AI 中文总结
本研究提出一种群论多副本方法，利用混合量子态副本的光学变换与高斯幺正算符的对易关系构造非高斯性见证，可通过实验检测玻色系统的非高斯性并扩展至多模系统。
AI 中文摘要
高斯态是连续变量量子信息的基础，但由于高斯集合的非凸性，表征非高斯性仍具挑战性。现有见证通常依赖维格纳 negativity（负性）或其他信息论量。本研究开发了一种群论多副本方法以检测玻色系统中的非高斯性，研究混合量子态副本的无源线性光学变换，并分析其与应用于每个副本的相同高斯幺正算符的对易关系。正交副本混合变换与高斯作用的辛部分对易，而位移部分将对称性限制于集体模式的稳定子。该结构产生了一类所有单模高斯态都满足的见证，通过纯度确定热参考参数，这些恒等式的违反可证明非高斯性。我们用若干单模示例说明该方法，并提出基于无源干涉和光子数分辨探测的实验方案，表明相关多副本期望值可从有界相位可观测量估计。最后，我们将该构造扩展至多模系统，并讨论相同对称性框架如何产生非高斯性的定量度量。
英文摘要
Gaussian states are fundamental in continuous-variable quantum information, yet characterizing non-Gaussianity remains challenging due to the non-convexity of the Gaussian set. Existing witnesses typically rely on Wigner negativity or other information-theoretic quantities. In this work, we develop a group-theoretic, multi-copy approach to detect non-Gaussianity in bosonic systems. We study passive linear optical transformations that mix copies of a quantum state and analyze their commutation with identical Gaussian unitaries applied to each copy. Orthogonal copy-mixing transformations commute with the symplectic part of the Gaussian action, while the displacement part restricts the symmetry to the stabilizer of the collective mode. This structure yields a family of witnesses satisfied by all single-mode Gaussian states. Fixing the thermal reference parameter via the purity, violation of these identities certifies non-Gaussianity. We illustrate the method with several single-mode examples and present an experimental protocol based on passive interferometry and photon-number-resolved detection, showing that the relevant multi-copy expectation values can be estimated from bounded phase observables. Finally, we extend the construction to multi-mode systems and discuss how the same symmetry framework may lead to quantitative measures of non-Gaussianity.
