Separations requiring substantially more shared entanglement

Determine whether there exists a communication problem with a large separation between entanglement-assisted classical and entanglement-unassisted quantum communication for which every entanglement-assisted classical protocol achieving that separation requires shared entanglement superpolynomial in the unassisted quantum communication complexity, or even superpolynomial in the input size.

Background

The constructed protocol uses Θ(n) shared EPR pairs, while the unassisted quantum communication complexity is Θ(n{1/3}); thus the entanglement supply is polynomial in the unassisted communication cost. The authors ask whether substantially larger entanglement requirements can be forced, ideally alongside an asymptotic or exponential communication separation. They indicate that this possibility is suggested by results concerning nonlocal games.

References

Can an asymptotic separation (ideally exponential) between these models require substantially more entanglement? Specifically, is there a communication problem exhibiting a large separation between the entanglement-assisted and entanglement-unassisted models for which every entanglement-assisted classical protocol achieving such a separation requires an amount of shared entanglement superpolynomial in the unassisted quantum communication complexity, or even in the input size?

— 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 2