Open-System Contracts

Stage Order Changes The Ledger

device channel before readout

Open-system stages are ordered ledgers: the device channel changes the true counts before readout assignment changes the observed counts. The order is exact only for the declared matrices and probabilities; real devices blur it with drift, correlated errors, finite statistics, and imperfect calibration.

Readout assignment is applied after the device channel has changed the ledger. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Readout assignment is applied after the channel

The channel output probabilities are 4/5 zero and 1/5 one before readout assignment.

ptrue=(45,15)p_{\text{true}}=(\frac{4}{5},\frac{1}{5})
Assignment after channelThe prediction uses the post-channel true probabilities.true probabilitieszero 4/5one 1/5assignmentobserved probszero 13/20one 7/20over 100 shots65 zero reads35 one reads

The observed ledger is not the device ledger

The assignment rows turn those 100 shots into 65 zero reads and 35 one reads.

Nread=(65,35)N_{\text{read}}=(65,35)
Observed readout ledgerThe readout matrix is the final classical stage.true probabilitieszero 4/5one 1/5assignmentobserved probszero 13/20one 7/20over 100 shots65 zero reads35 one reads