Consider the state of a bipartite system | Ψ Ψ ⟩ ⟩ ∈ ∈ H A ⊗ ⊗ H B . Every such state | Ψ Ψ ⟩ ⟩ can be represented in an appropriately chosen basis as: | Ψ Ψ ⟩ = ∑ ∑ i = 1 M A | B a i | Φ Φ i A Φ Φ i B ⟩ where | Φ Φ i A Φ Φ i B ⟩ ⟩ = | Φ Φ i A ⟩ ⟩ ⊗ ⊗ | Φ Φ i B ⟩ ⟩ are formed with vectors | Φ Φ i A ⟩ ⟩ that make an orthonormal basis in H A and, correspondingly, vectors | Φ Φ i B ⟩ ⟩ , which form an orthonormal basis in H B , with the coefficients a i being real and positive, ∑ ∑ i = 1 M A | B a i 2 = 1 . This is called the Schmidt decomposition (SD) of a state. In general the summation goes up to M A | B = min ( dim ⁡ ⁡ ( H A ) , dim ⁡ ⁡ ( H B ) ) . The Schmidt rank of a bipartite split is given by the number of non-zero Schmidt coefficients. If the Schmidt rank is one, the split is characterized by a product state. The vectors of the SD are determined up to a phase and the eigenvalues and the Schmidt rank are unique.