Manuscript Oai069-A@1 · Oai069-A.tex · section · a4913aab

All matrix units, not a few selected observables

Complete coverage and simultaneous finite-confidence certification › All matrix units, not a few selected observables · lines 979–1011

Oai069-A@1#eq:targetchoi

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For an input block $C \otimes K$ , put

n = 2 g .

Let $O = J_{out} \otimes C_{out}$ , of dimension

o = 2 d .

Allow a tested complete channel

Φ_{ν, k} : B (C \otimes K) \to B (O)

for every predeclared decoder/access task $ν$ and input sector $k$ . The implementation may corrupt its returned label. That possibility is not removed from the certificate.

The ideal target on block $k$ is

T_{k} (ρ) = ∣ k ⟩ ⟨ k ∣ \otimes Tr_{K} ρ .

Its normalized Choi state is

J (T_{k}) = P_{Bell, Q_{C} C_{out}} \otimes \frac{I _{Q_{K}}}{g} \otimes ∣ k ⟩ ⟨ k ∣_{J_{out}},

with the indicated fixed rearrangement into $Q_{C}, Q_{K}, J_{out}, C_{out}$ order.

Displayed formulas in this passage

Oai069-A@1#eq:targetchoi · line 1002
$J (T_{k}) = P_{Bell, Q_{C} C_{out}} \otimes \frac{I _{Q_{K}}}{g} \otimes ∣ k ⟩ ⟨ k ∣_{J_{out}},$
unlabeled · line 982
$n = 2 g .$
unlabeled · line 986
$o = 2 d .$
unlabeled · line 990
$Φ_{ν, k} : B (C \otimes K) \to B (O)$
unlabeled · line 998
$T_{k} (ρ) = ∣ k ⟩ ⟨ k ∣ \otimes Tr_{K} ρ .$

All matrix units, not a few selected observables

Displayed formulas in this passage

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