From Riemannian Trichromacy to Quantum Color Opponency via Hyperbolicity

We propose a mathematical description of human color perception that relies on a hyperbolic structure of the space $${\mathcal {P}}$$ of perceived colors. We show that hyperbolicity allows us to reconcile both trichromaticity, from a Riemannian point of view, and color opponency, from a quantum viewpoint. In particular, we will underline how the opponent behavior can be represented by a rebit, a real analog of a qubit, whose state space is endowed with the Hilbert metric.