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Transitions in the Learnability of Global Charges from Local Measurements
Fergus Barratt1, Utkarsh Agrawal1,2, Andrew C Potter3
1Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA.
Physical Review Letters
|December 3, 2022
Summary
An eavesdropper can efficiently learn a quantum system's global charge using local measurements. Phase transitions emerge based on measurement rates and available information about quantum dynamics.
Area of Science:
- Quantum Information Science
- Condensed Matter Physics
- Quantum Many-Body Systems
Background:
- Monitored quantum systems possess global conserved charges.
- Local measurements can potentially reveal information about these global properties.
- Understanding information flow in quantum systems is crucial for quantum technologies.
Purpose of the Study:
- To quantify the efficiency of an eavesdropper learning a global conserved charge from local measurements.
- To identify phase transitions in eavesdropping efficiency as a function of measurement rate and information access.
- To develop and analyze methods for reconstructing global charge from local data.
Main Methods:
- Analysis of monitored quantum systems with global conserved charges.
- Development of classical classifiers for reconstructing global charge from local projective measurements.
- Investigation of random unitary circuits with U(1) symmetry.
- Study of phase transitions in classifier performance in the thermodynamic limit.
- Numerical exploration of improved classifiers with partial knowledge of unitary gate patterns.
Main Results:
- Phase transitions in eavesdropping efficiency were discovered, dependent on measurement rate and eavesdropper's knowledge.
- An optimal classical classifier was presented for reconstructing the global charge in U(1) symmetric random unitary circuits.
- The existence of phase transitions in classifier performance was demonstrated in the thermodynamic limit.
- Numerical studies showed improved classifier performance with partial knowledge of unitary gate patterns.
Conclusions:
- Local measurements can be surprisingly effective for inferring global properties of quantum systems.
- The measurement rate and the eavesdropper's access to system dynamics critically influence information extraction.
- Phase transitions provide a framework for understanding the abrupt changes in eavesdropping capabilities.
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