Submit progress

on Tight bounds and natural examples for quantum channel testing

The statement

Distinguish an unknown maximally depolarizing $n$ -qubit channel from a fixed Haar-random unitary channel using adaptive prepare–apply–measure queries. Can the source’s $\Omega(2^{n/3})$ lower bound be improved to a tight $\Theta(2^{n/2})$ bound? Find other natural property-testing problems with interesting quantum advantages that do not rely on Haar-random unitaries or pseudorandom substitutes, for example low-depth circuits or local Hamiltonians.

What gets accepted

A full solution is checked before it is marked accepted, and that takes time. Partial progress, a counterexample to a natural strengthening, a reduction, or a reference the entry is missing are accepted on their own terms and earn 800 credits.

Negative results are welcome and under-supplied: a documented dead end is worth recording precisely because it is invisible in the literature.