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  Markov chain Monte Carlo estimation of quantum states

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.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-46B2-D Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-46B3-B
Genre: Journal Article

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PhysRevA.79.032114.pdf (Publisher version), 448KB
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 Creators:
DiGuglielmo, J.1, 2, Author
Messenger, C.3, Author              
Fiurasek, J., Author
Hage, B.2, Author              
Samblowski, A.1, 2, Author
Schmidt, T.1, 2, Author
Schnabel, R.2, Author              
Affiliations:
1AEI-Hannover, MPI for Gravitational Physics, Max Planck Society, ou_24009              
2Laser Interferometry & Gravitational Wave Astronomy, AEI-Hannover, MPI for Gravitational Physics, Max Planck Society, ou_24010              
3Observational Relativity and Cosmology, AEI-Hannover, MPI for Gravitational Physics, Max Planck Society, ou_24011              

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 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.

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 Dates: 2009
 Publication Status: Published in print
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 Identifiers: eDoc: 439741
ISI: 000264770200029
DOI: 10.1103/PhysRevA.79.032114
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Title: Physical Review A
Source Genre: Journal
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Pages: - Volume / Issue: 79 (3) Sequence Number: 032114 Start / End Page: - Identifier: -