On quantum statistical inference. (English summary) With discussion and reply by the authors. J. R. Stat. Soc. Ser. B Stat. Methodol. 65 (2003), no. 4, 775–816. This is an excellent survey article on developments in the subject of statistical inference connected to measurements of quantum systems. Firstly there is a good introduction to quantum statistical models and notions of quantum score and quantum information and also there is a general discussion of the relationship between classical and quantum probability and statistics. Discussed in more detail are: (i) two classes of parametric models, the quantum exponential and quantum transformation models; (ii) quantum analogues of some ideas of classical statistical inference, such as sufficiency and the likelihood principle; (iii) quantum analogues of Fisher information. Comments on the paper by several experts are also included and this makes the paper even more interesting for probabilists and statisticians. This review paper is timely and it will be very useful for researchers in the field of “quantum information”
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