AI 中文总结
本文建立统一理论框架，从测地线偏差方程推导探测器哈密顿量，对比经典与量子引力波效应，证明量子引力波可诱导纠缠等非经典关联，为探测引力量子性提供途径。
AI 中文摘要
传播中的引力波能否作为引力量子本质的操作性探针？我们通过发展一个统一的理论框架来解决这一问题，该框架将时空几何、量子信息和引力波物理相结合。从线性化广义相对论中的测地线偏差方程出发，我们直接从时空几何推导出有效的探测器哈密顿量，并构建了探测器子系统与经典及量子化的传播引力波场相互作用时的完整量子动力学。这一统一表述使得我们能够在同一物理框架内直接比较引力辐射的经典描述与量子描述。我们证明，经典引力波背景可以诱导探测器态产生混合性，但无法在探测器子系统之间产生真正的量子关联。相反，量子化的引力波能够相干地介导引力诱导的纠缠、量子相干性、量子记忆和非经典关联，为传播引力辐射的量子本质提供了清晰的操作性特征。我们进一步讨论了介观量子力学振荡器如何为实验探测这些效应提供有前景的途径。我们的结果建立了一个基于几何和量子信息的框架，用于通过传播引力波探索量子引力。
英文摘要
Can propagating gravitational waves serve as operational probes of the quantum nature of gravity? We address this question by developing a unified theoretical framework that combines spacetime geometry, quantum information, and gravitational-wave physics. Starting from the geodesic deviation equation in linearized General Relativity, we derive the effective detector Hamiltonian directly from spacetime geometry and construct the complete quantum dynamics for detector subsystems interacting with both classical and quantized propagating gravitational-wave fields. This unified formulation enables a direct comparison between classical and quantum descriptions of gravitational radiation within the same physical framework. We demonstrate that classical gravitational-wave backgrounds can induce mixedness in the detector state but cannot generate genuine quantum correlations between the detector subsystems. In contrast, quantized gravitational waves coherently mediate gravity-induced entanglement, quantum coherence, quantum memory, and nonclassical correlations, providing clear operational signatures of the quantum nature of propagating gravitational radiation. We further discuss how mesoscopic quantum mechanical oscillators offer a promising route towards experimentally probing these effects. Our results establish a geometric and quantum-information-based framework for exploring quantum gravity through propagating gravitational waves.
CommentsProceedings of Quantum Universe 2025 (QU2025), Avellino, Italy, 27-31 October 2025. Submitted to the International Journal of Geometric Methods in Modern Physics (IJGMMP) for publication in the QU2025 Special Issue
