English

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 kk-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)\U(d), we derive an explicit formula for the complexity, which also clarifies why the semidefinite program hierarchy collapses in the k=dk=d 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

R2 v1 2026-07-01T09:21:34.627Z