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arXiv:2011.07560 · Physical review. D/Physical review. D.

Weak value amplification in high energy physics: A case study for precision measurement of CP violation in B meson decays

S. Higashino, Yuichiro Mori, Y. Takubo, T. Higuchi, A. Ishikawa, Izumi Tsutsui

Published Aug 9, 2021• 2 citations
arXivHTMLPDF

Abstract

The technique of weak value amplification, proposed by Aharonov et al. in 1988, has been applied for various fields of physics for the purpose of precision measurement, which is made possible by exploiting the freedom of ``postselection'' specifying actively the final state in the physical process. Here we report the feasibility of utilizing the technique of weak value amplification in high-energy particle physics, especially in measuring the $CP$-violating parameters in $B$ meson decays, where the effective lifetime of the decay mode is expected to be prolonged statistically due to the postselection. Our analysis shows that, when adopted in the Belle II experiment at the SuperKEKB collider, the effective lifetime may be prolonged up to 2.6 times, and that the measurement precision of the $CP$-violating parameters will also be improved by its effect.

DOI
10.1103/physrevd.104.033001

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弱値増幅における最適プローブと統計的検定

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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

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精密測定への弱値増幅の応用可能性について

Yuichiro Mori

The novel notion of a physical quantity called 'weak value', which was proposed by Aharonov et al. in 1988, has attracted much attention in the fields of quantum foundations and quantum measurement.In particular, the fact that through proper state selections the weak value can be made arbitrarily large, exceeding the conventional bound set by the maximum eigenvalue of the physical observable, has been widely regarded as a promising source for precision measurement.Indeed, in recent years we have seen increasingly many reports of successful applications of the weak value in photonic systems with various instances of observables amplified effectively.However, it has also been recognized that there are two major obstacles in realizing this weak value amplification (WVA).First, it is unclear under what conditions the WVA becomes effective due to the conflict between the ambiguity caused by the state selections and the amplification effect.Second, the required state selections may not be available depending on the systems one is dealing with.In order to expand the applicability of the WVA, one must solve these problems properly.In this dissertation, we first review the basics of precision measurement and the WVA and then present our method of evaluation for the WVA considering the measurement uncertainty including the ambiguity of the WVA.We applied our method of evaluation for the two celebrated experiments to confirm the basic validity of the results of the two experiments.In addition, as a new application of the WVA, we consider the time evolution of unstable particles to find that the decay time distribution is generally characterized by the weak value of the Hamiltonian and that the state selections can indeed be performed by measuring the particles produced during the decay.Our result indicates that the WVA may also be applicable to the system of unstable particles.

•Mar 19, 2021•0 citations
The technique of weak value amplification, proposed by Aharonov et al. in 1988, has been applied for various fields of physics for the purpose of precision measurement, which is made possible by exploiting the freedom of ``postselection'' specifying actively the final state in the physical process. Here we report the feasibility of utilizing the technique of weak value amplification in high-energy particle physics, especially in measuring the CPCPCP-violating parameters in BBB meson decays, where the effective lifetime of the decay mode is expected to be prolonged statistically due to the postselection. Our analysis shows that, when adopted in the Belle II experiment at the SuperKEKB collider, the effective lifetime may be prolonged up to 2.6 times, and that the measurement precision of the CPCPCP-violating parameters will also be improved by its effect.
Novel Approach to Measuring CPCPCP Violation in BBB Meson Decays: A Case Study of Weak Measurement in High Energy Physics
The weak measurement, proposed by Aharonov {\it et al.} in 1988, has been applied for various fields of physics for the purpose of precision measurement, which is made possible with the help of the 'postselection' specifying actively the final state in the physical process. Here we report for the first time the feasibility of applying the weak measurement in high energy particle physics, especially in measuring the CPCPCP-violating parameters in BBB meson decays, where the effective lifetime of the decay mode is expected to be prolonged statistically due to the postselection. Our analysis shows that, when adopted in the Belle II experiment at the SuperKEKB collider, the effective lifetime may be prolonged up to 2.62.62.6 times, and that the measurement precision of the CPCPCP-violating parameters will be improved by about 20\%.
We study the possibility of varying the measured lifetime of a decaying particle based on the technique of weak value amplification in which an additional filtering process called postselection is performed. Our analysis made in a direct measurement scheme presented here shows that, for simple two-level systems, the lifetime may be prolonged more than three times compared to the original one, while it can also be shortened arbitrarily by a proper choice of postselection. This result is consistent with our previous analysis on the possible prolongation of the lifetime of BBB mesons that may be observed in laboratories, and suggests room for novel applications of weak-value amplification beyond precision measurement conventionally considered.
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
Abstract We present a general framework of examining the validity of weak measurement—the standard procedure to acquire Aharonov’s weak value—which has been used intensively in recent years for precision measurement, exploiting the amplification mechanism available for the weak value. Our framework allows one to deal systematically with various causes of uncertainties intrinsic to the actual measurement process as well as those found in the theoretical analysis employed to describe the system. Using our framework, we examine in detail the two seminal experiments, Hosten’s detection measurement of the spin Hall effect of light [Hosten and Kwiat 2008 Science 319 787] and Dixon’s ultra sensitive beam deflection measurement [Dixon et al 2009 Phys. Rev. Lett. 102 173601]. Our analysis shows that their results are well within the range of amplification (actually in the vicinity of the optimal point) where the weak measurements are valid. This suggests that our framework is both practical and sound, and may be useful to determine beforehand the possible extent of amplification in the future weak measurement experiments.
The weak-value amplification is extensively considered in precision metrology in order to achieve a higher sensitivity. Despite the practical benefits in amplifying small physical quantities, its metrological advantage still arouses a broad debate due to the low postselection probability of success. In this paper, by employing the quantum Fisher information metric, we show that the precision of estimating an unknown parameter can be improved by introducing a precoupling process with properly chosen interaction operators. We point out this result is credible for both real and imaginary weak values. By tracking the meter wave functions, we find this enhancement of estimation precision comes from a precoupling induced modulation of the meter wave function, thus the most sensitive regime with respect to the parameter is reached. In addition, the estimation error is investigated by considering the difference between the theoretical and estimated value. The analysis suggests that this kind of error can be effectively suppressed by averaging the estimations resulted from different initial meter states. These results are finally illustrated by an exact numerical simulation where the advantages of our proposal are displayed by the comparison to the standard weak-value amplification scheme.
The novel notion of a physical quantity called 'weak value', which was proposed by Aharonov et al. in 1988, has attracted much attention in the fields of quantum foundations and quantum measurement.In particular, the fact that through proper state selections the weak value can be made arbitrarily large, exceeding the conventional bound set by the maximum eigenvalue of the physical observable, has been widely regarded as a promising source for precision measurement.Indeed, in recent years we have seen increasingly many reports of successful applications of the weak value in photonic systems with various instances of observables amplified effectively.However, it has also been recognized that there are two major obstacles in realizing this weak value amplification (WVA).First, it is unclear under what conditions the WVA becomes effective due to the conflict between the ambiguity caused by the state selections and the amplification effect.Second, the required state selections may not be available depending on the systems one is dealing with.In order to expand the applicability of the WVA, one must solve these problems properly.In this dissertation, we first review the basics of precision measurement and the WVA and then present our method of evaluation for the WVA considering the measurement uncertainty including the ambiguity of the WVA.We applied our method of evaluation for the two celebrated experiments to confirm the basic validity of the results of the two experiments.In addition, as a new application of the WVA, we consider the time evolution of unstable particles to find that the decay time distribution is generally characterized by the weak value of the Hamiltonian and that the state selections can indeed be performed by measuring the particles produced during the decay.Our result indicates that the WVA may also be applicable to the system of unstable particles.