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On the Quantumness of Multiparameter Estimation Problems for Qubit Systems.

Sholeh Razavian1,2, Matteo G A Paris2,3, Marco G Genoni2,3

  • 1Faculty of Physics, Azarbaijan Shahid Madani University, Tabriz 5375171379, Iran.

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Summary
This summary is machine-generated.

Quantum mechanics limits estimation precision through non-commutative observables. A new measure, quantumness R, quantifies parameter incompatibility in qubit systems, proving useful for multiparameter estimation models.

Keywords:
multiparameter estimationquantum metrologyquantum probesquantum sensing

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Area of Science:

  • Quantum mechanics
  • Quantum information theory
  • Statistical inference

Background:

  • Multiparameter estimation is crucial in quantum mechanics, with precision limits tied to non-commuting observables.
  • Understanding parameter incompatibility is key to optimizing quantum estimation protocols.

Purpose of the Study:

  • To evaluate quantumness R, a measure of parameter incompatibility, for various qubit estimation problems.
  • To assess the utility of quantumness R in characterizing multiparameter quantum statistical models.

Main Methods:

  • Considered several estimation problems for qubit systems.
  • Calculated quantumness R, an upper bound for the difference between Holevo and SLD Cramér-Rao bounds.
  • Compared R with the direct difference between the Holevo and SLD bounds.

Main Results:

  • Quantumness R was evaluated for multiple qubit estimation problems.
  • R generally aligns with the difference between Holevo and SLD bounds, indicating its usefulness.
  • For some models, R may overestimate incompatibility as the bound is not always tight.

Conclusions:

  • Quantumness R is a valuable tool for characterizing multiparameter quantum estimation problems.
  • While generally effective, R's accuracy depends on the tightness of the underlying bounds for specific models.