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arXiv:1304.1352 · Physical Review A

Reply to “Comment on ‘Optimal probe wave function of weak-value amplification’ ”

Yuki Susa, Yutaka Shikano, Akio Hosoya

Published Apr 12, 2013• 4 citations
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Abstract

It is pointed out that the ``counterexample'' presented in the Comment is a family of probe wave functions which are increasingly broad as the shift becomes large. Furthermore, the author's variational calculation is not correct in the sense that we have to gauge fix the freedom of the phase translation. It is shown that there are two kinds of solutions, normalizable and un-normalizable. The former is our optimal solution, and the latter is what he found. It seems only the former is relevant from a practical point of view.

DOI
10.1103/physreva.87.046102

Related papers

Comment on “Optimal probe wave function of weak-value amplification”

Antonio Di Lorenzo

First, a misconception about the spectrum of a confined particle is evidentiated. Then, the results are shown to be incorrect by means of a counter-example, an explicit preparation for the probe is given that yields an arbitrary amplification, and the source of the error is pointed out.

arXiv:1210.3274•Physical Review A•Apr 12, 2013•6 citations

Reply to comments on "Weak value amplification is suboptimal for estimation and detection"

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Kedem's Comment [arXiv:1402.1352] on our Letter [PRL 112, 040406 (2014)] contains only the criticism that we did not consider complex weak values. We point out follow-up work which uses the same analysis as in our Letter, includes any type of weak values and draws the same conclusion. Vaidman's Comment [arXiv:1402.0199] on our Letter can be deconstructed in to two distinct logical fallacies.

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This is the reply to [arXiv:1711.00764], in which the authors claim that there is crucial normalization error in PRL 116, 040502 (2016) and that some quantities appearing in the method of PRL 116, 040502 (2016) are not experimentally measurable. We show that the claim of [arXiv:1711.00764] is not correct and that the quantities appearing in PRL 116, 040502 (2016) can be measured.

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Optimal probe wave function of weak-value amplification

Yuki Susa, Yutaka Shikano, Akio Hosoya

The weak measurement proposed by Aharonov and his colleagues extracts information about a physical quantity of the system by the postselection as shifts of the argument of the probe wave function. The more the postselected state is orthogonal to the preselected state, the larger the shift determined by the weak value becomes. Recently, the signal amplification by the weak measurement has been extensively studied. In the present work, we explicitly obtain the optimal probe wave function and the amplification factor for a given weak value, which is calculated from the experimental setup. It is shown that the amplification factor has no upper bound, in contrast to the Gaussian probe wave function, and that the amplified signal is sharp.

arXiv:1203.0827•Physical Review A•May 11, 2012•63 citations

Reply to “Comment on ‘The variational principle and simple properties of the ground-state wave function,’ ” by S. K. Foong, D. Kiang, and Y. Nogami [Am. J. Phys. 71 (7), 731 (2003)]

