Manuscript I@2 · I.tex · section · 85631fa7

Proof B: decohered fine-graining

Diagonal anchoring: independent finite proofs › Proof B: decohered fine-graining · lines 1686–1710

The witness uses

n + ⌈ lo g_{2} M ⌉ + ⌈ lo g_{2} k max m_{k} ⌉

qubits. For weights $(1/3, 2/3)$ , one choice is

\frac{1}{3} (∣ 0 ⟩ ∣ 00 ⟩ ∣ 0 ⟩ + ∣ 1 ⟩ ∣ 01 ⟩ ∣ 0 ⟩ + ∣ 1 ⟩ ∣ 10 ⟩ ∣ 1 ⟩) .

The three-qubit symmetry witness is smaller for that particular law.

The numerical fine-graining argument does not use (S5) as a probability-symmetry premise. The structural class still contains (S5); no independence theorem for the complete assumption package is claimed.

Displayed formulas in this passage

unlabeled · line 1689
$n + ⌈ lo g_{2} M ⌉ + ⌈ lo g_{2} k max m_{k} ⌉$
unlabeled · line 1695
$\frac{1}{3} (∣ 0 ⟩ ∣ 00 ⟩ ∣ 0 ⟩ + ∣ 1 ⟩ ∣ 01 ⟩ ∣ 0 ⟩ + ∣ 1 ⟩ ∣ 10 ⟩ ∣ 1 ⟩) .$

Nearby in this section

theorem: Theorem: Fine-graining anchoring