Terra incognita of the quantum dimension – Two qubits

Let us consider the combinations of two photons and the potential measurement results (□□, □■, ■□, ■■).
If the photons are not entangled, the measurement results are independent of one another. Let us begin our considerations with this case. Probabilities from two independent events can be multiplied.

In the quantum dimension, we obtain a three-dimensional parameter space for each photon (or qubit) in this case. As a result, obtain a six-dimensional parameter space of all product states of two independent photons in the quantum dimension.
Were the photon pairs thus always to be independent of one another, the quantum dimension would have six dimensions.
However, photons can be entangled with one another. What can be concluded from the latter in regard to the actual number of dimensions?

To infer the quantum dimension behind the measurement results, the four combined probabilities P□□, P □■, P■□, P■■ need to be generalised to become complex amplitudes. Thus, each probability is generalized to a turning wheel. Each turing wheel has a phase and a radius. Overall, the number of parameters is thus doubled, from four to eight. Due to conservation of probability, the number of free parameters for two qubits in the quantum dimension equals 8-1=7.
The quantum dimension of two independent photons does, however, only have six dimensions. How can the difference be interpreted?
The fact of a seventh dimension in the quantum dimension shows that two photons cannot always be considered independent of one another. Photons that have a polarisation oscillation that can be found in this seventh dimension are entangled.
The seventh dimension is defined by the parameter c, concurrence. It specifies the degree of entanglement: For c = 0, the photons are independent of one another, for c = 1 they are maximally entangled.