Entropic Characterization of Quantum States with Maximal Evolution under Given Energy Constraints

Area of Science:

• Quantum Mechanics
• Quantum Information Theory
• Statistical Mechanics

Background:

• Understanding quantum system dynamics is crucial for quantum technologies.
• Quantifying dynamical evolution requires robust measures.
• Existing measures may not fully capture system state changes over time.

Purpose of the Study:

• Define a novel measure, D[t1, t2], for the dynamical evolution of quantum systems.
• Investigate the properties of this measure, particularly its asymptotic behavior.
• Formulate an entropic variational problem to characterize states with maximal dynamical evolution.

Main Methods:

• Defining a dynamical evolution measure based on state distinguishability over time.
• Analyzing the asymptotic behavior of the measure D[t1, t2] as time interval increases.
• Relating the measure to linear entropy of the energy distribution.
• Formulating an entropic variational problem with energy constraints.

Main Results:

• The measure D[t1, t2] quantifies dynamical evolution by state distinguishability.
• D[t1, t2] rapidly approaches an asymptotic value related to linear entropy.
• This asymptotic value depends on the energy distribution of the quantum state.
• An entropic variational problem is formulated for states exhibiting maximal evolution.

Conclusions:

• The developed measure provides a quantitative tool for assessing quantum dynamical evolution.
• The connection to linear entropy offers a new perspective on quantum state dynamics.
• The entropic variational problem identifies specific quantum states under energy constraints.