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Complexity and efficiency of minimum entropy production probability paths from quantum dynamical evolutions.

Carlo Cafaro1, Shannon Ray2, Paul M Alsing2

  • 1SUNY Polytechnic Institute, Albany, New York 12203, USA.

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We introduce information geometry to analyze quantum driving schemes. Optimal quantum state transfer minimizes entropy production, balancing information geometric complexity and entropic efficiency.

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Area of Science:

  • Quantum mechanics
  • Information geometry
  • Thermodynamics

Background:

  • Quantum driving schemes are crucial for controlling quantum systems.
  • Characterizing these schemes requires understanding complexity and efficiency.

Purpose of the Study:

  • To provide an information geometric framework for characterizing quantum driving schemes.
  • To analyze the trade-offs between complexity and efficiency in quantum state transfer.

Main Methods:

  • Utilized information geometry and Riemannian metrization on probability paths.
  • Employed a minimum action principle to identify optimal (geodesic) paths.
  • Defined and calculated Information Geometric Complexity (IGC) and entropic efficiency.

Main Results:

  • Optimal quantum paths minimize total entropy production.
  • Derived analytical estimates for IGC and entropic efficiency.
  • Established relationships between entropic speed, efficiency, and IGC.

Conclusions:

  • Higher entropic speed correlates with lower entropic efficiency and higher IGC.
  • The framework offers a method for ranking and optimizing quantum driving schemes.