Manuscript X-I-ST@1 · X-I-ST.tex · section · 9745fd40

Numerical report encoding and an exact error formula

Complete destructive instruments and their composition › Numerical report encoding and an exact error formula · lines 1819–1832

X-I-ST@1#eq:numericinstrument

Back to manuscript

For a finite list $v_{j} \in [- 1, 1]$ , define $p_{y} (v) = (1 + y v) /2$ , $y = \pm 1$ , and

I_{v} (Z) = j, y \sum ∣ j, y, w_{j} ⟩ ⟨ j, y, w_{j} ∣_{R} \otimes p_{y} (v_{j}) D_{j} Z D_{j}^{†} .

A supplied real coefficient can be scaled by $z \mapsto z / (1 + ∣ z ∣)$ ; any approximation or enclosure used for installation remains part of the input contract.

Displayed formulas in this passage

X-I-ST@1#eq:numericinstrument · line 1823
$I_{v} (Z) = j, y \sum ∣ j, y, w_{j} ⟩ ⟨ j, y, w_{j} ∣_{R} \otimes p_{y} (v_{j}) D_{j} Z D_{j}^{†} .$

Nearby in this section

proposition: Proposition: Complete numerical-report comparison
section: Numerical report encoding and an exact error formula