Manuscript Em04-A@2 · Em04-A-v2.tex · definition · f5b28abc

Definition: Specified instrument

Finite local instruments and typed records · lines 927–940

A finite instrument from $H_{in}$ to $H_{out}$ has Kraus operators $M_{a μ}$ with

E_{a} = μ \sum M_{a μ}^{†} M_{a μ}, a \sum E_{a} = I_{in} .

Set

Φ_{a} (M) = μ \sum M_{a μ} M M_{a μ}^{†}, Φ (M) = a \sum ∣ a ⟩ ⟨ a ∣_{R} \otimes Φ_{a} (M) .

The record includes every outcome, including failure labels.

Displayed formulas in this passage

unlabeled · line 930
$E_{a} = μ \sum M_{a μ}^{†} M_{a μ}, a \sum E_{a} = I_{in} .$
unlabeled · line 935
$Φ_{a} (M) = μ \sum M_{a μ} M M_{a μ}^{†}, Φ (M) = a \sum ∣ a ⟩ ⟨ a ∣_{R} \otimes Φ_{a} (M) .$