GHZ-W Genuinely Entangled Subspace Verification with Adaptive Local Measurements
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866908504113020928 |
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| author | Zheng, Congcong Xu, Ping Wang, Kun Zhang, Zaichen |
| author_facet | Zheng, Congcong Xu, Ping Wang, Kun Zhang, Zaichen |
| contents | Genuinely entangled subspaces (GESs) are valuable resources in quantum information science. Among these, the three-qubit GHZ-W GES, spanned by the three-qubit Greenberger-Horne-Zeilinger (GHZ) and W states, is a universal and crucial entangled subspace resource for three-qubit systems. In this work, we develop two adaptive verification strategies, the XZ strategy and the rotation strategy, for the three-qubit GHZ-W GES using local measurements and one-way classical communication. These strategies are experimentally feasible, efficient and possess a concise analytical expression for the sample complexity of the rotation strategy, which scales approximately as $2.248ε^{-1}\lnδ^{-1}$, where $ε$ is the infidelity and $1-δ$ is the confidence level. Furthermore, we comprehensively analyze the two-dimensional two-qubit subspaces and classify them into three distinct types, which include unverifiable entangled subspaces, revealing intrinsic limitations in local verification of entangled subspaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_19540 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | GHZ-W Genuinely Entangled Subspace Verification with Adaptive Local Measurements Zheng, Congcong Xu, Ping Wang, Kun Zhang, Zaichen Quantum Physics Genuinely entangled subspaces (GESs) are valuable resources in quantum information science. Among these, the three-qubit GHZ-W GES, spanned by the three-qubit Greenberger-Horne-Zeilinger (GHZ) and W states, is a universal and crucial entangled subspace resource for three-qubit systems. In this work, we develop two adaptive verification strategies, the XZ strategy and the rotation strategy, for the three-qubit GHZ-W GES using local measurements and one-way classical communication. These strategies are experimentally feasible, efficient and possess a concise analytical expression for the sample complexity of the rotation strategy, which scales approximately as $2.248ε^{-1}\lnδ^{-1}$, where $ε$ is the infidelity and $1-δ$ is the confidence level. Furthermore, we comprehensively analyze the two-dimensional two-qubit subspaces and classify them into three distinct types, which include unverifiable entangled subspaces, revealing intrinsic limitations in local verification of entangled subspaces. |
| title | GHZ-W Genuinely Entangled Subspace Verification with Adaptive Local Measurements |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2412.19540 |