Quantum tomographic reconstruction with error bars: a Kalman filter approach

Quantum tomographic reconstruction with error bars: a Kalman filter approach,10.1088/1367-2630/11/2/023028,New Journal of Physics,Koenraad M. R. Auden

Quantum tomographic reconstruction with error bars: a Kalman filter approach   (Citations: 3)
BibTex | RIS | RefWorks Download
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 well-founded 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 follow-up 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
Cumulative Annual
View Publication
The following links allow you to view full publications. These links are maintained by other sources not affiliated with Microsoft Academic Search.
    • ...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 Dobeket al. Experimental security analysis a four-photon 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 n-dimensional 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...

Sort by: