The complexity of semidefinite programs for testing $k$-block-positivity
Abstract
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.
Fields of Study & Subjects
Quantum Information and Cryptography
Quantum Computing Algorithms and Architecture
Advanced Optimization Algorithms Research
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 27 January 2026
- Language
- EN
- Document type
- Preprint