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Updated: May 18, 2026

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
09:23

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

Published on: May 30, 2014

Weak and strong typicality in quantum systems.

Lea F Santos1, Anatoli Polkovnikov, Marcos Rigol

  • 1Department of Physics, Yeshiva University, New York, New York 10016, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 26, 2012
PubMed
Summary
This summary is machine-generated.

Researchers explored mixed states from many-body lattice Hamiltonians. They found that both diagonal and entanglement entropy match thermodynamic entropy under different tracing conditions, confirming thermal predictions for observables.

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Last Updated: May 18, 2026

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
09:23

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

Published on: May 30, 2014

Area of Science:

  • Quantum Many-Body Physics
  • Statistical Mechanics
  • Quantum Information Theory

Background:

  • Investigating mixed states derived from lattice Hamiltonian eigenstates is crucial for understanding quantum systems.
  • The relationship between entanglement entropy and thermodynamic entropy in such systems remains an active area of research.

Purpose of the Study:

  • To analyze the properties of mixed states generated by tracing out parts of many-body lattice systems.
  • To determine the conditions under which diagonal and von Neumann entropies equate to thermodynamic entropy.
  • To compare predictions from reduced, diagonal, and canonical density matrices for few-body observables.

Main Methods:

  • Studied mixed states obtained from eigenstates of many-body lattice Hamiltonians.
  • Performed partial tracing over a variable fraction of the lattice sites.
  • Analyzed diagonal entropy, von Neumann (entanglement) entropy, and few-body observables.

Main Results:

  • Identified two distinct scenarios: weak typicality (few sites traced) and strong typicality (large fraction traced).
  • Demonstrated that diagonal entropy matches thermodynamic entropy in weak typicality.
  • Showed that von Neumann entropy matches thermodynamic entropy in strong typicality.
  • Observed remarkable similarity between results from reduced, diagonal, and canonical density matrices for observables.
  • Confirmed that diagonal ensemble results align with thermal predictions across different tracing fractions.

Conclusions:

  • The study establishes clear conditions for the emergence of thermalization in many-body quantum systems via tracing.
  • Results indicate the robustness of thermal predictions for physical quantities regardless of the traced fraction.
  • This work provides insights into the nature of typicality and thermalization in quantum statistical mechanics.