An asymmetric assignment scan keeps the prepared-zero correct rate fixed at 9/10 while the prepared-one correct rate drops across three rows: 9/10 (symmetric baseline), 7/10 (mild asymmetry), and 5/10 (a coin flip) exactly for the stated toy calibration counts. Real readout hardware often shows exactly this shape, since a decay-during-readout effect tends to make the excited state harder to read correctly than the ground state; this toy model does not simulate that decay process, only its resulting asymmetric accuracy numbers.

Real readout is often asymmetric between prepared states; three rows move from a symmetric baseline to a coin-flip one-state error rate. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Earlier scans always moved both rows together

Chapter six's diagonal-strength scan holds the two prepared-state correct rates equal by construction and moves them together. This chapter's baseline row starts equal too: both prepared states read correctly with probability 9/10.

Azz=910=Aoo=110A_{zz}=\frac{9}{10}=A_{oo}=\frac{1}{10}
Symmetric baseline matrixBoth diagonal probabilities match in this row.assignment matrixread zeroread onetrue zero9/109 shots1/101 shotstrue one9/109 shots1/101 shots

This scan holds one row fixed and degrades only the other

The next two rows keep the prepared-zero correct rate fixed while only the prepared-one correct rate drops -- no earlier scan in this book holds one row fixed while moving the other alone. This is the same shape a decay-during-readout effect would leave: the excited state is harder to read correctly than the ground state.

AzzAoo91011091031091012\begin{array}{c|c}A_{zz}&A_{oo}\\\frac{9}{10}&\frac{1}{10}\\\frac{9}{10}&\frac{3}{10}\\\frac{9}{10}&\frac{1}{2}\\\end{array}
Mild asymmetry matrixThe middle row's prepared-one accuracy has dropped.assignment matrixread zeroread onetrue zero9/109 shots1/101 shotstrue one7/107 shots3/103 shots

The strongest row reads prepared-one as a coin flip

In the last row, prepared one reads correctly only 1/2 of the time, while prepared zero is unchanged. The two prepared states no longer share one calibration number.

Azz=910,Aoo=12A_{zz}=\frac{9}{10},\quad A_{oo}=\frac{1}{2}
Strong asymmetry matrixThe final row is rendered as the checked coin-flip case.assignment matrixread zeroread onetrue zero9/109 shots1/101 shotstrue one1/25 shots1/25 shots