Weak measurements beyond the Aharonov-Albert-Vaidman formalism

Wu, Shengjun; Li, Yang

doi:10.1103/physreva.83.052106

Cited by 87 publications

(65 citation statements)

References 26 publications

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“…Despite its simplicity, this model is sufficiently general in the sense that it covers the settings adopted in recent experiments of weak measurement [7,8]. We also note that the condition A 2 = Id, under which the previous works [9,11,12] performed a full order calculation of the shift, is in fact a special case of our setting ({λ 1 , λ 2 } = {−1, 1}). Identifying the usual position and momentum operators on L 2 (R) with Q =x and P =p, and using the shorthand, m := (λ 1 + λ 2 )/2 and r := (λ 2 − λ 1 )/2, we find…”

Section: Observable With Two-point Spectrummentioning

confidence: 99%

“…with r given by the survival rate (9). To each of these N outcomes, inequality (15) holds with the lower bound of the probability (22).…”

Section: Uncertainty Of Weak Measurementmentioning

confidence: 99%

“…This was addressed recently in [9], which extended the treatment of [10] to the full order of the coupling g between the system and the measurement device, where the amplification is analysed based on the average shift of the meter device. For a special case in which the observable A fulfils the condition A 2 = Id and the meter wave functions are assumed to be of Gaussian states, it has been shown that the amplification rate, as well as the signal-to-noise ratio, has an upper limit [11,12].…”

Section: Introductionmentioning

confidence: 99%

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Merit of amplification by weak measurement in view of measurement uncertainty

Lee¹,

Tsutsui²

2014

Quantum Stud.: Math. Found.

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Aharonov's weak value is a physical quantity obtainable by weak measurement, which admits amplification through state selections. The amplification is expected to be useful for precision measurement, but it is achieved at the expense of statistical deterioration due to the selections, which brings the question as to whether it can provide a truly superior means over the conventional measurement. We approach this problem by taking measurement uncertainty into account, and present a probabilistic evaluation of its impact to the final result of the measurement in weak measurement. By examining the significance condition for detecting the coupling g, we show that the trade-off relation between the amplification effect and the statistical deterioration does permit a finite range of usable amplification where the superiority is ensured. Apart from the Gaussian state models employed for demonstration, our argument is mathematically rigorous and general; it is free from approximation and valid for arbitrary observables A and couplings g.

show abstract

Section: Observable With Two-point Spectrummentioning

confidence: 99%

“…with r given by the survival rate (9). To each of these N outcomes, inequality (15) holds with the lower bound of the probability (22).…”

Section: Uncertainty Of Weak Measurementmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Merit of amplification by weak measurement in view of measurement uncertainty

Lee¹,

Tsutsui²

2014

Quantum Stud.: Math. Found.

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“…Thus it is worth pursuing the true behavior of the amplification factor in the full analysis. Recently, Wu and Li [14] extended the general formulation by Jozsa [7] and gave a formal power expansion analysis of the weak measurement. They also discussed its effect with a simple example.…”

mentioning

confidence: 99%

Limits on amplification by Aharonov-Albert-Vaidman weak measurement

Koike

Tanaka

2011

Phys. Rev. A

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We analyze the amplification by the Aharonov-Albert-Vaidman weak quantum measurement on a Sagnac interferometer [P. B. Dixon et al., Phys. Rev. Lett. 102, 173601 (2009)] up to all orders of the coupling strength between the measured system and the measuring device. The amplifier transforms a small tilt of a mirror into a large transverse displacement of the laser beam. The conventional analysis has shown that the measured value is proportional to the weak value, so that the amplification can be made arbitrarily large in the cost of decreasing output laser intensity. It is shown that the measured displacement and the amplification factor are in fact not proportional to the weak value and rather vanish in the limit of infinitesimal output intensity. We derive the optimal overlap of the pre-and post-selected states with which the amplification become maximum. We also show that the nonlinear effects begin to arise in the performed experiments so that any improvements in the experiment, typically with an amplification greater than 100, should require the nonlinear theory in translating the observed value to the original displacement.Introduction.-The standard theory of measurement in quantum mechanics deals with the situation that one performes a measurement on a quantum state to obtain a measured value and the resulting state according to certain probabilitic laws. It was established by von Neumann [1] in the case of projective measurements and generalized later to non-projective measurements [2][3][4]. In experiments as well as in theory, weak measurements, where the system is weakly coupled with, hence weakly disturbed by, the measuring device, have been widely considered and have proved to be useful.Aharonov, Albert, and Vaidman (AAV) [5] proposed a particular type of weak measurement which is characterized by the pre-and post-selection (PPS) of the system. One prepares the initial state |i of the system and that |Φ i of the device, and after a certain interaction between the system and the meter, one post-selects a state |f of the system and reads the meter value. If one measures an observable A of the system, one obtains the weak value

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“…The first works towards an understanding of the formal and mathematical aspects of the theory. Takingh = 1 , a derivation similar to the original one by Aharonov, Albert and Vaidman (AAV) [2]: f |e −igÂk |i |m ≈ f |i e −ig A wk |m ; A w = f |Â|i f |i (1) aforementioned approximations [5,6], and the full-order, exact evolution of the meter [7] all fall within the purview of Tsutsui's first category and have been the subject of many studies. Ref.…”

Section: Introductionmentioning

confidence: 99%

Seeing opportunity in every difficulty: protecting information with weak value techniques

Knee

Briggs

2018

Quantum Stud.: Math. Found.

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A weak value is an effective description of the influence of a pre and post-selected 'principal' system on another 'meter' system to which it is weakly coupled. Weak values can describe anomalously large deflections of the meter, and deflections in otherwise unperturbed variables: this motivates investigation of the potential benefits of the protocol in precision metrology. We present a visual interpretation of weak value experiments in phase space, enabling an evaluation of the effects of three types of detector noise as 'Fisher information efficiency' functions. These functions depend on the marginal distribution of the Wigner function of the 'meter', and give a unified view of the weak value protocol as a way of protecting Fisher information from detector imperfections. This approach explains why weak value techniques are more effective for avoiding detector saturation than for mitigating detector jitter or pixelation.

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Weak measurements beyond the Aharonov-Albert-Vaidman formalism

Cited by 87 publications

References 26 publications

Merit of amplification by weak measurement in view of measurement uncertainty

Merit of amplification by weak measurement in view of measurement uncertainty

Limits on amplification by Aharonov-Albert-Vaidman weak measurement

Seeing opportunity in every difficulty: protecting information with weak value techniques

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