Transitions in the Learnability of Global Charges from Local Measurements

Fergus Barratt, Utkarsh Agrawal, Andrew C. Potter, Sarang Gopalakrishnan, and Romain Vasseur
Phys. Rev. Lett. 129, 200602 – Published 10 November 2022
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Abstract

We consider monitored quantum systems with a global conserved charge, and ask how efficiently an observer (“eavesdropper”) can learn the global charge of such systems from local projective measurements. We find phase transitions as a function of the measurement rate, depending on how much information about the quantum dynamics the eavesdropper has access to. For random unitary circuits with U(1) symmetry, we present an optimal classical classifier to reconstruct the global charge from local measurement outcomes only. We demonstrate the existence of phase transitions in the performance of this classifier in the thermodynamic limit. We also study numerically improved classifiers by including some knowledge about the unitary gates pattern.

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  • Received 8 July 2022
  • Accepted 18 October 2022

DOI:https://doi.org/10.1103/PhysRevLett.129.200602

© 2022 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied PhysicsStatistical Physics & ThermodynamicsQuantum Information, Science & Technology

Authors & Affiliations

Fergus Barratt1, Utkarsh Agrawal1,2, Andrew C. Potter3, Sarang Gopalakrishnan4,5, and Romain Vasseur1

  • 1Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA
  • 2Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California, USA
  • 3Department of Physics and Astronomy, and Quantum Matter Institute, University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z1
  • 4Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
  • 5Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA

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Issue

Vol. 129, Iss. 20 — 11 November 2022

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