Manuscript Em03-C@1 · Em03-C-v1.tex · section · 47dd71ec

Exact record identity and tail

C1 interface: joint carriers and referenced records › Exact record identity and tail · lines 682–704

Em03-C@1#eq:jointrecord

For $ρ_{12 S R}$ , define the positive blocks

ρ_{S R}^{(n)} = ⟨ n_{1}, n_{2} ∣ ρ_{12 S R} ∣ n_{1}, n_{2} ⟩ .

Let

T_{a} (n) = (min (n_{1}, a_{1}), min (n_{2}, a_{2})) .

The ideal full record is

Ω_{a, S R} (ρ) = k \leq a \sum ∣ y_{k} ⟩ ⟨ y_{k} ∣ \otimes T_{a} (n) = k \sum ρ_{S R}^{(n)} .

Displayed formulas in this passage

Em03-C@1#eq:jointrecord · line 695
$Ω_{a, S R} (ρ) = k \leq a \sum ∣ y_{k} ⟩ ⟨ y_{k} ∣ \otimes T_{a} (n) = k \sum ρ_{S R}^{(n)} .$
unlabeled · line 685
$ρ_{S R}^{(n)} = ⟨ n_{1}, n_{2} ∣ ρ_{12 S R} ∣ n_{1}, n_{2} ⟩ .$
unlabeled · line 690
$T_{a} (n) = (min (n_{1}, a_{1}), min (n_{2}, a_{2})) .$