for $t_{int}\approx 0.4/\gamma \sim 10$ ns. At the same interaction time, the unconditional gate fidelity (Fig. \[fig:FidelityTransient\], *right*, full line) is about $94\%$, while the conditional gate fidelity reaches the value of $99\%$ (Fig. \[fig:FidelityTransient\], *right*, dashed line). The conditional gate fidelity is obtained in correspondence with a success probability of the gate equal to $0.94$, calculated from the norm of the Monte-Carlo wave function [@Carmichael93]. The probe and trigger group velocities are calculated to be $v_g \simeq 3 \times 10^6$ ms$^{-1}$, yielding a gas cell length $L = v_g t_{int} \simeq 3.1$ cm. The value of $g_j$ yields an interaction volume $V \simeq 2 \cdot 10^{-3}$ cm$^3$, corresponding to a gas cell diameter of about $330$ $\mu$m and to an atomic density $N_a/V \simeq 5 \cdot 10^{10}$ cm$^{-3}$.

To give a further example and to deepen our discussion of QPG performance and the CPS-fidelity trade-off, we now show the optimal results for the experimentally available pulses produced in the experiment of Darquié *et al.* [@Darquie2005] (see Fig. \[fig:CpsFtransient\]). The length of a pulse produced in [@Darquie2005] is 26 ns ($\simeq \gamma^{-1}$). The optimal parameters of Fig. \[fig:CpsFtransient\] give the unconditional gate fidelity (Fig. \[fig:CpsFtransient\] *right*, solid line) of $85\%$, 