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Complete Resource Theory of Quantum Incompatibility as Quantum Programmability.

Francesco Buscemi1, Eric Chitambar2, Wenbin Zhou1

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Measurement incompatibility, a nonclassical quantum phenomenon, is characterized using programmable measurement devices. This research establishes a quantum resource theory for incompatibility, detailing its convertibility conditions.

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Area of Science:

  • Quantum Information Science
  • Quantum Foundations
  • Quantum Measurement Theory

Background:

  • Measurement incompatibility is a fundamental quantum phenomenon where joint outcomes of multiple measurements cannot be defined.
  • This nonclassical effect is crucial for quantum information tasks like Bell inequality violation and quantum steering.
  • Existing characterizations often lack a resource-based framework for quantifying and manipulating incompatibility.

Purpose of the Study:

  • To characterize measurement incompatibility using the concept of programmable measurement devices and quantum programmability.
  • To construct a quantum resource theory specifically for measurement incompatibility.
  • To derive conditions for the convertibility of programmable measurement devices.

Main Methods:

  • Characterization of incompatibility through the lens of programmable measurement devices, emphasizing temporal freedom in device programming.
  • Development of a quantum resource theory based on the processing capabilities of these programmable devices.
  • Derivation of convertibility conditions using quantum state discrimination techniques incorporating post-measurement information.

Main Results:

  • Measurement incompatibility is identified as the essential quantum resource in programmable devices with classical control and output.
  • A complete set of convertibility conditions for programmable measurement devices has been established.
  • The resource theory provides a formal framework for understanding and manipulating quantum measurement incompatibility.

Conclusions:

  • Programmable measurement devices offer a novel perspective for understanding and quantifying measurement incompatibility.
  • The developed quantum resource theory provides a powerful tool for analyzing incompatibility in quantum information processing.
  • This work advances the understanding of fundamental quantum resources and their applications in quantum technologies.