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Reversible Framework for Quantum Resource Theories.

Fernando G S L Brandão1,2, Gilad Gour3

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This summary is machine-generated.

Quantum resource theories (QRTs) are essential for quantum information and thermodynamics. This study shows that QRTs are asymptotically reversible under specific conditions, with conversion rates determined by unique resource quantifiers.

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Area of Science:

  • Quantum Information Science
  • Quantum Thermodynamics
  • Theoretical Physics

Background:

  • Physical system properties like entanglement and asymmetry are recognized as crucial resources in quantum information and thermodynamics.
  • Quantum Resource Theories (QRTs) have been developed to study how these resources can be manipulated and utilized under specific restrictions.

Purpose of the Study:

  • To discuss the general structure of Quantum Resource Theories (QRTs).
  • To establish conditions under which a QRT becomes asymptotically reversible.
  • To identify the unique measure quantifying resources in the asymptotic limit.

Main Methods:

  • Analysis of the general structure of QRTs.
  • Investigation of conditions for asymptotic reversibility, focusing on the set of allowed operations and free states.
  • Derivation of the asymptotic conversion rate using regularized relative entropy and smoothed logarithmic robustness.

Main Results:

  • A QRT is asymptotically reversible if its set of allowed operations is maximal, meaning it includes all operations that do not asymptotically generate a resource.
  • Under these conditions, the asymptotic conversion rate is uniquely determined.
  • This rate is given by the regularized relative entropy of the resource, which also equals its smoothed logarithmic robustness.

Conclusions:

  • The study provides a general framework for understanding the reversibility and quantification of resources within QRTs.
  • The findings establish a direct link between the maximal set of allowed operations and asymptotic reversibility.
  • The regularized relative entropy is identified as the definitive quantifier for resources in the asymptotic limit.