Answers are grounded in this paper and cite their sources.
This research presents criteria for testing block-positivity in complex matrices, indicating the potential for wider applications in quantum systems.
We present an effective set of necessary and sufficient criteria for block-positivity of matrices of order $4$ over C. The approach is based on Sturm sequences and quartic polynomial positivity conditions presented in recent literature. The procedure allows us to test whether a given 4× 4 complex matrix corresponds to an entanglement witness, and it is exact when the matrix coefficients belong to the rationals, extended by i. The method can be generalized to H₂d systems for $d>2$ to provide necessary but not sufficient criterion for block-positivity. We also outline an alternative approach to the problem relying on Gröbner bases.
No takes yet. Share an insight, caveat, or question.
Grzelka et al. (2025) studied this question.
Synapse has enriched 8 closely related papers on similar clinical questions. Consider them for comparative context: