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Investigating bias in maximum-likelihood quantum-state tomography.

G B Silva1, S Glancy2, H M Vasconcelos1

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Maximum-likelihood quantum-state tomography can be biased. Higher purity state estimates show significant bias, resulting in lower purity values than the true states.

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Area of Science:

  • Quantum information science
  • Quantum optics
  • Quantum state estimation

Background:

  • Maximum-likelihood quantum-state tomography (ML-QST) provides consistent estimators if the likelihood model is accurate.
  • However, finite datasets can introduce bias into ML-QST estimators.
  • Bias in an estimator is defined as the difference between the expected estimate and the true parameter value.

Purpose of the Study:

  • To investigate bias in maximum-likelihood quantum-state tomography.
  • To determine how bias is influenced by state purity, measurement count, and measurement basis diversity.

Main Methods:

  • Numerical simulations of optical homodyne tomography for squeezed thermal states.
  • Tomography performed under varied experimental conditions.
  • Bias estimation focused on the purity of the reconstructed quantum state.

Main Results:

  • Estimates for higher purity quantum states exhibit substantial bias.
  • The bias leads to an underestimation of the true state purity.
  • Bias is dependent on factors including state purity and the number of measurements.

Conclusions:

  • Maximum-likelihood quantum-state tomography is susceptible to bias, particularly for pure states.
  • The number of measurements and bases used impacts the degree of bias.
  • Careful consideration of bias is necessary for accurate quantum state reconstruction.