Manuscript Em03-B@2 · Em03-B-v2.tex · section · c1a0977d

Exact tails and mean bias

The B1–B3 mathematical interface › Exact tails and mean bias · lines 619–635

Em03-B@2#eq:generalbias

For an arbitrary normal oscillator state of finite mean $μ$ ,

μ - E_{ideal} κ = B_{N} (ρ) := tr (ρ (N_{h} - N)_{+}) = j = N + 1 \sum^{\infty} ρ Pr (N_{h} \geq j) .

Let

Ω_{\infty A} (ρ) = n = 0 \sum^{\infty} ∣ n ⟩ ⟨ n ∣ \otimes ρ_{A}^{(n)} .

The finite decoded record is embedded into this countable record space by assigning zero weight above $N$ .

Displayed formulas in this passage

Em03-B@2#eq:generalbias · line 622
$μ - E_{ideal} κ = B_{N} (ρ) := tr (ρ (N_{h} - N)_{+}) = j = N + 1 \sum^{\infty} ρ Pr (N_{h} \geq j) .$
unlabeled · line 629
$Ω_{\infty A} (ρ) = n = 0 \sum^{\infty} ∣ n ⟩ ⟨ n ∣ \otimes ρ_{A}^{(n)} .$