Phase and Recombination

Recombination Stage Reveals

phase becomes an outcome

A later recombination gate turns the stored phase relation into exact counts. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Recombination turns phase into counts

The recombination stage maps the phased state to the one outcome.

HZ∣+⟩=∣1⟩HZ\lvert +\rangle=\lvert 1\rangle
Phase recombinedThe final bars are zero then one.state1 zero0 onestate0 zero1 onez basis1/2zero1/2onez basis0zero1oneHprepZphaseHread

The count budget moves only at recombination

The scan separates the hidden phase row from the final row where the measured budget changes.

stagepzeroponestart1212phase1212recombined01\begin{array}{c|c|c}\text{stage}&p_{\text{zero}}&p_{\text{one}}\\\text{start}&\frac{1}{2}&\frac{1}{2}\\\text{phase}&\frac{1}{2}&\frac{1}{2}\\\text{recombined}&0&1\\\end{array}
Recombination scanThe final row is where the stored phase appears.state1 zero0 onestate0 zero1 onez basis1/2zero1/2onez basis0zero1oneHprepZphaseHread

The final probabilities are exact

The final zero probability is 0 and the final one probability is 1.

pzero=0,pone=1p_{\text{zero}}=0,\quad p_{\text{one}}=1
Final readout budgetThe recombined state gives a deterministic result.state1 zero0 onestate0 zero1 onez basis1/2zero1/2onez basis0zero1oneHprepZphaseHread