Symmetry-resolved dynamical purification in synthetic quantum matter

Abstract

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