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Uniform Additivity in Classical and Quantum Information.

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Information theory uses entropies to measure resource interconversions, but nonadditivity complicates calculations. This study introduces uniform additivity, simplifying these evaluations and revealing identical classical and quantum functions.

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Area of Science:

  • Quantum Information Theory
  • Mathematical Physics
  • Information Theory

Background:

  • Information theory quantifies resource interconversion rates using entropies.
  • Nonadditivity in entropic formulas often makes calculations intractable.
  • Additivity offers a tractable path for characterizing optimal rates in specific cases.

Purpose of the Study:

  • To study uniform additivity as a method for evaluating entropic formulas.
  • To provide a complete characterization of uniform additivity.
  • To identify new additive quantities and explore connections between classical and quantum information theory.

Main Methods:

  • Investigated the properties of uniform additivity for information-theoretic formulas.
  • Analyzed the conditions under which entropic formulas exhibit additivity.
  • Characterized uniformly additive functions in both classical and quantum information contexts.

Main Results:

  • Uniform additivity provides an easily evaluated framework that captures known additive quantum formulas.
  • A new additive quantity arising from uniform additivity was discovered.
  • Classical and quantum uniformly additive functions with one auxiliary variable were found to be identical.

Conclusions:

  • Uniform additivity offers a powerful and simplified approach to analyzing resource interconversions in information theory.
  • The study highlights a significant convergence between classical and quantum information theory through uniformly additive functions.
  • This work paves the way for further research into additive quantities and their applications.