One-way quantum–classical separation for total functions

Determine whether an asymptotic separation between quantum and classical one-way communication complexity exists for a total Boolean function when shared entanglement is unavailable.

Background

The paper distinguishes the entanglement-assisted classical model from the entanglement-unassisted quantum model and surveys known quantum–classical separations for total functions. Although strong separations are known in other communication settings, the authors identify the one-way total-function case without shared entanglement as unresolved. This question is also restated among the explicit open problems in the conclusion.

References

Whether any asymptotic quantum--classical separation for a total function is possible when the quantum protocol is one-way remains an open question.

— An exponential separation between entanglement-assisted and unassisted one-way quantum communication  (2610.02099 - Anselm et al., 1 Oct 2026) in Section 1, subsection “Background”

In the absence of shared entanglement, does an asymptotic separation between quantum and classical one-way communication complexity exist for a total function, using the subgroup membership problem or otherwise?

— An exponential separation between entanglement-assisted and unassisted one-way quantum communication  (2610.02099 - Anselm et al., 1 Oct 2026) in Section “Conclusion and open problems”, item 3