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Canonical Typicality under General Quantum Channels.

Pedro S Correia1, Gabriel Dias Carvalho2,3, Thiago R de Oliveira3

  • 1Departamento de Ciéncias Exatas, <a href="https://ror.org/01zwq4y59">Universidade Estadual de Santa Cruz</a>, Ilhéus, Bahia 45662-900, Brazil.

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Summary
This summary is machine-generated.

We introduce generalized subsystems using quantum channels to study complex quantum systems. This approach reveals that most quantum states exhibit canonical typicality, a behavior influenced by channel entropy.

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Area of Science:

  • Quantum Information Science
  • Statistical Quantum Mechanics
  • Complex Quantum Systems

Background:

  • Traditional statistical quantum mechanics may not capture all relevant degrees of freedom in complex quantum systems.
  • Controlling complex quantum systems necessitates new methods for defining and analyzing subsystems.

Purpose of the Study:

  • To define generalized subsystems in quantum mechanics using quantum channels.
  • To investigate the behavior of these generalized subsystems and their associated canonical states.
  • To explore the concept of canonical typicality for generalized subsystems.

Main Methods:

  • Employing quantum channels to define generalized subsystems.
  • Analyzing the properties of these subsystems derived from microscopic pure states.
  • Investigating the relationship between canonical typicality and channel entropy.

Main Results:

  • Generalized subsystems can capture pertinent degrees of freedom beyond traditional approaches.
  • Almost any microscopic pure state of the whole system exhibits canonical typicality when described as a generalized subsystem.
  • The observed canonical typicality is dependent on the entropy of the quantum channel used.

Conclusions:

  • Quantum channels provide a powerful tool for defining generalized subsystems in quantum mechanics.
  • The concept of canonical typicality is robust and applicable to these generalized subsystems.
  • Channel entropy plays a crucial role in determining the canonical typicality of generalized quantum subsystems.