Manuscript Hawk02-B@2 · Hawk02-B.tex · section · 95ea744f

Explicit optimal single-cell recovery

Explicit optimal single-cell recovery · lines 564–594

Hawk02-B@2#eq:decoder, Hawk02-B@2#thm:B3, Hawk02-B@2#eq:singleoptimum

For $q_{N} < 1$ , let $P_{N} = J_{N} J_{N}^{†}$ and define

D_{N} (Y) = J_{N}^{†} Y J_{N} + Tr ((I_{R} - P_{N}) Y) \frac{I _{C}}{d} .

For $q_{N} = 1$ , define $D_{N} = T_{I_{C} / d}$ . The unused-subspace rule is fixed and trace preserving.

The coherent-mode decoder receives all radiation cells, their internal labels, and knowledge of $J_{N}$ . It receives neither memory nor reference, uses no early key, and does not postselect. Section sec:controls gives a less demanding time-resolved decoder with the same optimum.

The declared decoder is CPTP, and

D_{N} N_{N} = (1 - q_{N}) id_{C} + q_{N} T_{I_{C} / d} .

For all $q_{N} \in [0, 1]$ ,

ε_{rec} (N_{N}) = q_{N} (1 - \frac{1}{d ^{2}}) .

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Hawk02-B@2#eq:decoder · line 567
$D_{N} (Y) = J_{N}^{†} Y J_{N} + Tr ((I_{R} - P_{N}) Y) \frac{I _{C}}{d} .$
Hawk02-B@2#eq:singleoptimum · line 589
$ε_{rec} (N_{N}) = q_{N} (1 - \frac{1}{d ^{2}}) .$
unlabeled · line 585
$D_{N} N_{N} = (1 - q_{N}) id_{C} + q_{N} T_{I_{C} / d} .$

Explicit optimal single-cell recovery

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