Separation in broader communication models

Establish whether an exponential separation for a total function can be obtained between entanglement-assisted classical simultaneous-message-passing protocols and unassisted one-way or two-way quantum protocols, and determine whether such a separation exists when the entanglement-assisted protocol is one-way and the unassisted quantum protocol is two-way or when both models permit arbitrary two-way communication.

Background

The paper proves an exponential separation only in the one-way setting, comparing entanglement-assisted classical communication with unassisted quantum communication. The conclusion asks whether analogous separations persist when the communication models are changed to simultaneous message passing, two-way quantum communication, or fully interactive communication. The authors note technical obstacles: the bounded-order subgroup membership problem has an efficient two-way classical protocol and does not appear to have an efficient entanglement-assisted SMP protocol, while lower bounds against two-way unassisted quantum protocols would require techniques that distinguish them from entanglement-assisted protocols.