Error probability analysis in quantum tomography: a tool for evaluating experiments

Takanori Sugiyama, Peter S. Turner, Mio Murao

Research output: Contribution to journalArticle (Academic Journal)peer-review

10 Citations (Scopus)


We expand the scope of the statistical notion of error probability, i.e., how often large deviations are observed in an experiment, in order to make it directly applicable to quantum tomography. We verify that the error probability can decrease at most exponentially in the number of trials, derive the explicit rate that bounds this decrease, and show that a maximum likelihood estimator achieves this bound. We also show that the statistical notion of identifiability coincides with the tomographic notion of informational completeness. Our result implies that two quantum tomographic apparatuses that have the same risk function, (e.g. variance), can have different error probability, and we give an example in one qubit state tomography. Thus by combining these two approaches we can evaluate, in a reconstruction independent way, the performance of such experiments more discerningly.
Original languageEnglish
JournalPhysical Review A: Atomic, Molecular and Optical Physics
Publication statusPublished - 2011

Bibliographical note

14pages, 2 figures (an analysis of an example is added, and the proof of Lemma 2 is corrected)


  • quant-ph
  • math.ST
  • stat.TH


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