Operational relevance of commuting-operator versus tensor-product distinctions

Determine whether the distinction between commuting-operator and tensor-product models can be exploited by an adversary in quantum key distribution and whether it can change the achievable key rates.

Background

The paper formulates one-sided DIQKD using a characterized finite-dimensional matrix algebra and an uncharacterized universal C*-algebra, yielding a unique tensor product because matrix algebras are nuclear. It contrasts this with fully device-independent settings, where commuting-operator and tensor-product models may differ, particularly in the presence of infinite-dimensional or unbounded entanglement. Whether these mathematical distinctions have an actual cryptographic impact remains unresolved.