基于随机零差与外差测量的连续变量态矩
Continuous-variable state moments from randomized homodyne and heterodyne measurements
AI总结：
本文提出一种基于随机零差与外差测量的连续变量态矩生成函数影子层析协议，可高效并行估计多模矩，仅需数千次测量即可完成纠缠检测与光损耗表征等任务，适用于多种连续变量模拟场景。
AI中文摘要：
连续变量（CV）量子态自然由其矩表征，矩定义为单模或多模梯算符乘积的期望值。许多CV哈密顿量和量子算法直接基于这些矩构建，因此需要一种利用有限态测量估计矩的高效方法。本文提出一种基于随机零差与外差测量的CV态矩生成函数（MGF）的影子层析协议，所得影子可高效并行估计多个多模矩。复杂度分析表明，将某一矩估计至给定精度所需测量次数随矩的阶数呈指数增长。最后，我们通过两项任务评估这些矩估计器的精度：一是通过Shchukin-Vogel协议检测高斯与非高斯态的纠缠，二是表征光子芯片中的光损耗。结果显示，仅需数千次随机测量即可完成两项任务。所需测量次数少，结合高效样本处理，使该协议适用于广泛的CV模拟任务。
英文摘要：
Continuous-variable (CV) quantum states are naturally characterized by their moments, defined as expectation values of products of single- or multimode ladder operators. Many CV Hamiltonians and quantum algorithms are formulated directly in terms of these moments, and therefore an efficient procedure to estimate moments with limited state measurements is necessary. In this paper, we present a protocol for shadow tomography of moment-generating functions (MGFs) of CV states based on randomized homodyne and heterodyne measurements. The resulting shadows enable an efficient and concurrent estimation of many multimode moments. Our complexity analysis shows that the number of measurements required to estimate a certain moment to a given precision grows exponentially in the order of the moments. Finally, we assess the precision of these moment estimators by applying them to two tasks: detecting entanglement in both Gaussian and non-Gaussian states via the Shchukin-Vogel protocol, and characterizing optical loss in a photonic chip. We demonstrate that both tasks can be accomplished with only a few thousand randomized measurements. The small number of required measurements, combined with efficient sample processing, makes our protocol applicable to a wide range of CV simulation tasks.
