Three coupling inputs show where the product-state determinant crosses the boundary. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
Uncoupled plus-plus stays product
The off row keeps four equal probabilities. Its determinant magnitude is 0.
∣det∣=0,n=0
Two CNOT inputs cross the determinant boundary
The two coupled rows use different target inputs, but both make a nonzero determinant magnitude.
rowoffzeroone∣det∣02121n011
The target-one row is a separate checked input
Changing the target input does not reuse a caption. The CNOT row is checked again from its own source state.