Non-Gaussian Quantum State Engineering with Postselected von Neumann Measurements

TL;DR

This work develops a protocol for non-Gaussian state engineering via postselected von Neumann measurements with a two-level system coupled to a Gaussian pointer satisfying $A^{2}=\mathbb{I}$, without restricting to weak coupling. By varying pointer inputs (e.g., $|\alpha,\xi\rangle$, $|\alpha\rangle$, or $|0\rangle$) and the postselection-augmented weak value $\langle A\rangle_{w}$, the method generates a broad family of single- and two-mode non-Gaussian states, including squeezed cat, two-mode entangled cat, and Bell-like states, with tunable amplitudes and high success probabilities. Non-Gaussianity is characterized through Wigner function negativity, while entanglement is quantified by linear entropy and concurrence, showing enhanced correlations beyond standard Gaussian resources. The approach promises scalable, high-purity non-Gaussian state preparation applicable to CV quantum information tasks and experimental implementations across photonic and atom-optical platforms.

Abstract

We introduce a feasible protocol for generating non-Gaussian (nG) states via postselected von Neumann measurement for continuous-variable quantum information processing. The method uses a two-level system coupled to a Gaussian pointer state through an observable $A$ with $A^{2}=\mathbb{I}$. By operating beyond the weak-coupling regime and selecting different pointer states -- squeezed, coherent, or vacuum -- allows generation of a wide range of nG states, including squeezed cat states, two-mode entangled cat states, approximate Bell states, and a continuum of intermediate nG states with considerable success probabilities. The properties of these states are widely tunable via the postselection-induced weak value and the measurement interaction strength. We characterize the non-Gaussianity via Wigner function negativities and quantify entanglement using linear entropy and concurrence. The protocol offers a scalable route to high-purity nG state engineering.

Figures (9)

• Figure 1: Schematic diagram of nG state generation via postselected von Neumann measurement. The pre-selected measured system state and pointer evolved under interaction coupling and followed by post-selection implemented on measured system. The output state $\vert\Phi\rangle$ is generated with definite probability.
• Figure 2: The Wigner function of the output state $\vert\Psi_{2}\rangle$ for different system parameters. (a) for input state $\vert\xi\rangle$; (b) for $\langle A\rangle_{w}=0$; (c) for $\langle A\rangle_{w}=10$; (d) for $\langle A\rangle_{w}=0.5$. Other parameters are taken as $s=1.5$, $r=1$, and $\phi=0$.
• Figure 3: The success probability of the output state $\vert\Psi_{2}\rangle$ as a function of the weak value parameter $\theta$ for different interaction strength parameters $s$. Here, we take $r=0.5$$\delta=0$, and $\phi=0$.
• Figure 4: The Wigner function of $\vert\Psi_{3}\rangle$ for different weak values. (a) for initial input coherent state; (b) for $\langle A\rangle_{w}=0$; (c) for $\langle A\rangle_{w}=10$ and (d) for $\langle A\rangle_{w}=-i$. Here, we take $\vert\alpha\vert=1$, $\vartheta=0$ and $s=1.5$.
• Figure 5: The success probability of postselection of the final pointer state $\vert\Psi_{4}\rangle$ as a function of weak value parameter $\theta$ for different interaction coupling strength $s$. Here, we take $\delta=0$.