The process can be decomposed in three steps, iterated for each bond (and, correspondingly, SD) in the chain: Step 1 : express the | Φ Φ α α 1 [ 2.. N ] ⟩ ⟩ 's in a local basis for qubit 2: | Φ Φ α α 1 [ 2.. N ] ⟩ ⟩ = ∑ ∑ i 2 | i 2 ⟩ ⟩ | τ τ α α 1 i 2 [ 3.. N ] ⟩ ⟩