Uncoupled Stage Factorizes - Quantum Computing Physical Bases: Control, Coupling, and Error Signals Step by Step

When the coupling stage is off, the two-qubit table remains a product ledger rather than a joint interaction. The factorization check is exact only for the stated amplitudes and no-coupling assumption; real hardware can still add residual coupling, leakage, calibration drift, decoherence, and readout uncertainty.

A stage with no coupling keeps a product state product. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

No coupling leaves the table factorable

With the coupling stage off, the determinant is 0. The table is still a product state.

\det=0

Zero determinant rows keep the product claim honest

The scan ties the product label to the determinant, not to the lesson caption.

\begin{array}{c|c|c}\text{input}&\det&\text{claim}\\\text{basis}\times\text{plus}&0&\text{product}\\\text{after I}&0&\text{product}\\\text{checked}&0&\text{product}\\\end{array}

The product label is checked

The renderer requires the product flag to match the determinant, so a caption cannot hide a non-product state.

\text{product claim follows determinant}