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Quantifying the Incompatibility of Quantum Measurements Relative to a Basis.

Georgios Styliaris1, Paolo Zanardi1

  • 1Department of Physics and Astronomy, and Center for Quantum Information Science and Technology, University of Southern California, Los Angeles, California 90089-0484, USA.

Physical Review Letters
|September 7, 2019
PubMed
Summary
This summary is machine-generated.

We introduce quantum measurement incompatibility, a concept related to converting probability distributions. This work connects incompatibility with quantum coherence and uncertainty relations for various measurements.

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Area of Science:

  • Quantum Information Theory
  • Quantum Measurement Theory

Background:

  • Quantum resource theories explore limitations and capabilities of quantum systems.
  • Understanding measurement limitations is crucial for quantum information processing.

Purpose of the Study:

  • Introduce a novel framework for quantum measurement incompatibility relative to a reference basis.
  • Quantify incompatibility using monotones and explore its connections to other quantum phenomena.

Main Methods:

  • Define incompatibility based on the convertibility of probability distributions via postprocessing.
  • Utilize multivariate majorization to establish an ordering of measurements.
  • Develop families of monotones to characterize incompatibility.

Main Results:

  • Established a preorder for quantum measurements based on incompatibility.
  • Demonstrated a quantitative link between incompatibility, quantum coherence, and entropic uncertainty relations for orthogonal measurements.
  • Generalized the framework to arbitrary positive-operator-valued (POVM) measurements.

Conclusions:

  • The introduced framework provides a new perspective on quantum measurement limitations.
  • Incompatibility serves as a valuable resource, quantifiable by monotones.
  • The findings deepen the understanding of the interplay between measurement, coherence, and uncertainty in quantum systems.