where { | e k ⟩ ⟩ } is a set of orthonormal basis vectors for Hilbert space, the Z k are complex numbers, and Z α α = [ Z 0 : Z 1 : … … : Z n ] is the standard notation for a point in the projective space CP in homogeneous coordinates. Then, given two points | ψ ψ ⟩ ⟩ = Z α α and | φ φ ⟩ ⟩ = W α α in the space, the distance (length of a geodesic) between them is