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

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 li...

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Bibliographic Details
Published in:arXiv.org 2024-07
Main Authors: Yi-Tao, Wang, Zhao-An, Wang, Zhi-Peng, Li, Xiao-Dong, Zeng, Jia-Ming, Ren, Liu, Wei, Yuan-Ze Yang, Guo, Nai-Jie, Lin-Ke, Xie, Jun-You, Liu, Yu-Hang, Ma, Jian-Shun Tang, Zhang, Chengjie, Chuan-Feng, Li, Guo, Guang-Can
Format: Article
Language:English
Subjects:
Eigenvectors
Measurement methods
Uncertainty
Online Access:Get full text
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Summary: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.
ISSN:2331-8422