Symmetry-resolved dynamical purification in synthetic quantum matter

When a quantum system initialized in product state is subjected to either coherent or incoherent dynamics, the entropy of any its connected partitions generically increases as function time, signalling inevitable spreading (quantum) information throughout system. Here, we show that, presence continuous symmetries and under ubiquitous experimental conditions, symmetry-resolved inhibited due competition dynamics: given number sectors, decreases dynamical purification. Such purification bridges between two distinct short intermediate time regimes, characterized by log-volume log-area law, respectively. It generic symmetric evolution, such occurs for different partition geometry topology, classes (local) Liouville dynamics. We then develop protocol measure entropies negativities synthetic systems based on random unitary toolbox, demonstrate generality using data from trapped ion experiments [Brydges et al., Science 364, 260 (2019)]. Our work shows that symmetry plays key role magnifying glass characterize many-body dynamics open systems, and, particular, noisy-intermediate scale devices.