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For nondegenerate quark masses, changing the constant quantum phases of quark fields preserves their diagonal mass terms. Adopt the conventionSuch quantum field rephasings alter individual entries of the CKM matrix without altering physics. Physical CP symmetry in this mixing sector means that some allowed convention makes the CKM matrix real. Toshihide Maskawa emphasized the distinction between complex entries and an irremovable CP-violating phase.^[ref]

Here is a constructive two-generation argument. For a generic $2\times 2$ unitary matrix, use the three effective row/column phases to make $V_{11},V_{12},V_{22}$ real and positive. Column orthogonality then forces $V_{21}$ to be real and negative. Row normalization leaves just the real rotation specified by the Cabibbo angle. Zero entries are limiting cases and introduce no weak phase. Thus two-generation quark mixing cannot violate CP symmetry through this mechanism, even when its entries initially look complex.

For three quark generations, the Jarlskog invariant provides an obstruction to repeating that construction: all four phase factors cancel from its defining quartet. If its imaginary part is nonzero, no choice of quantum field rephasings can make every entry real. With nondegenerate quark masses, this proves physical CP violation in the mixing sector. This argument concerns the weak interaction; it does not dispose of the separate Strong CP problem.