The complexity of semidefinite programs for testing -block-positivity
arXiv:2601.19159
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 $\U(d)$, we derive an explicit formula for the complexity, which also clarifies why the semidefinite program hierarchy collapses in the case.
20 pages