For starters, you have to extend Gleason’s theorem to apply it to qubits. In general I would start with John Bell’s book “Speakable and Unspeakable…” but a litt

For starters, you have to extend Gleason’s theorem to apply it to qubits. In general I would start with John Bell’s book “Speakable and Unspeakable…” but a little mathematical maturity is required. Then you can try Hardy’s paradox but it is not easy. I think getting rid of complex numbers is a mistake because phase information is important. These analogies you invoke totally use things like principal axis which is a similarity operation, center of mass which uses normal modes which are found using eigenvector, etc. The real rotation matrix (which can be described as a composition of reflections) has complex eigenvectors! Diagonalizing a diagonalizable matrix involves conjugating by a matrix (and transposed one) of its eigenvectors!