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Authors
Attila Magyar, Denes Petz, Katalin M. Hangos

Identifier
10.3182/20060329-3-AU-2901.00151

Index Terms
system identification,Bayesian estimation,quantum systems,regularization

Abstract
In this paper a Bayesian approach for estimating the state of a qubit is proposed. It consists of two phases. First a component-wise separate Bayesian estimate of the Bloch vector components is calculated in the form of β-distributions. Then a regularization step is performed to respect the constraint that the Bloch vector must be in the unit ball. The properties of the proposed algorithm are investigated by simulation.

References

[1] D'Alessandro, D. (2003). Controllability, observability
     and parameter identification of two coupled
     spin 1's. arXiv quant-ph/0307129, v. 1.
[2] D'Ariano, G. M., M. G. A. Paris and M. F. Sacchi
    (2003). Quantum tomography. arXiv quantph/0302028,
     v. 1.
[3] Helstrom, C. W. (1976). Quantum decision and
    estimation theory. Academic Press, New
    York.
[4] Kosut, R. L., I. Walmsley and H. Rabitz (2004).
    Optimal experiment design for quantum
    state and process tomography and hamiltonian
     parameter estimation. arXiv quantph/0411093,
     v. 1.
[5] Kosut, R. L., I. Walmsley and H. Rabitz (2005).
    Identification of quantum systems: Maximum
    linkelihood and optimal experiment design
    for state tomography. IFAC World Congress
    1.1, Prague (Czech Republic).
[6] Peterka, V. (1981). 'Bayesian system identification'
     in Trends and Progress in System Identification,
     P. Eykhofi, Ed., Pergamon Press,
    Oxford.
[7] Řehaček, J., B.-G. Englert and D. Kraszlikowski
    (2004). Minimal qubit tomography. arXiv
    quant-ph/0405084, v. 2.