A computation is a sequence of checked physical stage contracts. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

One stage output feeds the next

The balanced state feeds a phase stage, and that output feeds the recombination stage.

balancephaserecombine\text{balance}\to\text{phase}\to\text{recombine}
Checked stage chainEach gate box checks one stage output.state1 zero0 onestate0 zero1 onez basis1/2zero1/2onez basis0zero1oneHprepZphaseHread

Each stage reports the same conserved budget

The middle row shows why direct counts alone do not expose the phase; the final row shows recombination using it.

stagepzeroponebalance1212phase1212recombine01\begin{array}{c|c|c}\text{stage}&p_{\text{zero}}&p_{\text{one}}\\\text{balance}&\frac{1}{2}&\frac{1}{2}\\\text{phase}&\frac{1}{2}&\frac{1}{2}\\\text{recombine}&0&1\\\end{array}
Stage budget scanThe same chain supplies all three rows.state1 zero0 onestate0 zero1 onez basis1/2zero1/2onez basis0zero1oneHprepZphaseHread

The final state is determined

The checked chain ends in the one state with probability 1 for one and 0 for zero.

pone=1,pzero=0p_{\text{one}}=1,\quad p_{\text{zero}}=0
Stage output reusedThe final probability bars are computed.state1 zero0 onestate0 zero1 onez basis1/2zero1/2onez basis0zero1oneHprepZphaseHread