Physics – Quantum Physics
Scientific paper
2010-09-11
Phys. Rev. A 83, 012105 (2011)
Physics
Quantum Physics
14pages, 2 figures (an analysis of an example is added, and the proof of Lemma 2 is corrected)
Scientific paper
10.1103/PhysRevA.83.012105
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.
Murao Mio
Sugiyama Takanori
Turner Peter S.
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