This follows, as for a pure state, one has the density matrix ρ ρ t = | ψ ψ t ⟩ ⟩ ⟨ ⟨ ψ ψ t | . The quantum angle (Fubini–Study distance) is then D B ( ρ ρ 0 , ρ ρ t ) = arccos ⁡ ⁡ | ⟨ ⟨ ψ ψ 0 | ψ ψ t ⟩ ⟩ | and so one concludes D B = arccos ⁡ ⁡ 0 = π π / 2 when the initial and final states are orthogonal.