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This study introduces a new method to simultaneously estimate quantum states and measurements, reducing systematic errors common in quantum tomography. The technique uses high-fidelity operations and an optimization algorithm, demonstrated on a two-ion system.

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Area of Science:

  • Quantum Information Science
  • Quantum Computing
  • Quantum Metrology

Background:

  • Accurate estimation of quantum states and measurements is fundamental for quantum information processing.
  • Standard quantum tomography is susceptible to systematic errors arising from imperfect system knowledge.
  • Existing methods require complex procedures and are prone to inaccuracies.

Purpose of the Study:

  • To develop a procedure for simultaneous characterization of quantum states and measurements.
  • To mitigate systematic errors inherent in standard quantum tomography.
  • To provide a robust method applicable to state-of-the-art quantum systems.

Main Methods:

  • Utilized a single high-fidelity state preparation and a limited set of high-fidelity unitary operations.
  • Designed a novel experimental protocol and an optimization algorithm.
  • Employed an iterative likelihood maximization approach for state and measurement estimation.

Main Results:

  • Successfully mitigated systematic errors in quantum state and measurement characterization.
  • Demonstrated the procedure's effectiveness on simulated data from a two-trapped-ion experiment.
  • Developed a method using semi-definite programming to bound expectation values when unique state estimation is not possible.

Conclusions:

  • The proposed procedure offers a more accurate and robust alternative to standard quantum tomography.
  • The method is well-suited for current experimental quantum systems.
  • Provides a framework for handling ambiguities in state estimation through bounding techniques.