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Universal energy equalization under Haar-random unitary operations.

Hyogeon Park1, Minjae Kym2, Yong Woon Kim1

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This summary is machine-generated.

Finite quantum systems subjected to random operations shift energy towards infinite temperature, enabling work extraction. This equalization becomes typical in large systems, as shown in spin models and unitary quenches.

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Area of Science:

  • Quantum thermodynamics
  • Statistical mechanics
  • Quantum information theory

Background:

  • Finite quantum systems can be prepared in specific initial states, such as energy-diagonal ensembles.
  • Unitary operations, particularly Haar-random ones, are fundamental tools in quantum information and can drive system evolution.
  • Understanding energy dynamics and work extraction in quantum systems is crucial for developing quantum technologies.

Purpose of the Study:

  • To investigate the work done on finite quantum systems under Haar-random unitary operations.
  • To determine if energy distribution equalization occurs and its implications for work extraction.
  • To explore the conditions under which similar energy equalization phenomena arise, such as during unitary quenches.

Main Methods:

  • Theoretical analysis of work done on finite quantum systems subjected to Haar-random unitary operations.
  • Investigating the shift in energy distribution towards the infinite-temperature value.
  • Numerical simulations using a spin model to illustrate the predicted behavior.
  • Analyzing unitary quenches with Hamiltonians satisfying the Eigenstate Thermalization Hypothesis and spectral conditions.

Main Results:

  • On average, the system's energy shifts towards the infinite-temperature value, leading to energy distribution equalization.
  • States with energy above the infinite-temperature value are identified as a resource for work extraction.
  • The energy equalization trend becomes typical in large systems due to vanishing fluctuations.
  • Similar energy equalization is observed in unitary quenches when specific spectral conditions are met.

Conclusions:

  • Haar-random unitary operations drive finite quantum systems towards an infinite-temperature-like energy distribution.
  • This energy equalization process indicates that high-energy states can be utilized as a resource for work extraction.
  • The Eigenstate Thermalization Hypothesis, along with nondegeneracy and flatness conditions, is sufficient to reproduce Haar-typical energy equalization during unitary quenches.