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arXiv:2411.14210 · Physical Review A

Postselected von Neumann measurement with superpositions of orbital angular momentum pointer states

Janarbek Yuanbek, Yi-Fang Ren, Yusuf Turek

Published Jun 9, 2025• 1 citation
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Abstract

We investigated an orbital angular momentum (OAM) pointer within the framework of von Neumann measurements and discovered its significant impact on optimizing superpositions of Gaussian and Laguerre-Gaussian (LG) states. Calculations of the quadrature squeezing, the second-order cross-correlation function, the Wigner function, and the signal-to-noise ratio (SNR) support our findings. Specifically, by carefully selecting the anomalous weak value and the coupling strength between the measured system and the pointer, we demonstrated that the initial Gaussian state transforms into a non-Gaussian state after postselection. This transition highlights the potential of OAM pointers in enhancing the performance of quantum systems by tailoring state properties for specific applications.

DOI
10.1103/tnvf-nrq4

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We investigated an orbital angular momentum (OAM) pointer within the framework of von Neumann measurements and discovered its significant impact on optimizing superpositions of Gaussian and Laguerre-Gaussian (LG) states. Calculations of the quadrature squeezing, the second-order cross-correlation function, the Wigner function, and the signal-to-noise ratio (SNR) support our findings. Specifically, by carefully selecting the anomalous weak value and the coupling strength between the measured system and the pointer, we demonstrated that the initial Gaussian state transforms into a non-Gaussian state after postselection. This transition highlights the potential of OAM pointers in enhancing the performance of quantum systems by tailoring state properties for specific applications.
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.
We investigate the effects of postselected von Neumann measurements on the nonclassical properties of pair coherent states (PCS). We calculated key quantum characteristics, such as squeezing, photon statistics, entanglement between the two modes of PCS, and teleportation fidelity. Our results demonstrate that postselected von Neumann measurements enhance both the non-Gaussianity and nonclassicality of PCS. These findings are validated by analyzing the scaled joint Wigner function across various system parameters. We also notice that in weak measurement regimes, the teleportation fidelity via a PCS-based quantum channel under postselected von Neumann measurements could maintain successful teleportation for anomalous weak values of the measured system observable. The theoretical optimization scheme offers an alternative approach for improving PCS-based quantum information efficiency and facilitates practical implementations in quantum technologies.
Postselected von Neumann measurement characterized by postselection and weak value has been found to possess potential applications in quantum metrology and solved plenty of fundamental problems in quantum theory. As an application of this new measurement technique in quantum optics and quantum information processing, its effects on the features of single-mode radiation fields such as coherent state, squeezed vacuum state and Schrödinger cat sate are investigated by considering full-order effects of unitary evolution. The results show that the conditional probabilities of finding photons, second-order correlation functions, Qm -factors and squeezing effects of those states after the postselected measurement is significantly changed are comparable with the corresponding initial pointer states.
We investigate the effects of weak value amplification on the nonclassical properties of the two-mode squeezed vacuum state. We calculate the quadrature squeezing and second-order cross-correlation functions to demonstrate the advantages of postselective weak measurement (WM). We also examine the entanglement between the two modes by evaluating various entanglement criteria, including the Cauchy-Schwartz inequality, Hillery-Zubairy correlation, and Einstein-Podolsky-Rosen correlations. Our results show that postselected von Neumann measurements significantly optimize the two-mode squeezed vacuum state. Notably, the amplification effect of weak values plays a critical role in this process. We demonstrated that in the WM regime, as the weak values increase, the nonclassical properties of the two-mode squeezed vacuum state such as entanglement and correlations between the two modes become more pronounced compared to the original state. We also propose possible implementation methods for our approach using trapped ion systems and optical platforms. Our enhanced two-mode squeezed vacuum state may have potential applications in quantum information processing scenarios, such as single-photon generation, advanced imaging techniques, quantum computation, and long-distance quantum communication.
In this paper, ordinary and amplitude-squared squeezing as well as Wigner functions of single-photon-added coherent state after postselected von Neumann measurements are investigated. The analytical results show that the weak measurement procedure, which is characterized by postselection and weak value, can significantly change the principal squeezing feature of the single-photon-added coherent state. From the analysis of the Winger function we notice that in the strong measurement regime significant interference structures manifest and the negative regions become larger than the initial pointer state. Our results indicate that after postselected von Neumann measurement the degree of nonclassicality of single-photon-added coherent state is increased. It is anticipated that this work may provide alternate and effective methods for solving the state optimization problems based on the single-photon-added coherent state pointer via a postselected von Neumann measurement technique.
We investigate the effects of postselected von Neumann measurements on the nonclassical properties of pair coherent states (PCS). We calculated key quantum characteristics, such as squeezing, photon statistics, and entanglement between the two PCS modes. Our results demonstrate that postselected von Neumann measurements enhance both the non-Gaussianity and nonclassicality of PCS. These findings are validated by analyzing the scaled joint Wigner function across various system parameters. The theoretical optimization scheme offers an alternative approach for improving PCS-based quantum information efficiency and facilitates practical implementations in quantum technologies.