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Mixed State Deep Thermalization.

Xie-Hang Yu1, Wen Wei Ho2,3, Pavel Kos1

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This summary is machine-generated.

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.

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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.