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Journal Article

Markov chain Monte Carlo estimation of quantum states

MPS-Authors

DiGuglielmo,  J.
AEI-Hannover, MPI for Gravitational Physics, Max Planck Society;
Laser Interferometry & Gravitational Wave Astronomy, AEI-Hannover, MPI for Gravitational Physics, Max Planck Society;

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Messenger,  C.
Observational Relativity and Cosmology, AEI-Hannover, MPI for Gravitational Physics, Max Planck Society;

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Hage,  B.
Laser Interferometry & Gravitational Wave Astronomy, AEI-Hannover, MPI for Gravitational Physics, Max Planck Society;

Samblowski,  A.
AEI-Hannover, MPI for Gravitational Physics, Max Planck Society;
Laser Interferometry & Gravitational Wave Astronomy, AEI-Hannover, MPI for Gravitational Physics, Max Planck Society;

Schmidt,  T.
AEI-Hannover, MPI for Gravitational Physics, Max Planck Society;
Laser Interferometry & Gravitational Wave Astronomy, AEI-Hannover, MPI for Gravitational Physics, Max Planck Society;

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Schnabel,  R.
Laser Interferometry & Gravitational Wave Astronomy, AEI-Hannover, MPI for Gravitational Physics, Max Planck Society;

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PhysRevA.79.032114.pdf
(Publisher version), 448KB

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Citation

DiGuglielmo, J., Messenger, C., Fiurasek, J., Hage, B., Samblowski, A., Schmidt, T., et al. (2009). Markov chain Monte Carlo estimation of quantum states. Physical Review A, 79(3): 032114. doi:10.1103/PhysRevA.79.032114.


Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-46B2-D
Abstract
We apply a Bayesian data analysis scheme known as the Markov chain Monte Carlo to the tomographic reconstruction of quantum states. This method yields a vector, known as the Markov chain, which contains the full statistical information concerning all reconstruction parameters including their statistical correlations with no a priori assumptions as to the form of the distribution from which it has been obtained. From this vector we can derive, e.g., the marginal distributions and uncertainties of all model parameters, and also of other quantities such as the purity of the reconstructed state. We demonstrate the utility of this scheme by reconstructing the Wigner function of phase-diffused squeezed states. These states possess non-Gaussian statistics and therefore represent a nontrivial case of tomographic reconstruction. We compare our results to those obtained through pure maximum-likelihood and Fisher information approaches.