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

Implementation comparisons

Hamiltonian perturbations and finite-time certification › Implementation comparisons · lines 891–952

Hawk02-B@2#thm:B6, Hawk02-B@2#eq:robustexact, Hawk02-B@2#eq:robustrequested

A preparation estimate for one selected input is not (I1). For an otherwise identical preparation using different fixed auxiliary states, their trace distance gives an accessible preparation-channel allowance. Comparing chosen purifications may require a separate complete allowance.

Let $N^{(K)}$ be the actual precollection radiation channel. Define

ε_{implemented} = d_{⋄} (D L N^{(K)}, id_{C^{(K)}}) .

Under Assumption ass:implementation, put

e_{comp} = min {1, e_{prep} + e \sum h_{e}},

and

e_{tot} = min {1, e_{prep} + e \sum h_{e} + e_{collection} + e_{decoder}} .

Then

ε_{implemented} \leq min {1, 1 - ℓ \prod (1 - c_{d} q_{ℓ}) + e_{tot}} .

For identical mechanisms,

ε_{implemented} \leq min {1, K q_{N} + e_{tot}} .

For one cell the ideal term is $q_{N} c_{d}$ .

If ideal and actual complete outputs are identified before collection, their residual channels satisfy

δ_{leak} (C^{(K)}) \leq min {1, 1 - ℓ \prod (1 - c_{d} q_{ℓ}) + e_{comp}} .

An accessible collection allowance alone does not compare particular complete collection dilations with the same linear error.

Displayed formulas in this passage

Hawk02-B@2#eq:robustexact · line 924
$ε_{implemented} \leq min {1, 1 - ℓ \prod (1 - c_{d} q_{ℓ}) + e_{tot}} .$
Hawk02-B@2#eq:robustrequested · line 934
$ε_{implemented} \leq min {1, K q_{N} + e_{tot}} .$
unlabeled · line 901
$ε_{implemented} = d_{⋄} (D L N^{(K)}, id_{C^{(K)}}) .$
unlabeled · line 913
$e_{comp} = min {1, e_{prep} + e \sum h_{e}},$
unlabeled · line 918
$e_{tot} = min {1, e_{prep} + e \sum h_{e} + e_{collection} + e_{decoder}} .$
unlabeled · line 942
$δ_{leak} (C^{(K)}) \leq min {1, 1 - ℓ \prod (1 - c_{d} q_{ℓ}) + e_{comp}} .$

Implementation comparisons

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