Manuscript Hawk04-D@1 · Hawk04-D-v1.tex · section · 39b16f67

A nonzero-coupling negative control

Stage 4: information flow, entropy tests, and Page-time limits › A nonzero-coupling negative control · lines 1755–1781

The following check uses the commuting four-Majorana member of the family in Hawk04-A/B CheungHawk04A,CheungHawk04B. Take

H_{S} = J (I - S_{1} S_{2}), A = (S_{1} + S_{2}) /2, J > 0, g \neq = 0,

where $S_{j} = 2 c_{j}^{†} c_{j} - I$ . Insert the diary into the source states $s_{0} = ∣ 00 ⟩$ , $s_{1} = ∣ 11 ⟩$ . They have source energy zero and $A$ -eigenvalues $- 1, + 1$ . Couple to one finite-band scalar field with $f (ω) = 1/ 2 ω$ . Define

η_{i} (t) = g a_{i} \frac{e ^{- i ω t} - 1}{ω} f (ω), a_{0} = - 1, a_{1} = 1.

For a collected packet projection $P_{r}$ , let

c_{R} (t) = exp [- \frac{1}{2} ∥ P_{r} (η_{0} - η_{1}) ∥^{2}], z_{R} = 1 - c_{R}^{2} .

Displayed formulas in this passage

unlabeled · line 1760
$H_{S} = J (I - S_{1} S_{2}), A = (S_{1} + S_{2}) /2, J > 0, g \neq = 0,$
unlabeled · line 1770
$η_{i} (t) = g a_{i} \frac{e ^{- i ω t} - 1}{ω} f (ω), a_{0} = - 1, a_{1} = 1.$
unlabeled · line 1775
$c_{R} (t) = exp [- \frac{1}{2} ∥ P_{r} (η_{0} - η_{1}) ∥^{2}], z_{R} = 1 - c_{R}^{2} .$

A nonzero-coupling negative control

Displayed formulas in this passage

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