Jordi Mur-Petit, A. Polls, Ferran Mazzanti

American Journal of Physics•Jun 11, 2003•2 citations

弱値増幅における最適プローブと統計的検定

友紀 須佐, Yuki Susa

Recently, the weak-value amplification (WVA) has been extensively investigated as a promising quantum technique for improving an accuracy of a precision measurement.The basic idea of WVA comes from the weak measurement introduced by Aharonov, Albert, and Vaidman in 1988.The weak measurement is the indirect quantum measurement with the weak interaction and postselection of the final state of the measured system.The attention point is that we can measure the quantity called the weak value, which appears in the shift of the measuring probe given by the weak measurement.Because the weak value can be outside the range of the eigenvalues, the shift of the measuring probe obtained by the weak measurement becomes larger than the one given by the conventional measurement.This shift amplification effect by the weak value is the WVA, which has been studied for precisely measuring the small coupling constant.In this thesis, we propose the two possible applications of the WVA.First, we analytically obtain the optimal probe wave function for a given weak value by the variational method.It is shown that the amplification factor obtained by the optimal probe has noupper bound while the one in the Gaussian probe already reported by some researchers has the upper bound.Furthermore, the variance of the optimal probe after the measurement can be zero.We can derive the optimal probe by the Lagrange multiplier method for maximizing the shift of the probe position or minimizing the variance of the final distribution.Second we have developed the way which has a technical advantage of the WVA from the viewpoint of statistics.It is often argued that the WVA is not helpfull for the parameter estimation.Therefore we consider the statistical inferences that the WVA will be advantageous.We propose a method to determine whether the interaction is present or not and evaluate the capability of the WVA for this interaction detection problem by using the hypothesis testing in statistics.As the main result, it is shown that the merit of the WVA is the reduction of the possibility to miss the presence of the interaction more than the conventional measurement while keeping the probability of a misdetection, when the absolute value of the weak value is outside the range of the eigenvalues.In this discussion, we assume that the number of the obtained data is infinitely large and we neglect the data loss by the failure of the postseleciton.iii the deepest appreciation to my ex-supervisor

•Mar 1, 2016•0 citations
It is pointed out that the ``counterexample'' presented in the Comment is a family of probe wave functions which are increasingly broad as the shift becomes large. Furthermore, the author's variational calculation is not correct in the sense that we have to gauge fix the freedom of the phase translation. It is shown that there are two kinds of solutions, normalizable and un-normalizable. The former is our optimal solution, and the latter is what he found. It seems only the former is relevant from a practical point of view.
The weak measurement proposed by Aharonov and his colleagues extracts information about a physical quantity of the system by the postselection as shifts of the argument of the probe wave function. The more the postselected state is orthogonal to the preselected state, the larger the shift determined by the weak value becomes. Recently, the signal amplification by the weak measurement has been extensively studied. In the present work, we explicitly obtain the optimal probe wave function and the amplification factor for a given weak value, which is calculated from the experimental setup. It is shown that the amplification factor has no upper bound, in contrast to the Gaussian probe wave function, and that the amplified signal is sharp.
Recently, the weak-value amplification (WVA) has been extensively investigated as a promising quantum technique for improving an accuracy of a precision measurement.The basic idea of WVA comes from the weak measurement introduced by Aharonov, Albert, and Vaidman in 1988.The weak measurement is the indirect quantum measurement with the weak interaction and postselection of the final state of the measured system.The attention point is that we can measure the quantity called the weak value, which appears in the shift of the measuring probe given by the weak measurement.Because the weak value can be outside the range of the eigenvalues, the shift of the measuring probe obtained by the weak measurement becomes larger than the one given by the conventional measurement.This shift amplification effect by the weak value is the WVA, which has been studied for precisely measuring the small coupling constant.In this thesis, we propose the two possible applications of the WVA.First, we analytically obtain the optimal probe wave function for a given weak value by the variational method.It is shown that the amplification factor obtained by the optimal probe has noupper bound while the one in the Gaussian probe already reported by some researchers has the upper bound.Furthermore, the variance of the optimal probe after the measurement can be zero.We can derive the optimal probe by the Lagrange multiplier method for maximizing the shift of the probe position or minimizing the variance of the final distribution.Second we have developed the way which has a technical advantage of the WVA from the viewpoint of statistics.It is often argued that the WVA is not helpfull for the parameter estimation.Therefore we consider the statistical inferences that the WVA will be advantageous.We propose a method to determine whether the interaction is present or not and evaluate the capability of the WVA for this interaction detection problem by using the hypothesis testing in statistics.As the main result, it is shown that the merit of the WVA is the reduction of the possibility to miss the presence of the interaction more than the conventional measurement while keeping the probability of a misdetection, when the absolute value of the weak value is outside the range of the eigenvalues.In this discussion, we assume that the number of the obtained data is infinitely large and we neglect the data loss by the failure of the postseleciton.iii the deepest appreciation to my ex-supervisor