Balanced Control Then Coupling - Quantum Computing Physical Bases: Control, Coupling, and Error Signals Step by Step

A checked coupling map acts on the whole joint state. 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 table

A controlled map sends the balanced control and zero target into a joint table with two nonzero cells.

\text{CNOT}\left(\lvert +\rangle\lvert 0\rangle\right)

Only the matched joint cells carry probability

The coupled output is visible as two populated diagonal cells and two empty off-diagonal cells.

\begin{array}{c|c|c}\text{cell}&p&\text{role}\\\text{zero-zero}&\frac{1}{2}&\text{kept}\\\text{zero-one}&0&\text{empty}\\\text{one-one}&\frac{1}{2}&\text{kept}\\\end{array}

The two visible cells split the budget

The zero-zero and one-one cells each carry probability 1/2.

p_{\text{zero zero}}=p_{\text{one one}}=\frac{1}{2}