Wang Xiaowei, Zhan Xiang, Li Yulin, Xiao Lei, Zhu Gaoyan, Qu Dengke, Lin Quan, Yu Yue, Xue Peng
Beijing Computational Science Research Center, Beijing 100084, China.
School of Science, Nanjing University of Science and Technology, Nanjing 210094, China.
Phys Rev Lett. 2023 Oct 13;131(15):150803. doi: 10.1103/PhysRevLett.131.150803.
Quantum measurements play a fundamental role in quantum mechanics. Especially, generalized quantum measurements provide a powerful and versatile tool to extract information from quantum systems. However, how to realize them on an arbitrary higher-dimensional quantum system remains a challenging task. Here we propose a simple recipe for the implementation of a general positive-operator valued measurement (POVM) on a higher-dimensional quantum system via a one-dimensional discrete-time quantum walk with a two-dimensional coin. Furthermore, using single photons and linear optics, we realize experimentally a symmetric, informationally complete (SIC) POVM on a three-dimensional system with high fidelity. As an application, we realize a qutrit state tomography with SIC-POVM and confirm that the infidelity scaling achieved by the qutrit SIC-POVM is as good as that based on mutually unbiased bases. Our study paves the way to explore physics and information in higher-dimensional quantum systems and finds applications in various quantum information processing tasks that rely on generalized quantum measurements.
量子测量在量子力学中起着基础性作用。特别是，广义量子测量为从量子系统中提取信息提供了一种强大且通用的工具。然而，如何在任意高维量子系统上实现它们仍然是一项具有挑战性的任务。在此，我们提出一种简单方法，通过具有二维硬币的一维离散时间量子行走，在高维量子系统上实现一般的正算子值测量（POVM）。此外，利用单光子和线性光学，我们在三维系统上通过实验实现了具有高保真度的对称、信息完备（SIC）POVM。作为应用，我们用SIC-POVM实现了三量子比特态层析成像，并证实三量子比特SIC-POVM实现的非保真度标度与基于相互无偏基的情况一样好。我们的研究为探索高维量子系统中的物理和信息铺平了道路，并在依赖广义量子测量的各种量子信息处理任务中找到了应用。
