Manuscript Em03-B@2 · Em03-B-v2.tex · section · c1a0977d

An exact noise-free model control

End-to-end theorem and constructive tolerances › An exact noise-free model control · lines 1899–1925

Em03-B@2#eq:exactmodelcounts

With exact extraction, correctly prepared register, and ideal readout, let $q_{c} = ν_{c} / (1 + ν_{c})$ , where $ν_{c}$ is (eq:memorymean). Then the actual model's decoded law is

p (0) p (k) p (N) = 1 - q_{c} + q_{c}^{K + 1}, = (1 - q_{c}) q_{c}^{k}, 1 \leq k < N, = q_{c}^{N} - q_{c}^{K + 1} .

Its mean is

ν_{c} (1 - q_{c}^{N}) - N q_{c}^{K + 1} .

These formulas follow directly from (eq:extractionchannel); they also hold for $N = 1$ , with the middle line empty. Classical assignment noise subsequently gives

Pr (y) = j = 0 \sum^{N} W (y ∣ j) p (j) .

This is an analytical model control, not an experimentally measured Hawking histogram.

Displayed formulas in this passage

Em03-B@2#eq:exactmodelcounts · line 1904
$p (0) p (k) p (N) = 1 - q_{c} + q_{c}^{K + 1}, = (1 - q_{c}) q_{c}^{k}, 1 \leq k < N, = q_{c}^{N} - q_{c}^{K + 1} .$
unlabeled · line 1913
$ν_{c} (1 - q_{c}^{N}) - N q_{c}^{K + 1} .$
unlabeled · line 1920
$Pr (y) = j = 0 \sum^{N} W (y ∣ j) p (j) .$