Physics – Quantum Physics
Scientific paper
2008-10-31
New J. Phys. 11 043034 (2009)
Physics
Quantum Physics
Scientific paper
10.1088/1367-2630/11/4/043034
For a unified analysis on the phase estimation, we focus on the limiting distribution. It is shown that the limiting distribution can be given by the absolute square of the Fourier transform of $L^2$ function whose support belongs to $[-1,1]$. Using this relation, we study the relation between the variance of the limiting distribution and its tail probability. As our result, we prove that the protocol minimizing the asymptotic variance does not minimize the tail probability. Depending on the width of interval, we derive the estimation protocol minimizing the tail probability out of a given interval. Such an optimal protocol is given by a prolate spheroidal wave function which often appears in wavelet or time-limited Fourier analysis. Also, the minimum confidence interval is derived with the framework of interval estimation that assures a given confidence coefficient.
Hayashi Masahito
Imai Hiroshi
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