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arXiv · 2407.05332

Experimental investigation of direct non-Hermitian measurement and uncertainty relation towards high-dimensional quantum domain

Yi-Tao Wang·Zhao-An Wang·Zhi-Peng Li·Xiao-Dong Zeng·Jia-Ming Ren·Wei Liu·Yuan-Ze Yang·Nai-Jie Guo·Lin-Ke Xie·Jun-You Liu·Yu-Hang Ma·Jian-Shun Tang·Chengjie Zhang·Chuan-Feng Li·Guang-Can Guo
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Abstract

Non-Hermitian dynamics in quantum systems have unveiled novel phenomena, yet the implementation of valid non-Hermitian quantum measurement remains a challenge, because a universal quantum projective mechanism on the complete but skewed non-Hermitian eigenstates is not explicit in experiment. This limitation hinders the direct acquisition of non-Hermitian observable statistics (e.g., non-Hermitian population dynamics), also constrains investigations of non-Hermitian quantum measurement properties such as uncertainty relation. Here, we address these challenges by presenting a non-Hermitian projective protocol and investigating the non-Hermitian uncertainty relation. We derive the uncertainty relation for pseudo-Hermitian (PH) observables that is generalized beyond the Hermitian ones. We then investigate the projective properties of general quantum states onto complete non-Hermitian eigenvectors, and present a quantum simulating method to apply the valid non-Hermitian projective measurement on a direct-sum dilated space. Subsequently, we experimentally construct a quantum simulator in the quantum optical circuit and realize the 3-dimensional non-Hermitian quantum measurement on the single-photon qutrit. Employing this platform, we explore the uncertainty relation experimentally with different PH metrics. Our non-Hermitian quantum measurement method is state-independent and outputs directly the non-Hermitian quantum projective statistics, paving the way for studies of extensive non-Hermitian observable in quantum domain.

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Yi-Tao Wang, Zhao-An Wang, Zhi-Peng Li, Xiao-Dong Zeng, Jia-Ming Ren, Wei Liu, Yuan-Ze Yang, Nai-Jie Guo, Lin-Ke Xie, Jun-You Liu, Yu-Hang Ma, Jian-Shun Tang, Chengjie Zhang, Chuan-Feng Li, Guang-Can Guo. 2024-07-07. Experimental investigation of direct non-Hermitian measurement and uncertainty relation towards high-dimensional quantum domain. https://arxiv.org/abs/2407.05332

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