Manuscript Oai283-A@1 · Oai283-A.tex · section · 6fb75895

Source-weight inference is not general channel tomography

Operational certification of the logical channel › Source-weight inference is not general channel tomography · lines 1025–1053

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Suppose a calibrated binary record has probability

q_{θ} = a_{0} + b_{0} θ, b_{0} > 0, 0 \leq θ \leq 1.

For $N$ independent shots,

θ = proj_{[0, 1]} \frac{Z - a _{0}}{b _{0}}

obeys

P {∣ θ - θ ∣ > \frac{b _{cal} + lo g ( 2/ α ) / ( 2 N )}{b _{0}}} \leq α

when $b_{cal}$ bounds the probability calibration error. Projection and Hoeffding prove the statement.

This is the source-weight inference pattern of En10-A/B CheungEn10A,CheungEn10B. To use it in a channel test, one must identify the binary probability being estimated and supply an informationally complete collection if a general channel is claimed.

Displayed formulas in this passage

unlabeled · line 1028
$q_{θ} = a_{0} + b_{0} θ, b_{0} > 0, 0 \leq θ \leq 1.$
unlabeled · line 1032
$θ = proj_{[0, 1]} \frac{Z - a _{0}}{b _{0}}$
unlabeled · line 1038
$P {∣ θ - θ ∣ > \frac{b _{cal} + lo g ( 2/ α ) / ( 2 N )}{b _{0}}} \leq α$

Source-weight inference is not general channel tomography

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