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Results in Physics

Enhancing signal and signal-to-noise ratio with post-selection and nonclassical states

Meng-yao Guo, Jun‐Hao Liu, Ya-yei Yu, Zhi‐Ming Zhang

Published Oct 12, 2021• 3 citations
Publisher

Abstract

We propose a weak measurement scheme with post-selection based on the cross-Kerr interaction between two optical fields. We demonstrate that our scheme can measure smaller physical effects and obtain a larger signal-to-noise ratio compared to the weak measurement scheme without post-selection. We also show that the initial pointer states with nonclassical properties can increase the successful post-selection probability, offer a bigger signal-to-noise ratio compared to the coherent states.

DOI
10.1016/j.rinp.2021.104868

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We propose a weak measurement scheme with post-selection based on the cross-Kerr interaction between two optical fields. We demonstrate that our scheme can measure smaller physical effects and obtain a larger signal-to-noise ratio compared to the weak measurement scheme without post-selection. We also show that the initial pointer states with nonclassical properties can increase the successful post-selection probability, offer a bigger signal-to-noise ratio compared to the coherent states.
We investigate, within the weak measurement theory, the advantages of nonclassical pointer states over semiclassical ones for coherent, squeezed vacuum, and Schr\"odinger cat states. These states are utilized as pointer states for the system operator $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{A}$ with property ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{A}}^{2}=\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{I}$, where $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{I}$ represents the identity operator. We calculate the ratio between the signal-to-noise ratio of nonpostselected 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 nonclassical pointer states to be superior to semiclassical ones. This can improve the precision of the measurement process.
Postselected weak measurement is a useful protocol for amplifying 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-to-noise 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.
We study quantum measurement with preselection and postselection, and derive the precise expressions of the measurement results without any restriction on the coupling strength between the system and the measuring device. For a qubit system, we derive the maximum pointer shifts by choosing appropriate initial and finial states. A significant amplification effect is obtained when the interaction between the system and the measuring device is very weak, and typical ideal quantum measurement results are obtained when the interaction is strong. The improvement of the signal-to-noise ratio (SNR) and the enhancement of the measurement sensitivity (MS) by weak measurements are studied. Without considering the probability decrease due to postselection, the SNR and the MS can be both significantly improved by weak measurements; however, neither SNR nor MS can be effectively improved when the probability decrease is considered.
Abstract Post-selected measurement is used as a fundamental axiom in quantum optics. Here, a standard model of post-selected measurement with the input coherent pointer state is considered and the influence of weak value parameters on the quantum phase distribution function is studied on the basis of some analytical calculations. On the other hand, the effects of post-selected measurement on quantum phase fluctuations of the input coherent pointer states have been investigated, where the Barnett-Pegg formalism for the measured phase operators is assumed. It has been observed that the quantum phase fluctuations depend on some parameters such as the coupling strength, average value of input photon number, phase angle of the input coherent pointer state and two fundamental parameters of the complex weak value. Lastly, the presence of nonclassical effect is also checked for different parameters of quantum phase fluctuations.
We investigate how post-selected von Neumann measurements modify the nonclassical properties of two-mode entangled coherent states (ECSs). From the conditional pointer state, we characterize squeezing, photon statistics, intermode correlations, entanglement, fidelity, and post-selection probability. Anomalous weak values with moderate coupling enhance squeezing, antibunching, sub-Poissonian statistics, intermode correlations, and bipartite entanglement, while fidelity captures the crossover from weak perturbation to strong distinguishability. These results demonstrate post-selection as a tunable approach to engineering ECSs.
Through the von Neumann interaction followed by post-selection, we can extract not only the eigenvalue of an observable of the measured system but also the weak value. In this post-selected von Neumann measurement, the initial pointer state of the measuring device is assumed to be a fundamental Gaussian wave function. By considering the optical implementation of the post-selected von Neumann measurement, higher-order Gaussian modes can be used. In this paper, we consider the Hermite–Gaussian (HG) and Laguerre–Gaussian (LG) modes as pointer states and calculate the average shift of the pointer states of the post-selected von Neumann measurement by assuming the system observable with and for an arbitrary interaction strength, where represents the identity operator. Our results show that the HG and LG pointer states for a given coupling direction have advantages and disadvantages over the fundamental Gaussian mode in improving the signal-to-noise ratio. We expect that our general treatment of the weak values will be helpful for understanding the connection between weak- and strong-measurement regimes and may be used to propose new experimental setups with higher-order Gaussian beams to investigate further the applications of weak measurement in optical systems such as the optical vortex.