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Measuring Incompatibility and Clustering Quantum Observables with a Quantum Switch.

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We introduce a new measure, mutual eigenspace disturbance (MED), to quantify the incompatibility between quantum measurements. This measure can be estimated using a quantum switch and applied to quantum machine learning for clustering measurements.

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Area of Science:

  • Quantum Mechanics
  • Quantum Information Theory
  • Quantum Technologies

Background:

  • Incompatible observables are fundamental to quantum mechanics.
  • These incompatibilities are crucial for advancing quantum technologies.
  • Quantifying measurement incompatibility is essential for quantum information processing.

Purpose of the Study:

  • Introduce a novel measure for quantifying the incompatibility between quantum measurements, termed Mutual Eigenspace Disturbance (MED).
  • Develop an efficient estimation method for MED using quantum phenomena.
  • Demonstrate the utility of MED in quantum machine learning applications.

Main Methods:

  • Defined Mutual Eigenspace Disturbance (MED) as a metric quantifying disturbance between measurement eigenspaces.
  • Utilized a quantum switch setup to enable indefinite ordering of quantum processes for efficient MED estimation.
  • Developed an unsupervised machine learning algorithm for clustering von Neumann measurements based on MED.

Main Results:

  • MED quantifies the disturbance between eigenspaces of incompatible quantum observables.
  • The quantum switch facilitates efficient estimation of MED and quantification of quantum process noncommutativity.
  • The unsupervised algorithm successfully clusters unknown von Neumann measurements, demonstrating MED's practical application.

Conclusions:

  • MED offers a robust metric for quantum measurement incompatibility.
  • The quantum switch provides a versatile tool for estimating incompatibility and analyzing quantum processes.
  • The developed algorithm shows promise for noise-resilient quantum machine learning tasks, particularly in measurement analysis.