发表机构
Technische Universität Wien, Atominstitut & Vienna Center for Quantum Science and Technology (VCQ); Charles University, Faculty of Mathematics and Physics（维也纳工业大学，原子研究所与维也纳量子科学与技术中心; 查理大学，数学与物理学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出基于连续变量量子态一阶、二阶统计矩的保真度界来检测施密特数，认证高维纠缠，并在高斯与非高斯态上验证其有效性。
AI 中文摘要
高维量子系统中纠缠的维度通过施密特数来量化，其较大值预示着量子通信和量子计算方面的潜在优势。在有限维系统中，一种常用的实用施密特数检测方法基于对具有大纠缠维度的纯态的保真度估计或这些保真度的下界。然而，对于模式纠缠的连续变量系统，相应的测量通常难以实现。在此，我们引入并评估了基于任意连续变量量子态的第一和第二统计矩（这些矩在实际中更易于测量）的施密特数检测的保真度界。我们提供了允许评估这些界的解析公式，并针对高斯态和非高斯态族（包括双模压缩热态和光子增加位移双模压缩真空态）进行了测试。我们将我们的界与基于相同测量的其他高维纠缠认证方法进行了比较。
英文摘要
The dimensionality of entanglement in high-dimensional quantum systems is quantified by the Schmidt number, whose large value signals potential advantages for quantum communication and quantum computation. A commonly used approach to practical Schmidt-number detection in finite-dimensional systems is based on the estimation of fidelities to pure states with large entanglement dimensionality or lower bounds to these fidelities. However, for mode-entangled continuous-variable systems, the corresponding measurements are typically difficult to realize. Here, we introduce and assess fidelity bounds for Schmidt-number detection based on practically more accessible measurements of the first and second statistical moments of arbitrary continuous-variable quantum states. We provide analytical formulas that allow evaluating these bounds and test them for families of Gaussian and non-Gaussian states, including two-mode squeezed thermal states and photon-added displaced two-mode squeezed vacuum states. We compare our bounds to other methods for the certification of high-dimensional entanglement based on the same measurements.
Comments15 + 4 pages, 7 figures
