Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.19159 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915863759683584 |
|---|---|
| author | Chen, Qian Collins, Benoît |
| author_facet | Chen, Qian Collins, Benoît |
| contents | We extend \cite{chen2025srkbp} by analyzing the complexity of the $k$-block-positivity testing algorithm that stems from the optimization problem in Definition \ref{definition:SDP-k-block-positivity}. In this paper, we investigate a symmetry reduction scheme based on rectangular shaped Young diagrams. Connecting the complexity to the dimensions of irreducible representations of $\U(d)$, we derive an explicit formula for the complexity, which also clarifies why the semidefinite program hierarchy collapses in the $k=d$ case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_19159 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The complexity of semidefinite programs for testing $k$-block-positivity Chen, Qian Collins, Benoît Quantum Physics We extend \cite{chen2025srkbp} by analyzing the complexity of the $k$-block-positivity testing algorithm that stems from the optimization problem in Definition \ref{definition:SDP-k-block-positivity}. In this paper, we investigate a symmetry reduction scheme based on rectangular shaped Young diagrams. Connecting the complexity to the dimensions of irreducible representations of $\U(d)$, we derive an explicit formula for the complexity, which also clarifies why the semidefinite program hierarchy collapses in the $k=d$ case. |
| title | The complexity of semidefinite programs for testing $k$-block-positivity |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2601.19159 |