Dense indistinguishability conjecture for adaptive quantum query algorithms

Prove that every T-query quantum algorithm has distinguishing advantage at most C T^a delta^b between a (1-delta)-dense oracle distribution and the uniform oracle distribution, for absolute constants C, a >= 0, and b > 0.

Background

A distribution over Boolean oracles is (1-delta)-dense when every marginal has min-entropy at least (1-delta) times its dimension. The conjecture asserts that bounded-query quantum algorithms cannot substantially distinguish such distributions from uniformly random oracles.

The paper proves the conjecture for one massively parallel quantum-query layer and derives restricted extensions, but the adaptive quantum-query case remains the unresolved general target motivating the computationally hidden flipped set approach.