where | ψ ψ 1 ⟩ ⟩ and | ψ ψ 2 ⟩ ⟩ are assumed orthogonal and of dimension 2, for simplicity. On the other hand, a quantum superposition of these two states with equal probability amplitudes results in the pure state | ψ ψ ⟩ ⟩ = ( | ψ ψ 1 ⟩ ⟩ + | ψ ψ 2 ⟩ ⟩ ) / 2 , with density matrix