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Precision-guaranteed quantum tomography.

Takanori Sugiyama1, Peter S Turner, Mio Murao

  • 1Department of Physics, Graduate School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, Japan 113-0033.

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|November 5, 2013
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Summary
This summary is machine-generated.

We introduce a new quantum state tomography estimator to precisely evaluate quantum state preparation accuracy. This method rigorously quantifies estimation and preparation precision for various quantum systems and measurements.

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Area of Science:

  • Quantum Information Science
  • Quantum Computing
  • Experimental Quantum Physics

Background:

  • Quantum state tomography (QST) is the standard for verifying lab-prepared quantum states against ideal targets.
  • Current QST lacks rigorous methods to evaluate the precision of state preparation.
  • Assessing the accuracy of quantum state estimation and preparation is crucial for reliable quantum technologies.

Purpose of the Study:

  • To develop a novel estimator for quantum state tomography.
  • To provide rigorous methods for evaluating the precision of state preparation in tomographic experiments.
  • To enable precise assessment of both state estimation and preparation accuracy.

Main Methods:

  • Proposed a new estimator for quantum state tomography.
  • Derived an explicit formula to calculate the probability of estimates being close to the true prepared state.
  • The formula is applicable to arbitrary finite-dimensional systems, informationally complete measurement sets, and general loss functions (infidelity, Hilbert-Schmidt, trace distances).

Main Results:

  • The proposed estimator yields physically valid estimates that are close to the true prepared state with high probability.
  • An explicit formula was derived for calculating this probability for arbitrary systems.
  • The formula allows evaluation of differences between estimated and prepared states, and prepared and target states.

Conclusions:

  • This work provides the first rigorous method for evaluating the precision of state preparation in quantum tomographic experiments.
  • The developed formula offers a powerful tool for quantifying accuracy in quantum state estimation.
  • This advancement is critical for the reliable development and verification of quantum states and protocols.