  We introduce a quantification of genuine three-party pure-state coherence for
wave fields, classical and quantum, by borrowing concepts from classical
optics. The tensor structure of a classical paraxial light beam composed of
three principle degrees of freedom is shown to be equivalent to that of a
three-qubit quantum state. The traditional basis-independent optical coherence
quantity called degree of polarization is then determined to be the desired
quantitative two-party coherence measure. When appropriately generalized, a set
of fundamental constraint relations is derived among three two-party
coherences. The constraint relations can be geometrically interpreted and
visualized as tetrahedra nested within a coherence cube. A measure of
three-party coherence is defined based on the constraints. We are reporting
completed experimental tests and confirmations of the constraints as well as
measurement of three-party coherence in the optical context. Our approach based
on classical optics also opens an alternative way to analyze quantum coherence.
