Readout Channel Applied Last - Quantum Computing Physical Bases: Control, Coupling, and Error Signals Step by Step

Keep the quantum coupling claim separate from the later classical readout channel. The pinned determinant row gives 1/2 before readout, so the joint state is already non-product before any assignment matrix is applied; measured systems still need calibration checks, crosstalk limits, decoherence budgets, and readout-noise uncertainty.

The joint-state coupling claim and the readout channel claim stay separate. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Coupling changes the joint state before readout

The coupling stage creates a non-product joint table before any classical assignment matrix is applied.

\text{couple before readout}

The coupling claim is checked before calibration

The determinant row belongs to the quantum stage; the readout row belongs to the later classical stage.

\begin{array}{c|c|c}\text{stage}&\text{number}&\text{claim}\\\text{coupling}&\frac{1}{2}&\det\neq0\\\text{readout}&80&\text{counts}\\\text{order}&2&\text{separate}\\\end{array}

The determinant closes the coupling claim

The determinant is 1/2, so the state is not product before readout.

\det=\frac{1}{2}