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Scattering-Induced Spin Entanglement and Phase-Space Non-Classicality Driven by Coherent State Superpositions

Sepide Soltani, Ali Mahdifar, Ebrahim Ghanbari-Adivi

Published Sep 1, 2026• 0 citations

Abstract

Abstract The generation of quantum entanglement through scattering processes is a fundamental mechanism in quantum information science. In this work, we investigate how coherent-state superpositions, represented as spatial Gaussian wave-packet superpositions, modify nonclassical phase-space features and enhance entanglement production during the scattering of a single particle from a localized spin impurity governed by a Heisenberg-type interaction. We construct even and odd superpositions of coherent states and analyze their time evolution using Fourier-space propagation. The corresponding Wigner distributions are computed analytically, revealing os-cillatory interference fringes and negative-valued regions that quantify nonclassicality. Using the nonclassical volume as a metric, we show that increasing the spatial separation between the Gaussian components enhances nonclassicality, eventually saturating at a stable asymptotic maximum. By incorporating these superposed states as incident wave packets, we compute the post-scattering spin entanglement between the reflected particle and the impurity using the negativity measure. Our results demonstrate that the symmetry of the initial coherent-state superposition fundamentally governs the stability of the generated entanglement: while the even superposition exhibits parameter-sensitive, oscillatory entanglement as the wave-packet separation increases, the odd superpo-sition yields a robust, decay-resistant entanglement plateau across all separation scales. These findings highlight the critical role of engineered nonclassical initial states in optimizing scattering-based quantum technologies

DOI: 10.21203/rs.3.rs-10341807/v1

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Within a plane-wave approximation in scattering, an incoming wave packet's Wigner function stays positive everywhere, which obscures such purely quantum phenomena as nonlocality and entanglement. With the advent of the electron microscopes with subnanometer-sized beams, one can enter a genuinely quantum regime where the latter effects become only moderately attenuated. Here we show how to probe negative values of the Wigner function in scattering of a coherent superposition of two Gaussian packets with a nonvanishing impact parameter between them (a Schrödinger's cat state) by atomic targets. For hydrogen in the ground 1s state, a small parameter of the problem, a ratio a/σ_{⊥} of the Bohr radius a to the beam width σ_{⊥}, is no longer vanishing. We predict an azimuthal asymmetry of the scattered electrons, which is found to be up to 10%, and argue that it can be reliably detected. The production of beams with the not-everywhere-positive Wigner functions and the probing of such quantum effects can open new perspectives for noninvasive electron microscopy, quantum tomography, particle physics, and so forth.

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Glauber's coherent state is denoted by

\ketα

and its two-mode extension is represented by

\ket{α,β}

. In this work, we introduce a two-mode superposition operator

A=tab+ra^\dagger b^\dagger

, whose action on the two-mode coherent state produces the two-mode coherent superposed quantum state

\ketψ=(tab+ra^\dagger b^\dagger)\ket{α,β}

. We investigate the nonclassicality and quantum non-Gaussianity of this state by means of the Wigner distribution and Wigner logarithmic negativity. Once its intrinsic nonclassical and non-Gaussian structure is established, the state is employed as the entangled resource in the Braunstein-Kimble continuous-variable (CV) teleportation protocol. We compute the ideal teleportation fidelity for coherent and squeezed inputs and analyze how the strengths of nonclassicality and non-Gaussianity influence the teleportation efficiency. Our results identify specific parameter regimes where enhanced non-Gaussian features or increased nonclassicality enable fidelities beyond the classical threshold, thereby revealing the operational significance of engineered two-mode quantum states in CV quantum information processing.

The controlled generation of quantum entanglement from separable states remains a central challenge in quantum information science. Here, we investigate entanglement generation using two related control paradigms: coherent path superposition of local unitary operations and stochastic implementations of Pauli channels under coherent control. We show that entangled states belonging to the Bell, GHZ and W classes, can be deterministically generated from fully separable inputs by coherently superposing alternative sets of local unitary transformations. Conditions on the local operators for entanglement generation are derived, and the resulting states are shown to be locally unitary equivalent to standard multipartite entangled states. We further extend the analysis to noisy scenarios, where separable mixed states evolve through pairs of Pauli channels arranged in path-superposition and indefinite causal order configurations. Closed-form expressions for the output states are obtained, and entanglement is quantified using concurrence. By exploring representative channel families across their parameter space, we identify regimes where stochastic entanglement emerges, determine the associated success probabilities, and characterize trade-offs between entanglement and purity.