We can model a photon going through the interferometer by considering that at each point it can be in a superposition of only two paths: the "lower" path which starts from the left, goes straight through both beam splitters, and ends at the top, and the "upper" path which starts from the bottom, goes straight through both beam splitters, and ends at the right. The quantum state of the photon is therefore a vector ψ ψ ∈ ∈ C 2 that is a superposition of the "lower" path ψ ψ l = ( 1 0 ) and the "upper" path ψ ψ u = ( 0 1 ) , that is, ψ ψ = α α ψ ψ l + β β ψ ψ u for complex α α , β β . In order to respect the postulate that ⟨ ⟨ ψ ψ , ψ ψ ⟩ ⟩ = 1 we require that | α α | 2 + | β β | 2 = 1 .