Open-System Cross Scans

Readout Assignment Three-Row Scan

true budgets become observed reads

The same assignment matrix maps different true ledgers into different readout 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

Prepared-zero reads are still not all zero

The assignment matrix row for true zero is 3/4 zero reads and 1/4 one reads. From 100 shots, expected counts are 75 and 25.

Nread=(75,25)N_{\text{read}}=(75,25)
Readout assignment scan rowPrepared zero still carries assignment error.true probabilitieszero 1one 0assignmentobserved probszero 3/4one 1/4over 100 shots75 zero reads25 one reads

The audit mixture maps to sixty-five and thirty-five

The capstone true budget is 4/5 zero and 1/5 one. The same matrix predicts 65 zero reads and 35 one reads.

Nread=(65,35)N_{\text{read}}=(65,35)
Readout assignment scan rowThis row is the book's post-channel readout.true probabilitieszero 4/5one 1/5assignmentobserved probszero 13/20one 7/20over 100 shots65 zero reads35 one reads

An even true mixture stays even after symmetric assignment

With true probabilities 1/2 and 1/2, the symmetric assignment matrix predicts 50 zero reads and 50 one reads.

Nread=(50,50)N_{\text{read}}=(50,50)
Readout assignment scan rowThree rows show readout as matrix multiplication.true probabilitieszero 1/2one 1/2assignmentobserved probszero 1/2one 1/2over 100 shots50 zero reads50 one reads