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Chinese Physics B

Quantum Fisher Information of a Single-Photon Subtracted Squeezed Vacuum under Postselected von Neumann Measurement

Hunduz Halemjan, Chang Guohao, Shangyun Liu, Raziya Anwar, Ahmad Abliz, Akbar Islam

Published Apr 24, 2026• 0 citations
Publisher

Abstract

Abstract This paper mainly focuses on the optimization of the quantum Fisher information (QFI) for a single-photon subtracted squeezed vacuum (SPSSV) state within the framework of postselected von Neumann measurements. By utilizing the polarization and spatial degrees of freedom of the single-photon subtracted squeezed vacuum state as the measured system and the probe, respectively, the manipulation of the QFI is achieved via the probe state under standard postselected von Neumann measurement. The results demonstrate that a large QFI can invariably be obtained through the combinatory effects of the interaction strength and squeezing parameter, which characterizes the non-classical properties of the SPSSV state. The weak value is found to be crucial in increasing the QFI under weak interaction strength. Our findings clarify the weak-value amplification (WVA) effect on the QFI, thereby revealing the advantage of non-Gaussian states in information acquisition under postselected measurement. Meanwhile, this paper also presents the corresponding implementation scheme for optical experiments.

DOI
10.1088/1674-1056/ae6435

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Abstract This paper mainly focuses on the optimization of the quantum Fisher information (QFI) for a single-photon subtracted squeezed vacuum (SPSSV) state within the framework of postselected von Neumann measurements. By utilizing the polarization and spatial degrees of freedom of the single-photon subtracted squeezed vacuum state as the measured system and the probe, respectively, the manipulation of the QFI is achieved via the probe state under standard postselected von Neumann measurement. The results demonstrate that a large QFI can invariably be obtained through the combinatory effects of the interaction strength and squeezing parameter, which characterizes the non-classical properties of the SPSSV state. The weak value is found to be crucial in increasing the QFI under weak interaction strength. Our findings clarify the weak-value amplification (WVA) effect on the QFI, thereby revealing the advantage of non-Gaussian states in information acquisition under postselected measurement. Meanwhile, this paper also presents the corresponding implementation scheme for optical experiments.
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 address the precise characterization of coupling strength of nonlinear media in continuous-variable (CV) quantum systems using coherent and squeezed vacuum states as Gaussian probes, together with their photon-added and photon-subtracted counterparts as non-Gaussian probes. We consider three main classes of nonlinear Hamiltonians, namely quadrature nonlinearities, generalized squeezing and Kerr-type interactions. By analytically evaluating the quantum Fisher information (QFI), we compare the performance of Gaussian and non-Gaussian probes and assess the optimal probe based on the probe parameters, energy resource and non-Gaussianity. Our results are twofold as follows: first, for coherent-state family, the improvement provided by photon addition at fixed coherent amplitude originates mainly from the extra energy carried by the probe and does not provide a genuine metrological resource, since the same precision can be achieved by a Gaussian coherent-state signal of a larger energy, which can be more easily produced. Second, in contrast, photon addition and subtraction become effective resources when applied to already nonclassical states such as squeezed vacuum states. In this case, they lead to a significant enhancement of the QFI, particularly for higher-order interactions. Although Gaussian squeezed states remain optimal at equal energy constraint, photon-added and photon-subtracted squeezed states achieve comparable sensitives with significantly lower squeezing requirements. Since large squeezing level remains experimentally challenging, these non-Gaussian probes offer a practical route towards enhanced estimation of the nonlinear coupling strength within currently accessible squeezing regimes.
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.
The weak-value-amplification (WVA) technique has been extensively considered and debated in the field of quantum precision measurement, largely owing to the reduced Fisher information caused by the low probability of successful postselection. In this work we show that, rather than the transverse-spatial-wave-function meter typically considered, using the optical coherent state as a meter, the WVA measurement can outperform the conventional measurement not involving the strategy of postselection. We also show that the postselection procedure involved in the WVA scheme can make a mixture of coherent states work better than a pure coherent state with identical average photon numbers. This is in contrast to the main result proved in the absence of postselection. The postselection strategy can also result in the precision of Heisenberg scaling with the photon numbers without using expensive quantum resources. The present work may stimulate further interest in postselection strategy for quantum precision measurements.