The Pauli exclusion principle with a single-valued many-particle wavefunction is equivalent to requiring the wavefunction to be antisymmetric with respect to exchange. If | x ⟩ ⟩ and | y ⟩ ⟩ range over the basis vectors of the Hilbert space describing a one-particle system, then the tensor product produces the basis vectors | x , y ⟩ ⟩ = | x ⟩ ⟩ ⊗ ⊗ | y ⟩ ⟩ of the Hilbert space describing a system of two such particles. Any two-particle state can be represented as a superposition (i.e. sum) of these basis vectors: