Minimum Time for the Evolution to a Nonorthogonal Quantum State and Upper Bound of the Geometric Efficiency of Quantum Evolutions

Abstract

We present a simple proof of the fact that the minimum time TAB for quantum evolution between two arbitrary states jAi and jBi equals TAB = } cosx1F;1[jhAjBij]/DE with DE being the constant energy uncertainty of the system. This proof is performed in the absence of any geometrical arguments. Then, being in the geometric framework of quantum evolutions based upon the geometry of the projective Hilbert space, we discuss the roles played by either minimum-time or maximum energy uncertainty concepts in defining a geometric efficiency measure of quantum evolutions between two arbitrary quantum states. Finally, we provide a quantitative justification of the validity of the inequality 1 even when the system only passes through nonorthogonal quantum states.

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Document Details

Document Type
Technical Report
Publication Date
Aug 16, 2021
Accession Number
AD1196643

Entities

People

  • Carlo Cafaro
  • Paul M. Alsing

Organizations

  • SUNY Polytechnic Institute

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Air Force
  • Air Force Research Laboratories
  • Efficiency
  • Equations
  • Frequency
  • Geometry
  • Hilbert Space
  • Inequalities
  • Intervals
  • Magnetic Fields
  • Mathematics
  • Mechanics
  • Military Research
  • Physics
  • Physics Laboratories
  • Quantum Computing
  • Quantum Information
  • Quantum Mechanics
  • Quantum States
  • Time Intervals
  • Uncertainty

Fields of Study

  • Mathematics
  • Physics

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Computer Vision.
  • Theoretical Analysis.

Technology Areas

  • Quantum Computing
  • Space