and such that ⟨ ⟨ ↓ ↓ | ↑ ↑ ⟩ ⟩ = 0 and ⟨ ⟨ ↓ ↓ | ↓ ↓ ⟩ ⟩ = ⟨ ⟨ ↑ ↑ | ↑ ↑ ⟩ ⟩ = 1 , i.e., such that | ↑ ↑ ⟩ and | ↓ ↓ ⟩ form a basis and have diametrically opposite representations on the Bloch sphere, then let