Round reduction under additional physical hypotheses

Determine which additional hypotheses on a theory, such as the availability of coherent operations on a qubit to the verifier, imply that its interactive-proof class equals the class of three-message protocols.

Background

Quantum theory compresses every interactive proof to three messages, whereas classical theory does not do so unless PSPACE=AM. Since classical theory satisfies the paper’s four standing assumptions, those assumptions alone cannot imply a general round-reduction theorem.

The paper therefore asks for structural or operational conditions beyond the standing assumptions that would force three-message sufficiency in a general probabilistic theory. The suggested direction is the verifier’s ability to perform coherent operations on qubits.