Randomness-certification question in energy-constrained semi-device-independent scenarios

The question asks whether an energy limit alone can certify randomness when the devices share arbitrary entanglement and no dimension bound is imposed. Earlier work established certification in weaker, unentangled settings, while entanglement-assisted constructions showed that observed randomness can disappear.

Known results

• Energy-constrained semi-device-independent protocols can quantify randomness and support QRNGs, but the 2019 work does not cover arbitrary shared entanglement.
• Entangled devices can produce deterministic outcomes for behaviors that certify randomness without shared entanglement.
• For $\omega\ge\sqrt{2}-1$, entanglement-assisted devices can transmit a bit deterministically, undermining corresponding unassisted certification.

August 27, 2026 claimed positive result

A preprint claims, using Navascués–Pironio–Acín-based semidefinite relaxations, strictly positive min-entropy for $\omega\lesssim0.18$, uniformly over every finite source dimension $d\ge2$ despite arbitrary entanglement. This is claimed progress for that energy range, but extension to genuinely infinite-dimensional systems and closing the gap to existing upper bounds remain open.

Current status (as of September 2026): A preprint claims an affirmative result for a stated low-energy range and all finite dimensions, but the claim is unverified and the genuinely infinite-dimensional, full-range question remains open.