# Why do we use two optical modes per qubit in the KLM scheme?

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 $$|1\rangle\mapsto|1\rangle_{l_1}$$?

• How would you implement the coherent gates? It's super to move photons between modes than to create and annihilate them... Aug 20 '20 at 19:38
• Would it be correct to say that moving between modes is linear optics while creating a photon in a mode is nonlinear? Aug 21 '20 at 1:29

## 1 Answer

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