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arXiv · 2603.01802

Experimental realization and self-testing of semisymmetric informationally complete measurements via a one-dimensional photonic quantum walk

Xu Xu·Han-Yu Cheng·Meng-Yun Ma·Chao-Jie Sun·Yan Wang·Li-Jiong Shen·Zhe Sun·Qi-Ping Su·Chui-Ping Yang·Yong-Nan Sun
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Abstract

Generalized quantum measurements play a crucial role in quantum mechanics, and symmetric informationally complete positive operator-valued measurements (SIC POVMs) provide a powerful and flexible framework for extracting information from quantum systems. However, the existence of SIC-POVMs in every finite dimension remains an open question, which has stimulated extensive research into alternative classes of POVMs. Recently, Geng $et$ $al$. [Phys. Rev. Lett. 126, 100401 (2021)] proposed a broader class of SIC POVM, called semisymmetric informationally complete POVM (semi-SIC POVM), which extends beyond SIC POVM. In this work, we focus on the four-outcome POVMs and experimentally realize the semi-SIC POVMs using a one-dimensional discrete-time quantum walk. Additionally, employing single photons and linear optics, we perform an experimental self-testing of semi-SIC POVMs in the semi-device-independent manner. Our results pave the way for exploring quantum certification with generalized quantum measurements.

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Xu Xu, Han-Yu Cheng, Meng-Yun Ma, Chao-Jie Sun, Yan Wang, Li-Jiong Shen, Zhe Sun, Qi-Ping Su, Chui-Ping Yang, Yong-Nan Sun. 2026-03-02. Experimental realization and self-testing of semisymmetric informationally complete measurements via a one-dimensional photonic quantum walk. https://arxiv.org/abs/2603.01802

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