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Quantifying operational nonclassicality is key for quantum technologies. This study introduces resource theories for operations, defining measures to quantify coherence detection capabilities.

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Area of Science:

  • Quantum Information Science
  • Quantum Computing
  • Foundations of Quantum Mechanics

Background:

  • Quantifying nonclassicality typically focuses on quantum states.
  • Assessing the nonclassicality-detecting power of quantum operations is crucial for quantum technologies.
  • Existing frameworks lack rigorous methods to quantify operational nonclassicality.

Purpose of the Study:

  • To develop a rigorous framework for quantifying nonclassicality at the operational level.
  • To introduce resource theories for quantum operations.
  • To define and evaluate measures for quantifying an operation's ability to detect coherence.

Main Methods:

  • Construction of resource theories for quantum operations.
  • Utilizing resource-destroying maps.
  • Defining free operations and free superoperations (sequential and parallel composition).
  • Developing properties of functionals to quantify operational resources.

Main Results:

  • Established resource theories for quantum operations.
  • Introduced two measures for quantifying an operation's ability to detect coherence.
  • Provided methods for evaluating these coherence-detection measures.
  • One measure possesses an operational interpretation.

Conclusions:

  • Resource theories on the operational level provide a rigorous way to quantify nonclassicality.
  • The developed measures offer a way to assess the utility of quantum operations in detecting coherence.
  • This work lays the foundation for quantifying and utilizing operational nonclassicality in quantum information processing.