The complexity of semidefinite programs for testing k-block-positivity
Abstract
We extend chen2025srkbp by analyzing the complexity of the k-block-positivity testing algorithm that stems from the optimization problem in Definition 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 (d), we derive an explicit formula for the complexity, which also clarifies why the semidefinite program hierarchy collapses in the k=d case.
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