Manuscript En01-A@1 · En01-A.tex · definition · 558b972b

Definition: Coherent and dephased models

Recorded circuits and the two statistical models › Pinching, anchoring, and dilation · lines 961–977

En01-A@1#def:laws, En01-A@1#eq:X

For an effect $M$ and $J \subseteq N$ , define

P^{coh} (M) = tr (M ρ), P^{coll}_{J} (M) = tr (M Δ_{J} ρ) .

The difference operator is

X_{J} = ρ - Δ_{J} ρ = r \neq = r^{'} r_{J} \neq = r^{'}_{J} \sum p_{r} p_{r^{'}} ∣ Φ_{r} ⟩ ⟨ Φ_{r^{'}} ∣.

It is Hermitian and traceless, and the probability bias of $M$ is $tr (M X_{J})$ .

Displayed formulas in this passage

En01-A@1#eq:X · line 969
$X_{J} = ρ - Δ_{J} ρ = r \neq = r^{'} r_{J} \neq = r^{'}_{J} \sum p_{r} p_{r^{'}} ∣ Φ_{r} ⟩ ⟨ Φ_{r^{'}} ∣.$
unlabeled · line 963
$P^{coh} (M) = tr (M ρ), P^{coll}_{J} (M) = tr (M Δ_{J} ρ) .$