发表机构
CWI; QuSoft; University of Leiden; Department of Computer Science, University of Warwick; LMU Munich; MCQST; University of Amsterdam（荷兰数学与计算机科学研究中心; QuSoft量子计算中心; 莱顿大学; 华威大学计算机科学系; 慕尼黑大学; 慕尼黑量子科学与技术中心; 阿姆斯特丹大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究证明，仅需恒定数量的副本即可测试量子态是否为高斯态，突破了先前副本数随系统规模增长的限制，方法基于对称性及梯度流与谱界。
AI 中文摘要
玻色子和费米子高斯量子态是量子物理和量子信息处理中发挥核心作用的一族量子态。我们研究测试给定态是否为高斯态，或与任何高斯态的重叠有界的问题。先前对该测试问题的分析导致了所需的态副本数随模式数（系统大小）扩展的测试。在本工作中，我们证明态的恒定副本数就足够了。我们基于高斯态相同副本的对称性，并通过梯度流和先前为球面上Kac随机游走研究的谱界来界定到高斯态集合的距离，从而推导出这些结果。
英文摘要
Bosonic and fermionic Gaussian quantum states are families of quantum states that play a central role in quantum physics and quantum information processing. We study the problem of testing whether a given state is either Gaussian, or has bounded overlap with any Gaussian state. Previous analyses of this testing problem led to tests that require a number of copies of the state that scales with the number of modes (the system size). In this work we show that a constant number of copies of the state suffices. We derive these results based on the symmetries of identical copies of Gaussian states, and by bounding the distance to the set of Gaussian states through a gradient flow and a spectral bound studied previously for the Kac random walk on a sphere.
Comments19 pages, 1 figure
