Manuscript Hawk06-A@1 · Hawk06-A.tex · section · c59fe67c

Exact Haar decoupling and the emission threshold

Exact Haar decoupling and the emission threshold · lines 553–576

Let $Q ≃ L$ be an inaccessible test reference, and prepare

∣ Φ_{d} ⟩_{Q L} = \frac{1}{d} i = 1 \sum^{d} ∣ i ⟩_{Q} ∣ i ⟩_{L} .

For a cut $R B$ , omit the cut index and write $D = r b$ . Define

ω_{QB}^{U} = (id_{Q} \otimes C^{U}) (∣ Φ_{d} ⟩ ⟨ Φ_{d} ∣), σ_{B}^{U} = C^{U} (I_{L} / d),

X_{QB}^{U} = ω_{QB}^{U} - \frac{I _{Q}}{d} \otimes σ_{B}^{U} .

The state $σ_{B}^{U}$ is a feasible replacement state. It may depend on the known device $U$ , not on the variable input.

Displayed formulas in this passage

unlabeled · line 557
$∣ Φ_{d} ⟩_{Q L} = \frac{1}{d} i = 1 \sum^{d} ∣ i ⟩_{Q} ∣ i ⟩_{L} .$
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$ω_{QB}^{U} = (id_{Q} \otimes C^{U}) (∣ Φ_{d} ⟩ ⟨ Φ_{d} ∣), σ_{B}^{U} = C^{U} (I_{L} / d),$
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$X_{QB}^{U} = ω_{QB}^{U} - \frac{I _{Q}}{d} \otimes σ_{B}^{U} .$