A new bound on the rank of tensor product of W-states
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915656898707456 |
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| author | Canino, S. Casarotti, A. Santarsiero, P. |
| author_facet | Canino, S. Casarotti, A. Santarsiero, P. |
| contents | A W-state is an order d symmetric tensor of the form W_d=x^{d-1}y. We prove that the partially symmetric rank of W_{d_1}\otimes \cdots \otimes W_{d_k} is at most 2^{k-1}(d_1+\cdots +d_k-2k+2). The same bound holds for the tensor rank and it is an improvement of 2^k(k-1) over the best known bound. Moreover, we provide an explicit partially symmetric decomposition achieving this bound. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_05828 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A new bound on the rank of tensor product of W-states Canino, S. Casarotti, A. Santarsiero, P. Algebraic Geometry Commutative Algebra 14N07, 14N05, 15A69, 14M20 A W-state is an order d symmetric tensor of the form W_d=x^{d-1}y. We prove that the partially symmetric rank of W_{d_1}\otimes \cdots \otimes W_{d_k} is at most 2^{k-1}(d_1+\cdots +d_k-2k+2). The same bound holds for the tensor rank and it is an improvement of 2^k(k-1) over the best known bound. Moreover, we provide an explicit partially symmetric decomposition achieving this bound. |
| title | A new bound on the rank of tensor product of W-states |
| topic | Algebraic Geometry Commutative Algebra 14N07, 14N05, 15A69, 14M20 |
| url | https://arxiv.org/abs/2512.05828 |