Almost all even-particle pure states are determined by their half-body marginals
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916091664531456 |
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| author | Zhang, Wanchen Shi, Fei Zhang, Xiande |
| author_facet | Zhang, Wanchen Shi, Fei Zhang, Xiande |
| contents | Determining whether the original global state is uniquely determined by its local marginals is a prerequisite for some efficient tools for characterizing quantum states. This paper shows that almost all generic pure states of even $N$-particle with equal local dimension are uniquely determined among all other pure states (UDP) by four of their half-body marginals. Furthermore, we give a graphical description of the marginals for determining genuinely multipartite entangled states, which leads to several lower bounds on the number of required marginals. Finally, we present a construction of N-qudit states obtained from certain combinatorial structures that cannot be UDP by its k-body marginals for some k>N/2-1. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_07499 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Almost all even-particle pure states are determined by their half-body marginals Zhang, Wanchen Shi, Fei Zhang, Xiande Quantum Physics Determining whether the original global state is uniquely determined by its local marginals is a prerequisite for some efficient tools for characterizing quantum states. This paper shows that almost all generic pure states of even $N$-particle with equal local dimension are uniquely determined among all other pure states (UDP) by four of their half-body marginals. Furthermore, we give a graphical description of the marginals for determining genuinely multipartite entangled states, which leads to several lower bounds on the number of required marginals. Finally, we present a construction of N-qudit states obtained from certain combinatorial structures that cannot be UDP by its k-body marginals for some k>N/2-1. |
| title | Almost all even-particle pure states are determined by their half-body marginals |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2401.07499 |