Symmetry-resolved dynamical purification in synthetic quantum matter

TL;DR

This paper reveals that in symmetric quantum systems, symmetry-resolved information can decrease over time, leading to dynamical purification, which is experimentally measurable and relevant for understanding many-body open quantum dynamics.

Contribution

It introduces the concept of symmetry-resolved dynamical purification, demonstrating its occurrence across various quantum systems and developing a protocol for measuring related entropies and negativities.

Findings

Symmetry-resolved entropy decreases in certain sectors during evolution.

Dynamical purification occurs across different geometries and dynamics.

Experimental data from trapped ions confirms the theoretical predictions.

Abstract

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.