The common notions of separability apply for the Fubini–Study metric. More precisely, the metric is separable on the natural product of projective spaces, the Segre embedding. That is, if | ψ ψ ⟩ ⟩ is a separable state, so that it can be written as | ψ ψ ⟩ ⟩ = | ψ ψ A ⟩ ⟩ ⊗ ⊗ | ψ ψ B ⟩ ⟩ , then the metric is the sum of the metric on the subspaces: