 Quark rephasing and CP conservation

For nondegenerate quark masses, independent phase changes of the up- and down-quark mass eigenfields alter the numerical CKM matrix by row and column phases without changing physics. Thus CP symmetry requires that some allowed phase convention makes the matrix real, rather than requiring real entries in every convention. With $N$ generic families, removing $2N-1$ phases from a unitary matrix leaves $(N-1)(N-2)/2$ physical CP-violating phases and $N(N-1)/2$ mixing angles.