Manuscript Hawk07-B@1 · Hawk07-B.tex · section · b9785538

A beacon is weaker than the payload

Potential operational functions › A beacon is weaker than the payload · lines 1071–1092

The distinction is between a specified decoder, an optimal decoder, a selected test, and a full-code claim CheungOai290280.

A deterministic a posteriori route to full-code certification is a complete Choi comparison. If a calibrated reconstructed Choi matrix $J$ satisfies

J - J_{n} (Λ)_{1} \leq t,

then

∥ Λ - id_{L} ∥_{⋄} \leq d (J - ∣ Φ_{d} ⟩ ⟨ Φ_{d} ∣_{1} + t) .

This follows from the Choi conversion already proved. Obtaining the calibration allowance $t$ is an additional experimental-statistical task, not the observation of one beacon.

Displayed formulas in this passage

unlabeled · line 1080
$J - J_{n} (Λ)_{1} \leq t,$
unlabeled · line 1084
$∥ Λ - id_{L} ∥_{⋄} \leq d (J - ∣ Φ_{d} ⟩ ⟨ Φ_{d} ∣_{1} + t) .$

Nearby in this section

example: Example: Readable beacon, unrecoverable code
example: Example: High Bell fidelity need not give uniform accuracy