Definition: Snapshot

Let $R_{I,s}$ be restriction to the tick-$s$ interface in $I$: trace out external quantum systems and sum external classical labels. Define

For $p_{\lambda }=\mathrm{Tr}{\omega }_{I,\lambda }>0$, the conditional quantum state is ${\rho }_{I\mid \lambda }={\omega }_{I,\lambda }/p_{\lambda }$. No normalized state is assigned when $p_{\lambda }=0$.