Manuscript Hawk05-B@1 · Hawk05-B.tex · section · f2e5d4f5

Quantifiers and input types

One coherent emission history with a Haar hypothesis › Quantifiers and input types · lines 538–558

Hawk05-B@1#eq:Sk

Fix a pure logical input $∣ ψ ⟩$ independently of $U$ . Then $U J ∣ ψ ⟩$ is a Haar-distributed unit vector in $C^{D}$ . Define

ρ_{R_{k}}^{U, ψ} = Tr_{B_{k}} ∣ F_{k} U J ψ ⟩ ⟨ F_{k} U J ψ ∣, S_{k} (U, ψ) = S (ρ_{R_{k}}^{U, ψ}) .

All cuts in (eq:Sk) belong to one state and one sampled $U$ . We do not replace this history by independently sampled states at different cuts.

The fixed-pure-input entropy problem is distinct from recovery of every state of $C$ , including reference-entangled states.

Displayed formulas in this passage

Hawk05-B@1#eq:Sk · line 543
$ρ_{R_{k}}^{U, ψ} = Tr_{B_{k}} ∣ F_{k} U J ψ ⟩ ⟨ F_{k} U J ψ ∣, S_{k} (U, ψ) = S (ρ_{R_{k}}^{U, ψ}) .$