Adapt quantum-oracle lower-bound methods to general SDP formulations

Adapt the quantum-oracle methods used to prove stronger lower bounds for approximate disentanglers to general semidefinite extended formulations of the separable-state optimization problem.

Background

The paper emphasizes that the quantum-oracle approach of concurrent work applies to approximate disentanglers but does not directly apply to arbitrary objective-independent SDP formulations, which need not define quantum channels or QMA verifiers. The authors leave open whether those methods can be transferred to the broader SDP setting.

References

More broadly, can the methods used to prove stronger lower bounds for approximate disentanglers, particularly the quantum-oracle approach of Bostanci et al., be adapted to general SDP extended formulations of $h_{Sep}$?

— Semidefinite extension complexity of the separable set, with applications to approximate disentanglers  (2609.09033 - Gharibian et al., 8 Sep 2026) in Section 1, Introduction, paragraph “Open questions”