The data aggregation problem in quantum hypothesis testing

  • Simone Cialdi
  • Matteo G. A. ParisEmail author
Regular Article


We discuss the implications of quantum-classical Yule-Simpson effect for quantum hypothesis testing in the presence of noise, and provide an experimental demonstration of its occurrence in the problem of discriminating which polarization quantum measurement has been actually performed by a detector box designed to measure linear polarization of single-photon states along a fixed but unknown direction.


Quantum Information 


  1. 1.
    E.H. Simpson, J. Roy. Stat. Soc. B 13, 238 (1951)zbMATHGoogle Scholar
  2. 2.
    C.R. Blyth, J. Am. Stat. Ass. 67, 364 (1972)CrossRefzbMATHMathSciNetGoogle Scholar
  3. 3.
    P.J. Bickel, E.A. Hammel, J.W. O’Connell, Science 187, 398 (1975)ADSCrossRefGoogle Scholar
  4. 4.
    P.S. Bandyopadhyay, D. Nelson, M. Greenwood, G. Brittan, J. Berwald, Synthese 182, 185 (2011) CrossRefMathSciNetGoogle Scholar
  5. 5.
    M.G.A. Paris, J. Phys. A 45, 132001 (2012) ADSCrossRefMathSciNetGoogle Scholar
  6. 6.
    Y.L. Li, J.S. Tang, Y.T. Wang, Y.C. Wu, J.Y. Han, C. F. Li, G.C. Guo, Y. Yu, M.F. Li, G.W. Zha, Phys. Rev. A 88, 015804 (2013) ADSCrossRefGoogle Scholar
  7. 7.
    Y. Shi, arXiv:1203.2675 (2012)Google Scholar
  8. 8.
    M.G.A. Paris, Eur. Phys. J. ST 203, 61 (2012)CrossRefGoogle Scholar
  9. 9.
    D. Brivio, S. Cialdi, S. Vezzoli, B. Teklu, M.G. Genoni, S. Olivares, M.G.A. Paris, Phys. Rev. A 81, 012315 (2010) ADSCrossRefGoogle Scholar
  10. 10.
    M.G. Genoni, S. Olivares, D. Brivio, S. Cialdi, D. Cipriani, A. Santamato, S. Vezzoli, M.G.A. Paris, Phys. Rev. A 85, 043817 (2012) ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Dipartimento di Fisica dell’Università degli Studi di MilanoMilanoItalia
  2. 2.Sezione di MilanoINFNMilanoItaly
  3. 3.UdR Milano StataleCNISMMilanoItaly

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