The complexity of semidefinite programs for testing $k$-block-positivity
Quantum Physics
2026-03-17 v2
Abstract
We extend \cite{chen2025srkbp} by analyzing the complexity of the -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 , we derive an explicit formula for the complexity, which also clarifies why the semidefinite program hierarchy collapses in the case.
Cite
@article{arxiv.2601.19159,
title = {The complexity of semidefinite programs for testing $k$-block-positivity},
author = {Qian Chen and Benoît Collins},
journal= {arXiv preprint arXiv:2601.19159},
year = {2026}
}
Comments
20 pages