Interaction and commitment capacity over general quantum channels

Determine whether interactive communication can increase the classical string commitment capacity for quantum channels beyond the noninteractive capacity in general.

Background

The paper determines the noninteractive commitment capacity for a broad class of quantum channels with limited entanglement assistance and proves a universal upper bound of log₂ d + E for interactive protocols over a channel with input dimension d and entanglement rate E. For the considered channel class, this upper bound coincides with the noninteractive capacity whenever H(Z|F) ≥ log₂ d + E.

For the quantum erasure channel, the paper further proves that interaction does not increase the capacity for any entanglement rate. It remains unresolved whether this phenomenon extends to general quantum channels or whether interactive classical communication can strictly improve commitment rates in other cases.