Manuscript XVI-O1-ST@5 · XVI-O1-ST-v5.tex · section · dd45e0d1

Correlated reference branches

Retained exact synthetic examples › Correlated reference branches · lines 1927–1948

Let the clock basis be the columns of

U = \frac{1}{2} 1111 1 - 1 1 - 1 11 - 1 - 1 1 - 1 - 1 1

and let $A_{lab} ≅ E ≅ C^{2}$ . For

∣ Ψ ⟩ = \frac{∣ τ _{1} ⟩ ∣ 0 ⟩ _{A} ∣ 0 ⟩ _{E} + ∣ τ _{2} ⟩ ∣ 1 ⟩ _{A} ∣ 1 ⟩ _{E}}{2},

the nonzero blocks are $\frac{1}{2} ∣ 00 ⟩ ⟨ 00 ∣$ and $\frac{1}{2} ∣ 11 ⟩ ⟨ 11 ∣$ . Their sum is $Tr_{C} ∣ Ψ ⟩ ⟨ Ψ ∣$ . The unconditional reference is $I_{E} /2$ , while positive conditional references are $∣ 0 ⟩ ⟨ 0 ∣, ∣ 1 ⟩ ⟨ 1 ∣$ . Zero blocks are not normalized.

Displayed formulas in this passage

unlabeled · line 1930
$U = \frac{1}{2} 1111 1 - 1 1 - 1 11 - 1 - 1 1 - 1 - 1 1$
unlabeled · line 1937
$∣ Ψ ⟩ = \frac{∣ τ _{1} ⟩ ∣ 0 ⟩ _{A} ∣ 0 ⟩ _{E} + ∣ τ _{2} ⟩ ∣ 1 ⟩ _{A} ∣ 1 ⟩ _{E}}{2},$