Quantum measurements with preselection and postselection

Zhu, Xuanmin; Zhang, Yu-Xiang; Pang, Shengshi; Qiao, Chang; Liu, Quanhui; Wu, Shengjun

doi:10.1103/physreva.84.052111

Cited by 103 publications

(118 citation statements)

References 33 publications

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“…This generalizes the results of [59,60], and suggests that "classical" pointer states are not able to improve the SNR of postselected weak measurements.…”

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confidence: 55%

Improving the Precision of Weak Measurements by Postselection Measurement

2015

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Postselected weak measurement is a useful protocol to amplify weak physical effects. However, there has recently been controversy over whether it gives any advantage in precision. While it is now clear that retaining failed postselections can yield more Fisher information than discarding them, the advantage of postselection measurement itself still remains to be clarified. In this Letter, we address this problem by studying two widely used estimation strategies: averaging measurement results, and maximum likelihood estimation, respectively. For the first strategy, we find a surprising result that squeezed coherent states of the pointer can give postselected weak measurements a higher signal-tonoise ratio than standard ones while all standard coherent states cannot, which suggests that raising the precision of weak measurements by postselection calls for the presence of "nonclassicality" in the pointer states. For the second strategy, we show that the quantum Fisher information of postselected weak measurements is generally larger than that of standard weak measurements, even without using the failed postselection events, but the gap can be closed with a proper choice of system state. . It involves weak coupling between the system and the pointer, but the postselection on the system leads to a surprisingly counterintuitive effect: the average shift of the final pointer state can go far beyond the eigenvalue spectrum of the system observable (multiplied by the coupling constant), in sharp contrast to the projective quantum measurement. The mechanism behind this effect is the coherence between the pointer states translated by different eigenvalues of the system observable, which has an enlightening interpretation based on superoscillation [2].

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“…This generalizes the results of [59,60], and suggests that "classical" pointer states are not able to improve the SNR of postselected weak measurements.…”

supporting

confidence: 55%

Improving the Precision of Weak Measurements by Postselection Measurement

2015

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“…However, the amplification is saturated in an intermediate regime and rapidly drops in a strong measurement regime (s ≥ 1). This behavior results from a nonlinear aspect of the WVA [16][17][18][19]. Note that the maximum value of the frequency shift is larger as θ increases.…”

Section: B Evaluationmentioning

confidence: 96%

“…If the outcome of the measurement is exactly this weak value, it seems that we have an arbitrarily large outcome when the pre-and post-selections are nearly orthogonal [15]. However, when the weak value becomes large, non-linear effects of the von-Neumann measurement affect the outcome of the measurement [16][17][18][19]. As the result, the shift of the pointer variable has a maximum value and vanishes when the pre-and post-selected * Electronic address: anishi@yukawa.kyoto-u.ac.jp states are exactly orthogonal.…”

Section: Introductionmentioning

confidence: 99%

Weak-value amplification in a shot-noise-limited interferometer

2012

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We study the weak-value amplification (WVA) in a phase measurement with an optical interferometer in which shot noise limits the sensitivity. We compute the signal and the shot noise including the full-order interaction terms of the WVA, and show that the shot-noise contribution to a phase shift in a pointer variable is always larger than the final variance of the pointer variable. This yields difference in estimating noise level up to a factor of 1.5. To clarify an advantage for practical uses of the WVA, we discuss signal-to-noise ratio and its optimization in the presence of the shot noise.

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“…However, recent studies [44,45] have shown that zero-mean Gaussian pointer state cannot improve the SNR when considering postselection probability. Needless to say Gaussian beam is classical and one may naturally ask how about using non-classical pointer states, and what kind of advantages they have?…”

Section: Introductionmentioning

confidence: 99%

Advantages of nonclassical pointer states in postselected weak measurements

et al. 2015

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We investigate, within the weak measurement theory, the advantages of non-classical pointer states over semi-classical ones for coherent, squeezed vacuum, and Schröinger cat states. These states are utilized as pointer state for the system operatorÂ with propertyÂ 2 =Î, whereÎ represents the identity operator. We calculate the ratio between the signal-to-noise ratio (SNR) of non-postselected and postselected weak measurements. The latter is used to find the quantum Fisher information for the above pointer states. The average shifts for those pointer states with arbitrary interaction strength are investigated in detail. One key result is that we find the postselected weak measurement scheme for non-classical pointer states to be superior to semi-classical ones. This can improve the precision of measurement process.

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Quantum measurements with preselection and postselection

Cited by 103 publications

References 33 publications

Improving the Precision of Weak Measurements by Postselection Measurement

Improving the Precision of Weak Measurements by Postselection Measurement

Weak-value amplification in a shot-noise-limited interferometer

Advantages of nonclassical pointer states in postselected weak measurements

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