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

Definition: Protocols and coordinates

Scaling and short-time parameter dependence · lines 621–641

Em04-A@2#eq:coordinates

Protocol A fixes physical observation times $t$ . Protocol B fixes coherent observation times $τ = J t$ . Let

Γ_{2} = γ_{d} + \frac{γ _{r}}{2} .

When $Γ_{2} > 0$ , define

χ = \frac{J}{Γ _{2}} > 0, r = \frac{γ _{r}}{2 Γ _{2}} \in [0, 1] .

Equivalently,

γ_{r} = \frac{2 r J}{χ}, γ_{d} = \frac{( 1 - r ) J}{χ} .

Here $Γ_{2}$ is an isolated qubit's transverse decay rate under the specified convention, not the intersite dephasing rate.

Displayed formulas in this passage

Em04-A@2#eq:coordinates · line 629
$χ = \frac{J}{Γ _{2}} > 0, r = \frac{γ _{r}}{2 Γ _{2}} \in [0, 1] .$
unlabeled · line 625
$Γ_{2} = γ_{d} + \frac{γ _{r}}{2} .$
unlabeled · line 635
$γ_{r} = \frac{2 r J}{χ}, γ_{d} = \frac{( 1 - r ) J}{χ} .$