Manuscript Oai212-A@1 · Oai212-A.tex · section · 79323841

Finite-shot bounds

A common complete-channel, calibration, and shot ledger › Finite-shot bounds · lines 1444–1463

A finite test cannot certify an exact distributional identity or independence of an unlimited edge family. Those remain model assumptions unless supplied by a construction.

For the quench model, a two-copy SWAP measurement estimates local purity $r_{e} = e^{- w_{e}}$ . If $r_{e}$ has error at most $η$ and $w_{e} \leq K$ , with $η \leq e^{- K} /2$ , then

∣ - lo g r_{e} - w_{e} ∣ \leq 2 e^{K} η .

Since the SWAP outcome lies in ${- 1, 1}$ , estimating purity to $η$ for all $M$ edges is ensured by

N \geq \frac{2}{η ^{2}} lo g \frac{2 M}{α}

two-copy tests per edge. This displays the increasing cost of estimating large entropy weights.

Displayed formulas in this passage

unlabeled · line 1453
$∣ - lo g r_{e} - w_{e} ∣ \leq 2 e^{K} η .$
unlabeled · line 1458
$N \geq \frac{2}{η ^{2}} lo g \frac{2 M}{α}$

Nearby in this section

lemma: Lemma: Uniform bounded-record shot certificate