Nape Isaac, Rodríguez-Fajardo Valeria, Zhu Feng, Huang Hsiao-Chih, Leach Jonathan, Forbes Andrew
School of Physics, University of the Witwatersrand, Wits, South Africa.
School of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh, UK.
Nat Commun. 2021 Aug 27;12(1):5159. doi: 10.1038/s41467-021-25447-0.
High-dimensional entangled states are promising candidates for increasing the security and encoding capacity of quantum systems. While it is possible to witness and set bounds for the entanglement, precisely quantifying the dimensionality and purity in a fast and accurate manner remains an open challenge. Here, we report an approach that simultaneously returns the dimensionality and purity of high-dimensional entangled states by simple projective measurements. We show that the outcome of a conditional measurement returns a visibility that scales monotonically with state dimensionality and purity, allowing for quantitative measurements for general photonic quantum systems. We illustrate our method using two separate bases, the orbital angular momentum and pixels bases, and quantify the state dimensionality by a variety of definitions over a wide range of noise levels, highlighting its usefulness in practical situations. Importantly, the number of measurements needed in our approach scale linearly with dimensions, reducing data acquisition time significantly. Our technique provides a simple, fast and direct measurement approach.
高维纠缠态有望提升量子系统的安全性和编码容量。虽然可以见证并设定纠缠的界限，但以快速且准确的方式精确量化维度和纯度仍是一个悬而未决的挑战。在此，我们报告一种通过简单的投影测量同时返回高维纠缠态的维度和纯度的方法。我们表明，条件测量的结果返回一个与态维度和纯度单调缩放的可见度，从而允许对一般光子量子系统进行定量测量。我们使用两个独立的基，即轨道角动量基和像素基来说明我们的方法，并在广泛的噪声水平范围内通过各种定义量化态维度，突出其在实际情况中的实用性。重要的是，我们方法中所需的测量次数与维度呈线性缩放，显著减少了数据采集时间。我们的技术提供了一种简单、快速且直接的测量方法。
