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

What is transferred

Nonvacuum-calibrated recovery benchmark › What is transferred · lines 964–986

Define

a (K) = 1 - det (I + K)^{- 1} .

This is the selected nonvacuum probability, not a rate or a mean. It is preserved exactly by the flagged cutoff when the flag is classified as nonvacuum. A binary vacuum measurement gives

∣ a (K) - a (L) ∣ \leq d_{tr} (ρ_{K}, ρ_{L}) .

Also

0 \leq μ - a (K) \leq \frac{1}{2} (μ^{2} + tr K^{2}),

because $n - 1_{{n > 0}} \leq n (n - 1) /2$ .

Only $a (K)$ is transferred to the benchmark. Different correlated Gaussian states may give the same parameter. The benchmark decoder is not given their covariance or full finite state.

Displayed formulas in this passage

unlabeled · line 967
$a (K) = 1 - det (I + K)^{- 1} .$
unlabeled · line 973
$∣ a (K) - a (L) ∣ \leq d_{tr} (ρ_{K}, ρ_{L}) .$
unlabeled · line 977
$0 \leq μ - a (K) \leq \frac{1}{2} (μ^{2} + tr K^{2}),$