Manuscript Hawk04-A@1 · Hawk04-A.tex · section · 526092ba

A coherent cutoff is not priced by discarded probability

Additional debugging checks › A coherent cutoff is not priced by discarded probability · lines 2172–2192

For

∣ + ⟩ = (∣ 0 ⟩ + ∣ 1 ⟩) / 2, σ = \frac{1}{2} ∣ 0 ⟩ ⟨ 0 ∣ + \frac{1}{2} ∣ ⊥ ⟩ ⟨ ⊥ ∣,

direct diagonalization in the common three-dimensional space gives

d_{tr} (∣ + ⟩ ⟨ + ∣, σ) = \frac{5 + 1}{4} > \frac{1}{2} .

The two-dimensional difference block has eigenvalues $(1 + 5) /4$ and $(1 - 5) /4$ , and the failure block has eigenvalue $- 1/2$ .

The discarded-probability equality in the supplied En02-E concerns its commuting state-cutoff hypotheses CheungEn02E. Our regulator allowance instead follows from the complete isometries.

Displayed formulas in this passage

unlabeled · line 2175
$∣ + ⟩ = (∣ 0 ⟩ + ∣ 1 ⟩) / 2, σ = \frac{1}{2} ∣ 0 ⟩ ⟨ 0 ∣ + \frac{1}{2} ∣ ⊥ ⟩ ⟨ ⊥ ∣,$
unlabeled · line 2181
$d_{tr} (∣ + ⟩ ⟨ + ∣, σ) = \frac{5 + 1}{4} > \frac{1}{2} .$