Three named-pulse rows keep map domains and output probabilities source-bound. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

The flip pulse maps zero to one

The first row uses the reviewed flip-pulse domain: zero in, one out.

X0=1X\lvert 0\rangle=\lvert 1\rangle
Flip zero rowThe pulse output is checked by the named map.state1 zero0 onestate0 zero1 onez basis0zero1oneXpulseflip pulse

Three named-pulse rows keep the domain explicit

The balance-from-one row is not the same as the balance-from-zero row. Its output probabilities are still checked exactly.

rzoFz01Fo10Bo1212\begin{array}{c|c|c}r&z&o\\\text{Fz}&0&1\\\text{Fo}&1&0\\\text{Bo}&\frac{1}{2}&\frac{1}{2}\\\end{array}
Flip one rowThe second row renders the opposite flip input.state0 zero1 onestate1 zero0 onez basis1zero0oneXpulseflip pulse

Signed balance from one is a separate reviewed name

The signed balance row outputs equal probabilities but keeps its own pulse name and input-domain rule.

pzero=pone=12p_{\text{zero}}=p_{\text{one}}=\frac{1}{2}
Signed balance rowThe third row is a separate checked pulse contract.state0 zero1 onestate1/sqrt(2) zero-1/sqrt(2) onez basis1/2zero1/2oneHpulsesigned balance pulse from one