Imperfectly complete QCCC key agreement with unrestricted quantum queries

Determine whether imperfectly complete quantum-computation, classical-communication (QCCC) key agreement in the quantum random-oracle model can remain secure when the honest parties are allowed to make arbitrary quantum oracle queries.

Background

The paper situates this problem as the remaining general case of impossibility results for quantum key agreement in the quantum random-oracle model. Prior unconditional attacks cover perfectly complete QCCC protocols and certain imperfectly complete protocols in which the honest parties’ early oracle queries are classical, but they do not handle imperfectly complete protocols with unrestricted quantum oracle access.

A classical attack in the fully general setting is obstructed by the Simulation Conjecture of Austrin et al., which concerns whether a classical algorithm with polynomial query complexity can approximate the acceptance probability of a comparable quantum algorithm on most random oracles. The paper’s results instead address restricted settings involving classical early queries, leaving the unrestricted imperfectly complete case unresolved.