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Related Experiment Video

Updated: May 24, 2026

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
09:23

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

Published on: May 30, 2014

Efficient method for computing the maximum-likelihood quantum state from measurements with additive Gaussian noise.

John A Smolin1, Jay M Gambetta, Graeme Smith

  • 1IBM TJ Watson Research Center, Yorktown Heights, New York 10598, USA. smolin@us.ibm.com

Physical Review Letters
|March 10, 2012
PubMed
Summary
This summary is machine-generated.

We developed an efficient algorithm to compute the maximum-likelihood quantum state from noisy measurement data. This method efficiently finds the nearest physical quantum state (density matrix ρ) to a candidate state.

Related Experiment Videos

Last Updated: May 24, 2026

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
09:23

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

Published on: May 30, 2014

Area of Science:

  • Quantum Information Science
  • Quantum Computing
  • Quantum State Estimation

Background:

  • Accurate quantum state reconstruction is crucial for quantum information processing.
  • Experimental quantum measurements are often corrupted by Gaussian noise.
  • Existing methods for mixed quantum state estimation can be computationally intensive.

Purpose of the Study:

  • To develop an efficient computational method for maximum-likelihood quantum state estimation.
  • To handle noisy measurement outcomes in a complete orthonormal operator basis.
  • To ensure the reconstructed quantum state is physically valid (non-negative eigenvalues).

Main Methods:

  • The algorithm involves a basis change to obtain a candidate density matrix (μ).
  • It then identifies the nearest physical state to μ using the 2-norm.
  • A novel linear-time algorithm is used for finding the closest probability distribution.

Main Results:

  • The overall computational complexity is at most O(d^4) for basis change and O(d^3) for state reconstruction, where d is the quantum state dimension.
  • For Pauli operator bases, the basis change complexity reduces to O(d^3).
  • The method guarantees a physically valid density matrix (ρ).

Conclusions:

  • This efficient algorithm provides a practical solution for reconstructing mixed quantum states from noisy data.
  • The computational efficiency makes it suitable for high-dimensional quantum systems.
  • The method advances the field of quantum state tomography and characterization.