I think this is how SU(3) bears on quarks.
SU(3) is the set of transformations on the three dimensional complex vector space ℂ^{3} (more specifically an inner product space) to itself that do not change the magnitude of vectors.
If we assume some orthonormal basis {r, g, b} for that vector space then an arbitrary vector in the space can be uniquely written <x_{r}, x_{g}, x_{b}> = x_{r}r + x_{g}g + x_{b}b.
The x’s are complex numbers.
The magnitude of that vector is √(x_{r}x_{r}* + x_{g}x_{g}* + x_{b}x_{b}*) where x* is the complex conjugate of x and thus each xx* is real and non negative and the magnitude is real and non negative.
The quantum state of a quark is a vector in this space of magnitude 1. When the vector is r we say that the quark is red.
Ditto g and b.
We say that a quarks is either red, green or blue in the same sense that we usually say that the spin of an electron is up or down, or that a photon is polarized either horizontally or vertically.

From a mathematical perspective this is a queasy way to speak.
It is proper to say that a photon is polarized at 28° when it has just passed thru a polarizing filter set to that angle.
Physicists avoid speaking this way for the good reason that there is no experiment on a photon to determent its orientation.
We can also say that the amplitude of the electron is the superposition (cos 28°)|↑⟩ + (sin 28°)|→⟩, which means the same thing.
With the filter we can make the assertion knowing the photon’s recent history.
In the case of the photon there is a clear relation between the ‘horizontal’ of polarization to the ‘horizontal’ of the space in which the experiment is performed.
Physicists claim that there is no such relation between the coordinates of quark color space to coordinates of the geometry of the physics space.
The expressions “|↑⟩” and “|→⟩” are vectors in a complex 2D vector space.
I think that circularly polarized light is (|↑⟩ + i|→⟩)/√2.
SU(2) operates on this space.

Note that if we have a stream of photons that have just come thru the same filter then there is an experiment that we can do on the photons to get a good approximation to the orientation of the filter.

I do not know what physical evidence there is that relates quarks to SU(3).

See spin too.

### Symmetries