Fourier Analytic Approach to Phase Estimation

Abstract

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.

References in corpus (18)

• Quantum-enhanced measurements: beating the standard quantum limit
• Quantum metrology
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• Comparison between the Cramer-Rao and the mini-max approaches in quantum channel estimation
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• Rapid initial state preparation for the quantum simulation of strongly correlated molecules
• Multiple-phase quantum interferometry -- real and apparent gains of measuring all the phases simultaneously
• Multiparameter quantum metrology in the Heisenberg Limit regime: many repetition scenario vs. full optimization
• Phase estimation with photon number constraint
• Global Heisenberg scaling in noisy and practical phase estimation
• Quantum metrology in the finite-sample regime
• Unitary-process discrimination with error margin
• Fourier Analytic Approach to Quantum Estimation of Group Action
• A protocol for global multiphase estimation
• Adaptive identification of coherent states
• Quantum phase estimation based filtering: performance analysis and application to low-energy spectral calculation
• Indefinite causal order strategy does not improve the estimation of group action
• Heisenberg scaling based on population coding
• Quantum phase estimation with optimal confidence interval using three control qubits
• The Cramér-Rao approach and global quantum estimation of bosonic states