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Useful Dual Functional of Entropic Information Measures
Angelo Plastino1,2, Mario Carlos Rocca1,2,3, Flavia Pennini1,4,5
1Consejo Nacional de Investigaciones Científicas y Tecnológicas, (IFLP-CCT-CONICET)-C. C. 727, 1900 La Plata, Argentina.
Entropy (Basel, Switzerland)
|December 8, 2020
Summary
This study introduces a new objective measure to differentiate between various entropic functionals. By using probability distributions derived from wave functions, it provides a novel way to quantify information in quantum systems.
Area of Science:
- Quantum Mechanics
- Information Theory
- Statistical Mechanics
Background:
- Existing entropic functionals lack objective measures for differentiation.
- Born's proposal equates the square modulus of wave functions to probability distributions.
- Shannon's information measures have shown utility in pure-state quantum contexts.
Purpose of the Study:
- To develop a simple, objective measure for distinguishing between entropic functionals.
- To introduce a dual functional mapping entropic functionals to positive real numbers.
- To apply this framework to compare standard entropic measures.
Main Methods:
- Utilizing Born's proposal to define probability distributions from wave functions.
- Employing coherent states of the harmonic oscillator (CHO) as a standard.
- Leveraging the analytic closed-form expressions for CHOs.
Main Results:
- A novel dual functional, FαR, is generated.
- The functional maps entropic functionals to positive real numbers.
- Insights are gained into comparing various standard entropic measures.
Conclusions:
- The proposed method offers an objective way to assess and compare entropic functionals.
- Coherent states of the harmonic oscillator provide a robust framework for this analysis.
- This work advances the understanding of information measures in quantum mechanics.
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