Tensor network decompositions for absolutely maximally entangled states
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866910436931141632 |
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| author | Pozsgay, Balázs Wanless, Ian M. |
| author_facet | Pozsgay, Balázs Wanless, Ian M. |
| contents | Absolutely maximally entangled (AME) states of $k$ qudits (also known as perfect tensors) are quantum states that have maximal entanglement for all possible bipartitions of the sites/parties. We consider the problem of whether such states can be decomposed into a tensor network with a small number of tensors, such that all physical and all auxiliary spaces have the same dimension $D$. We find that certain AME states with $k=6$ can be decomposed into a network with only three 4-leg tensors; we provide concrete solutions for local dimension $D=5$ and higher. Our result implies that certain AME states with six parties can be created with only three two-site unitaries from a product state of three Bell pairs, or equivalently, with six two-site unitaries acting on a product state on six qudits. We also consider the problem for $k=8$, where we find similar tensor network decompositions with six 4-leg tensors. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2308_07042 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Tensor network decompositions for absolutely maximally entangled states Pozsgay, Balázs Wanless, Ian M. Quantum Physics Statistical Mechanics Absolutely maximally entangled (AME) states of $k$ qudits (also known as perfect tensors) are quantum states that have maximal entanglement for all possible bipartitions of the sites/parties. We consider the problem of whether such states can be decomposed into a tensor network with a small number of tensors, such that all physical and all auxiliary spaces have the same dimension $D$. We find that certain AME states with $k=6$ can be decomposed into a network with only three 4-leg tensors; we provide concrete solutions for local dimension $D=5$ and higher. Our result implies that certain AME states with six parties can be created with only three two-site unitaries from a product state of three Bell pairs, or equivalently, with six two-site unitaries acting on a product state on six qudits. We also consider the problem for $k=8$, where we find similar tensor network decompositions with six 4-leg tensors. |
| title | Tensor network decompositions for absolutely maximally entangled states |
| topic | Quantum Physics Statistical Mechanics |
| url | https://arxiv.org/abs/2308.07042 |