Manuscript En02-E@2 · En02-E-v2.tex · example · c2769986

Example: Exact phase-sensitive algebraic control

Analytical controls and numerical acceptance › A selected two-packet family · lines 1250–1287

En02-E@2#ex:control

For the synthetic, non-Schwarzschild covariance

K_{test} = \frac{1}{20} (3 - i i 3),

the eigenvalues are $1/10, 1/5$ ,

p_{0} = \frac{25}{33}, a = \frac{8}{33}, μ = \frac{3}{10}, T = \frac{1}{132} (17 - 5 i 5 i 17) .

In the explicit order $(∣ 1, 0 ⟩, ∣ 0, 1 ⟩)$ , the one-particle density block is

\frac{1}{4356} (425 - 125 i 125 i 425) .

For cutoff $N = 1$ , its number-moment matrix is the transpose:

C^{(1)} = \frac{1}{4356} (425 125 i - 125 i 425) .

These entries distinguish $K$ from $K^{T}$ .

The cutoff dimension including the flag is four, and

t_{N} (K_{test}) = \frac{103}{2178} .

The calibrated recovery errors are

ε_{IT} = \frac{25}{44}, ε_{op}^{even} (2, 3) = \frac{91}{132}, ε_{op}^{even} (3, 3) = ε_{op}^{odd} (2, 3) = \frac{25}{44} .

These are analytical values, not executed pilot results.

Displayed formulas in this passage

unlabeled · line 1253
$K_{test} = \frac{1}{20} (3 - i i 3),$
unlabeled · line 1258
$p_{0} = \frac{25}{33}, a = \frac{8}{33}, μ = \frac{3}{10}, T = \frac{1}{132} (17 - 5 i 5 i 17) .$
unlabeled · line 1265
$\frac{1}{4356} (425 - 125 i 125 i 425) .$
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$C^{(1)} = \frac{1}{4356} (425 125 i - 125 i 425) .$
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$t_{N} (K_{test}) = \frac{103}{2178} .$
unlabeled · line 1281
$ε_{IT} = \frac{25}{44}, ε_{op}^{even} (2, 3) = \frac{91}{132}, ε_{op}^{even} (3, 3) = ε_{op}^{odd} (2, 3) = \frac{25}{44} .$