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Quantum state tomography via linear regression estimation.

Bo Qi1, Zhibo Hou2, Li Li2

  • 1Key Laboratory of Systems and Control, ISS, and National Center for Mathematics and Interdisciplinary Sciences, Academy of Mathematics and Systems Science, CAS, Beijing 100190, P. R. China.

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|December 17, 2013
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Summary
This summary is machine-generated.

A new quantum state tomography algorithm, linear regression estimation (LRE), reconstructs quantum states efficiently. This method offers a faster alternative to maximum-likelihood estimation, with a computable error bound to guide optimal measurement selection.

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Area of Science:

  • Quantum information science
  • Quantum computing
  • Quantum mechanics

Background:

  • Quantum state tomography is crucial for characterizing quantum systems.
  • Existing methods like maximum-likelihood estimation can be computationally intensive.
  • Efficient state reconstruction is vital for advancing quantum technologies.

Purpose of the Study:

  • To introduce a simple and efficient algorithm for quantum state tomography.
  • To present a novel approach using linear regression estimation (LRE).
  • To provide an analytical tool for selecting optimal measurement bases.

Main Methods:

  • Formulating quantum state reconstruction as a linear regression parameter estimation problem.
  • Employing the least-squares method for parameter estimation.
  • Deriving an analytical upper bound for the asymptotic mean squared error (MSE).

Main Results:

  • The proposed LRE algorithm achieves a computational complexity of O(d^4).
  • An analytical MSE upper bound was derived, dependent on measurement bases.
  • Numerical simulations demonstrated LRE's superior speed compared to maximum-likelihood estimation.
  • The MSE bound provides guidance for selecting optimal measurement sets.

Conclusions:

  • LRE offers a computationally efficient and simple method for quantum state tomography.
  • The derived MSE bound is a valuable tool for optimizing measurement strategies.
  • This algorithm has the potential to accelerate research and development in quantum information processing.