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 entanglement dimensionality and purity, allowing for quantitative measurements for general photonic quantum systems. We illustrate our method using transverse spatial modes of photons that carry orbital angular momentum and verify high-dimensional entanglement over a wide range of state purities. Our approach advances the high-dimensional tool box for characterising quantum states by providing a simple and direct dimensionality and purity measure, even for mixed entangled states.
An Optimal Polarization-Entanglement Source: Frequency-Converted SPDC with Degeneracy, Indistinguishability, and Ultra-High Purity Configurable Over a Large Spectral Range
Quadratic Quantum Polarimetry with Entangled Photon Pairs
ARC Centre of Excellence for Transformative Meta-Optical Systems (TMOS), Department of Electronic Materials Engineering, Research School of Physics, The Australian National University（澳大利亚国立大学）；Institute of Applied Physics, Abbe Center of Photonics, Friedrich Schiller University Jena（耶拿弗里德里希·席勒大学应用物理研究所）；Opto-Electronics and Measurement Techniques, Advanced Electronics Centre, Faculty of Information Technology and Electrical Engineering, University of Oulu（奥卢大学信息技术与电气工程学院高级电子中心光电子与测量技术部门）；Institute of Quantum Precision Measurement, State Key Laboratory of Radio Frequency Heterogeneous Integration, College of Physics and Optoelectronic Engineering, Shenzhen University（深圳大学物理与光电工程学院量子精密测量研究所）；Aston Institute of Photonic Technologies, Aston University（阿斯顿大学光子技术研究所）
Quantum optical synthesis of high-dimensional ultrafast frequency-bin qudits
Graduate School of Informatics and Engineering, The University of Electro-Communications（电子通信大学信息工程研究生院）；Advanced ICT Research Institute, National Institute of Information and Communications Technology（国家信息通信技术研究所先进ICT研究所）；Institute for Advanced Science, The University of Electro-Communications（电子通信大学高等科学研究院）
