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

Lemma: Common-state fidelity bias

A proved calibration budget › Common-state preparation and reference model · lines 588–609 · proof included or linked

Oai265-B@2#lem:calibration, Oai265-B@2#eq:bcal

Let

F_{obs} = \frac{1 + m _{x} - m _{y} + m _{z}}{4} .

Then

∣ F_{obs} - F_{e} ∣ \leq b_{cal}, b_{cal} = δ + \frac{μ _{x} + μ _{y} + μ _{z}}{4} .

Proof. Measurement error changes the correlation combination by at most $\sum_{j} μ_{j} /4$ . The ideal combination for $σ$ equals $Tr (P_{2} σ)$ . Because $P_{2}$ is an effect, its expectation differs from $Tr (P_{2} J_{E})$ by at most $δ$ .

Displayed formulas in this passage

Oai265-B@2#eq:bcal · line 595
$∣ F_{obs} - F_{e} ∣ \leq b_{cal}, b_{cal} = δ + \frac{μ _{x} + μ _{y} + μ _{z}}{4} .$
unlabeled · line 591
$F_{obs} = \frac{1 + m _{x} - m _{y} + m _{z}}{4} .$

Nearby in this section

section: Common-state preparation and reference model