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Mixed State Deep Thermalization
Xie-Hang Yu1, Wen Wei Ho2,3, Pavel Kos1
1Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, 85748 Garching, Germany.
Physical Review Letters
|January 20, 2026
Summary
We introduce the mixed state projected ensemble (MSPE) for quantum systems with incomplete measurements. This new framework reveals deep thermalization universality and provides a physical method for sampling random density matrices.
Area of Science:
- Quantum Many-Body Physics
- Quantum Information Theory
Background:
- The pure state projected ensemble (PSPE) describes quantum systems with complete measurements, exhibiting deep thermalization.
- Real-world quantum simulations involve incomplete and lossy measurements, necessitating a more general framework.
Purpose of the Study:
- Introduce the mixed state projected ensemble (MSPE) as a generalization of PSPE for incomplete measurements.
- Investigate the emergence of thermalization universality in MSPEs.
- Analyze quantum information properties, specifically teleportation fidelity, within MSPEs.
Main Methods:
- Studied MSPEs generated by solvable (1+1)d dual-unitary quantum circuits.
- Identified limiting mixed state distributions for varying sizes of incomplete measurements.
- Derived the rate of universality emergence.
- Investigated quantum teleportation fidelity and its relation to quantum conditional entropy.
Main Results:
- Identified limiting mixed state distributions corresponding to known random density matrix ensembles.
- Found that teleportation fidelity exhibits a sharp transition based on measurement loss.
- Derived the rate at which universality emerges in the MSPE.
Conclusions:
- MSPE provides a framework for studying deep thermalization in realistic quantum systems with imperfect measurements.
- The study offers a physical method for sampling from abstract random density matrix ensembles.
- Results are relevant for current quantum simulation experiments and advance understanding of quantum equilibration.
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