Symmetry-resolved dynamical purification in synthetic quantum matter

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