A Bell correlation strength three-row scan holds same-bit correlation fixed at probability one while the split between the zero-zero and one-one branches moves toward even, so the checked determinant grows from row to row. The three rows split twelve-thirteenths and five-thirteenths (determinant 60/169), four-fifths and three-fifths (determinant 12/25), and the even split at one over square root of two on each branch (determinant 1/2, the maximal case already checked in chapter five) for the stated toy two-qubit ledger; real entangled-qubit pairs have finite gate fidelity, decoherence, and readout crosstalk that erode the same-bit correlation over time.
Three correlated two-qubit splits keep same-bit correlation while the checked determinant grows toward the maximal even split. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
An uneven split still gives same-bit correlation
The weakest row splits twelve-thirteenths and five-thirteenths between the zero-zero and one-one branches. Same-bit outcomes still have probability one; the split only changes how much weight each branch carries.
P00=169144,P11=16925
The determinant grows as the split becomes even
Three rows keep same-bit correlation while the split moves toward even. The determinant, computed from the two nonzero diagonal amplitudes, grows from row to row and is largest exactly at the even split from chapter five.
The even split reaches the maximal checked determinant
The third row is the Bell pair already checked in chapter five: an even split at one over square root of two on each branch, giving the largest determinant of the three rows.