Physical relevance of multinegative states

Determine whether multinegative states have any further physical relevance beyond their established role in providing upper bounds on asymptotic relative entropy of entanglement and exact PPT entanglement cost.

Background

The paper defines a quantum state as k-multinegative when its k-fold absolute partial transposition is not positive semidefinite. The authors prove that, when the corresponding iterated absolute partial transposition is positive semidefinite at a given level, its logarithmic trace upper-bounds both the asymptotic relative entropy of entanglement with respect to PPT states and the exact PPT entanglement cost.

Beyond this operational interpretation and the use of multinegative states as counterexamples to finite-collapse conjectures for entanglement-cost hierarchies, the paper does not establish whether multinegativity corresponds to additional physically meaningful properties or applications.

References

Apart from Lemma \ref{lemma:k-multinegativity}, which gives $k$-multinegativity a partial operational interpretation by providing an upper bound on $E_R$ and $E_{\text{c,PPT}{\text{exact}$, it is not clear whether multinegative states have any further physical relevance.

— Multinegativity and single-letter formulas for asymptotic entanglement  (2609.20698 - Brinster et al., 17 Sep 2026) in Section “k-multinegative states”