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One-Shot Operational Quantum Resource Theory.

Zi-Wen Liu1,2, Kaifeng Bu3,4, Ryuji Takagi2

  • 1Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada.

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Summary
This summary is machine-generated.

This study introduces a unified framework for one-shot quantum resource manipulation, analyzing optimal state conversion efficiencies. It establishes general bounds for quantum resource theories, applicable to entanglement, coherence, and more.

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Area of Science:

  • Quantum Information Science
  • Quantum Thermodynamics
  • Quantum Resource Theories

Background:

  • Characterizing and quantifying quantum resources is crucial for understanding quantum systems.
  • Previous studies often focused on specific resource types or multiple copies of quantum states.

Purpose of the Study:

  • To establish a unified, resource-nonspecific framework for one-shot quantum resource manipulation.
  • To determine the optimal efficiency of resource formation and distillation using a single quantum state copy.

Main Methods:

  • Analysis of optimal state conversion efficiencies under constraints.
  • Development of a resource-nonspecific approach to quantum resource theories.
  • Introduction of theory-dependent coefficients to generalize findings.

Main Results:

  • General bounds on optimal rates for quantum resource conversion were derived.
  • Resource measures based on smooth max-/min-relative entropies and hypothesis testing relative entropy were linked to operational meanings.
  • The framework was shown to encompass a wide range of quantum resource theories.

Conclusions:

  • The study provides a unified theory for manipulating quantum resources with single state copies.
  • The derived bounds offer fundamental insights into the efficiency of quantum state transformations.
  • The framework has broad applicability across various quantum resource theories, including entanglement and coherence.