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Symmetry-resolved dynamical purification in synthetic quantum matter

by Vittorio Vitale, Andreas Elben, Richard Kueng, Antoine Neven, Jose Carrasco, Barbara Kraus, Peter Zoller, Pasquale Calabrese, Benoit Vermersch, Marcello Dalmonte

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Submission summary

Authors (as Contributors): Marcello Dalmonte · Vittorio Vitale
Submission information
Arxiv Link: (pdf)
Date accepted: 2022-02-28
Date submitted: 2022-02-14 11:54
Submitted by: Vitale, Vittorio
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Atomic, Molecular and Optical Physics - Experiment
  • Atomic, Molecular and Optical Physics - Theory
  • Condensed Matter Physics - Theory
  • Quantum Physics


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.

Published as SciPost Phys. 12, 106 (2022)

Author comments upon resubmission

Dear Editor,

herewith we resubmit the paper "Symmetry-resolved dynamical purification in synthetic quantum matter" by Vittorio Vitale, Andreas Elben, Richard Kueng, Antoine Neven, Jose Carrasco, Barbara Kraus, Peter Zoller, Pasquale Calabrese, Benoit Vermersch and Marcello Dalmonte.

We thank you for the handling of our manuscript, and the Referees for the time and effort spent in reviewing it.

We include below a summary of the changes applied to the manuscript.

Sincerely yours,
Vittorio Vitale on behalf of the authors

List of changes

1) Clarification about weak symmetries, at the beginning of Sec. 3.1, where the general conditions for the theory are presented and after Eq. 17, in a footnote we introduced.

2) Correction of a typo in Fig. 6.

3) Correction of other minor typos in the manuscript.

4) Addition of reference "M. Aidelsburger, L. Barbiero, A. Bermudez, T. Chanda, A. Dauphin, D. González-Cuadra,P. R. Grzybowski, S. Hands, F. Jendrzejewski, J. Jünemannet al.,Cold atoms meet latticegauge theory, Philosophical Transactions of the Royal Society A380(2216), 20210064(2022)" as suggested by the Referee.

5) Appendix "Sectors Populations" and Fig.s 9-10-11, where the populations of the different symmetry sectors of the systems dynamics presented throughout the manuscript are discussed.

Reports on this Submission

Anonymous Report 1 on 2022-2-22 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:2101.07814v3, delivered 2022-02-22, doi: 10.21468/SciPost.Report.4497


As in my previous report:
1) Discovery of a qualitatively new event, namely that the competition between coherent and dissipative dynamics in an open many body system may lead at intermediate times to increased purity and entanglement in certain symmetry sectors although overall state becomes less pure with time.
2) Extensive set of examples demonstrating the behavior, including both numerics on a variety of realistic system and new analysis of previous experimental data.


Weaknesses identified in my previous reports were in my opinion properly addressed by the Authors.


In my opinion, the revised manuscript properly addresses the comments made by all the referees on the previous version. Given my previous assessment of the importance and novelty of this work, I would now recommend its publication in SciPost Physics.

Requested changes


  • validity: high
  • significance: high
  • originality: top
  • clarity: high
  • formatting: excellent
  • grammar: excellent

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