Manuscript Hawk02-D@1 · Hawk02-D.tex · section · e6e4b72f

Actual complete-residual recovery

Actual complete-residual recovery · lines 766–800

Hawk02-D@1#eq:beta

Let $J_{t} : C^{n} \to h$ send label $a$ to $u (t) \otimes e_{a}$ . It is a one-particle isometry. The complete evolved code isometry is

V_{t} = Γ (J_{t}) W,

with the fixed carrier vacuum appended.

When $p_{M} (t) > 0$ , define

r_{a} (t, M) = \frac{P _{r_{M}} J _{t} e _{a}}{p _{M} ( t )} .

These $n$ modes are orthonormal. Let

J_{R, t, M} e_{a} = r_{a} (t, M), A_{t, M} = Γ (J_{R, t, M}) W .

Then $A_{t, M} : C \to R_{M}$ is an isometry.

Define

β_{K} (s) = min {1, 2 [1 - (1 - s)^{K /2}]}, 0 \leq s \leq 1.

Displayed formulas in this passage

Hawk02-D@1#eq:beta · line 791
$β_{K} (s) = min {1, 2 [1 - (1 - s)^{K /2}]}, 0 \leq s \leq 1.$
unlabeled · line 771
$V_{t} = Γ (J_{t}) W,$
unlabeled · line 777
$r_{a} (t, M) = \frac{P _{r_{M}} J _{t} e _{a}}{p _{M} ( t )} .$
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$J_{R, t, M} e_{a} = r_{a} (t, M), A_{t, M} = Γ (J_{R, t, M}) W .$