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arXiv:2511.14079

Enhancing Non-classical Properties of Entangled Coherent States via Post-Selected von Neumann Measurements

Janarbek Yuanbek, Bruno Tenorio

quant-phSubmitted Nov 18, 2025• Announced Nov 19, 2025• 0 citations• Revised Dec 1, 2025 (v2)

v1 · Nov 18, 2025 v2 · Dec 1, 2025 v3 · Apr 19, 2026

Abstract

The present study systematically investigates the modulation mechanism of post-selected weak measurement (WM) on the non-classical properties of entangled coherent states (ECSs). The primary goal is achieving controllable enhancement of quantum resources such as entanglement and squeezing, while minimising disturbance to the quantum state. We theoretically analyze the post-selected weak measurement process, and its effectiveness in amplifying the non-classical features of ECSs. The von Neumann measurement model is employed to analytically describe the weak-value amplification of the pointer state. It is demonstrated that a significant enhancement of squeezing can be achieved by tuning the measurement coupling strength. The joint Wigner function analysis in phase space further reveals that, as the coupling strength increases, the coherent structure of the state evolves from symmetric double peaks to multi-branch quantum interference fringes. The entanglement, quantified by the Hillery-Zubairy criterion, exhibits a pronounced increase with stronger coupling, while the quantum Fisher information indicates a systematic improvement in phase estimation precision. The results obtained establish a tunable weak measurement framework for precise manipulation of continuous-variable entangled states. This provides a feasible theoretical pathway for enhancing quantum metrology and measurement-based state engineering.

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The present study systematically investigates the modulation mechanism of post-selected weak measurement (WM) on the non-classical properties of entangled coherent states (ECSs). The primary goal is achieving controllable enhancement of quantum resources such as entanglement and squeezing, while minimising disturbance to the quantum state. We theoretically analyze the post-selected weak measurement process, and its effectiveness in amplifying the non-classical features of ECSs. The von Neumann measurement model is employed to analytically describe the weak-value amplification of the pointer state. It is demonstrated that a significant enhancement of squeezing can be achieved by tuning the measurement coupling strength. The joint Wigner function analysis in phase space further reveals that, as the coupling strength increases, the coherent structure of the state evolves from symmetric double peaks to multi-branch quantum interference fringes. The entanglement, quantified by the Hillery-Zubairy criterion, exhibits a pronounced increase with stronger coupling, while the quantum Fisher information indicates a systematic improvement in phase estimation precision. The results obtained establish a tunable weak measurement framework for precise manipulation of continuous-variable entangled states. This provides a feasible theoretical pathway for enhancing quantum metrology and measurement-based state engineering.

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.

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.

The quantum Fisher information and quantum correlation parameters are employed to study the application of nonclassical light to the problem of parameter estimation. It is shown that the optimal measurement sensitivity of a quantum state is determined by its intermode correlations (which depends on path entanglement) and intramode correlations (which depends on the photon statistics). In light of these results, we consider the performance of quantum-enhanced optical interferometers. Furthermore, we propose a Heisenberg-limited metrology protocol involving standard elements from passive and active linear optics, for which the quantum Cram\'er-Rao bound is saturated with an intensity measurement. Interestingly, the quantum advantage for this scheme is derived solely from the nonclassical photon statistics of the probe state and does not depend on entanglement. We study the performance of this scheme in the presence of realistic losses and consequently predict a substantial enhancement over the shot-noise limit with current technological capabilities.

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.

We explore optical quantum engineering of phase-parameterized continuous-variable (CV) probe states to exploit nonclassical light to solve the problem of precise phase estimation. The optical interferometer consists of a single beam splitter (BS) with tunable transmittance and reflectance, and two single-mode squeezed vacuum states (SMSVs). The reference SMSV state is mixed with a weakly squeezed state carrying an unknown phase at the beam splitter to form an output hybrid entangled state. Then, in the measurement mode, the number of photons is measured to generate the target CV state parameterized by the unknown phase. Using the CV states, we propose a sub-Heisenberg metrology protocol in which the quantum Cramer-Rao (QCR) boundary is saturated by intensity measurement. The advantage of quantum engineering of CV probe states for ultra-precise phase estimation of unknown phase is due solely to the nonclassical photonic properties of the measurement induced CV states of definite parity and is independent of the mode entanglement.

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.