Manuscript Oai265-B@2 · Oai265-B-v2.tex · section · 94b6f42f

Three-setting measurement specification

Certification contract and complete experiment › Three-setting measurement specification · lines 338–382

Prepare

∣ Φ_{2} ⟩_{QC} = \frac{∣ 00 ⟩ + ∣ 11 ⟩}{2}, P_{2} = ∣ Φ_{2} ⟩ ⟨ Φ_{2} ∣ .

Only $C$ enters the memory and decoder. Ideally measure the same Pauli operator on $Q$ and $C^{'}$ .

Set

A_{x} = X \otimes X, A_{y} = Y \otimes Y, A_{z} = Z \otimes Z, (s_{x}, s_{y}, s_{z}) = (1, - 1, 1) .

For local outcomes $u, v \in {- 1, 1}$ , let $Z_{j} = uv$ , and define the oriented pass indicator

B_{j} = \frac{1 + s _{j} Z _{j}}{2} .

Setting	Local measurements	Parity	Ideal pass condition
$x$	$X_{Q}, X_{C^{'}}$	$uv$	$u = v$
$y$	$Y_{Q}, Y_{C^{'}}$	$uv$	$u = - v$
$z$	$Z_{Q}, Z_{C^{'}}$	$uv$	$u = v$

For bounded-score certification, every other complete outcome receives a predeclared score in $[- 1, 1]$ . Scoring unavailable readout by zero requires a proved bias allowance. No attempted trial is deleted.

Archive the attempt identifier, time, storage duration, decoder version, setting, local labels, flags, fallback action, and score. Settings must not change the pre-analyzer channel. Choosing the analyzer setting after the output has returned is one safeguard against setting-dependent device behavior.

Displayed formulas in this passage

unlabeled · line 341
$∣ Φ_{2} ⟩_{QC} = \frac{∣ 00 ⟩ + ∣ 11 ⟩}{2}, P_{2} = ∣ Φ_{2} ⟩ ⟨ Φ_{2} ∣ .$
unlabeled · line 350
$A_{x} = X \otimes X, A_{y} = Y \otimes Y, A_{z} = Z \otimes Z, (s_{x}, s_{y}, s_{z}) = (1, - 1, 1) .$
unlabeled · line 356
$B_{j} = \frac{1 + s _{j} Z _{j}}{2} .$