  Using the correspondence of a two dimensional paraxial and three dimensional
non-paraxial optical beams with the qubit and qutrit systems respectively, we
derive a complementarity relation between Hilbert-Schmidt coherence,
generalized predictability and linear entropy. The linear entropy, a measure of
mixedness is shown to saturate the complimentarity relation for mixed
bi-partite states, which for the pure two qubit and qutrit systems quantifies
the global entanglement and reduces the complimentarity relation to the
triality relation between coherence, predictability and entanglement.
