsto|1\rangle_{l_1}|0\rangle_{l_2}$.

Why couldn't we simply encode qubits as $|0\rangle\mapsto|0\rangle_{l_1}$ and $|1\rangle\mapsto|1\rangle_{l_1}$?

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  • $\begingroup$ How would you implement the coherent gates? It's super to move photons between modes than to create and annihilate them... $\endgroup$
    – M. Stern
    Aug 20 '20 at 19:38
  • $\begingroup$ Would it be correct to say that moving between modes is linear optics while creating a photon in a mode is nonlinear? $\endgroup$
    – mavzolej
    Aug 21 '20 at 1:29
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Mathematically, both options are ok. You can use "single-rail" or "dual-rail" encoding. Dual-rail has some implementation advantages. Look here for example : https://arxiv.org/pdf/1103.6071.pdf

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