Experimental investigation of direct non-Hermitian measurement and uncertainty relation towards high-dimensional quantum domain
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| Autores principales: | , , , , , , , , , , , , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| author | Wang, Yi-Tao Wang, Zhao-An Li, Zhi-Peng Zeng, Xiao-Dong Ren, Jia-Ming Liu, Wei Yang, Yuan-Ze Guo, Nai-Jie Xie, Lin-Ke Liu, Jun-You Ma, Yu-Hang Tang, Jian-Shun Zhang, Chengjie Li, Chuan-Feng Guo, Guang-Can |
| author_facet | Wang, Yi-Tao Wang, Zhao-An Li, Zhi-Peng Zeng, Xiao-Dong Ren, Jia-Ming Liu, Wei Yang, Yuan-Ze Guo, Nai-Jie Xie, Lin-Ke Liu, Jun-You Ma, Yu-Hang Tang, Jian-Shun Zhang, Chengjie Li, Chuan-Feng Guo, Guang-Can |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_05332 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Experimental investigation of direct non-Hermitian measurement and uncertainty relation towards high-dimensional quantum domain Wang, Yi-Tao Wang, Zhao-An Li, Zhi-Peng Zeng, Xiao-Dong Ren, Jia-Ming Liu, Wei Yang, Yuan-Ze Guo, Nai-Jie Xie, Lin-Ke Liu, Jun-You Ma, Yu-Hang Tang, Jian-Shun Zhang, Chengjie Li, Chuan-Feng Guo, Guang-Can Quantum Physics 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. |
| title | Experimental investigation of direct non-Hermitian measurement and uncertainty relation towards high-dimensional quantum domain |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2407.05332 |