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

• URL: http://arxiv.org/abs/2407.05332v1
• Date: Sun, 7 Jul 2024 11:20:27 GMT
• Title: Experimental investigation of direct non-Hermitian measurement and uncertainty relation towards high-dimensional quantum domain
• Authors: 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,
• Abstract summary: We present a non-Hermitian projective protocol and investigate the non-Hermitian uncertainty relation. 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.
• Score: 8.644552479467523
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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