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Keywords
(8)
bayesian inference
Covariance Matrix
Information Processing
Measurement Uncertainty
Quantum Optics
Tomographic Reconstruction
kalman filter
Maximum Likelihood
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On Inverse Moments of Nonnegative Random Variables
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Quantum tomographic reconstruction with error bars: a Kalman filter approach
Quantum tomographic reconstruction with error bars: a Kalman filter approach,10.1088/13672630/11/2/023028,New Journal of Physics,Koenraad M. R. Auden
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Quantum tomographic reconstruction with error bars: a Kalman filter approach
(
Citations: 3
)
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Koenraad M. R. Audenaert
,
Stefan Scheel
We present a novel quantum
tomographic reconstruction
method based on
Bayesian inference
via the
Kalman filter
update equations. The method not only yields the maximum likelihood/optimal Bayesian reconstruction but also a
covariance matrix
expressing the measurement uncertainties in a complete way. From this
covariance matrix
the error bars on any derived quantity can be easily calculated. This is a first step towards the broader goal of devising an omnibus reconstruction method that could be adapted to any tomographic setup with little effort and that treats measurement uncertainties in a statistically wellfounded way. In this first part, we restrict ourselves to the important subclass of tomography based on measurements with discrete outcomes (as opposed to continuous ones), and we also ignore any measurement imperfections (dark counts, less than unit detector efficiency, etc), which will be treated in a followup paper. We illustrate our general theory on real tomography experiments of quantum
optical information processing
elements.
Journal:
New Journal of Physics  NEW J PHYS
, vol. 11, no. 2, 2009
DOI:
10.1088/13672630/11/2/023028
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Citation Context
(2)
...Before a single interval, settings of individual polarization analyzers were selected randomly and independently on Alice’s and Bob’s side to project polarization in the eigenbasis of sx, sy, or sz. The density matrix of the generated state, depicted in Fig. 1(a,b), was reconstructed from fourfold coincidences using two independent techniques: the Kalman filter (KF) method [
2
] based on gaussian approximation and Bayesian inference which ...
Krzysztof Dobek
,
et al.
Experimental security analysis a fourphoton private state
...Recent applications in quantum physics, for example, include the calculation of running times of certain quantum computation algorithms [33], the study of random walks on ndimensional cubes [11], and exact calculations of the confidence region of a Beta estimator of the parameter p of a binomial distribution [
2
]...
Koenraad M. R. Audenaert
.
Inverse moments of univariate discrete distributions via the Poisson e...
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Citations
(3)
Experimental Extraction of Secure Correlations from a Noisy Private State
Krzysztof Dobek
,
Michal Karpinski
,
Rafal DemkowiczDobrzanski
,
Konrad Banaszek
,
Pawel Horodecki
Journal:
Physical Review Letters  PHYS REV LETT
, vol. 106, 2011
Experimental security analysis a fourphoton private state
Krzysztof Dobek
,
Michal Karpinski
,
Rafal DemkowiczDobrzanski
,
Konrad Banaszek
,
Pawel Horodecki
Published in 2011.
Inverse moments of univariate discrete distributions via the Poisson expansion
(
Citations: 1
)
Koenraad M. R. Audenaert
Published in 2008.