Comparing strong converse exponents for general versus ensemble‑restricted hash families

Determine whether the strong converse exponent for quantum privacy amplification when arbitrary hash functions are allowed is strictly smaller than the ensemble strong converse exponent obtained when restricting to (strongly) 2‑universal hash families.

Background

The paper proves lower and upper bounds on strong converse exponents for privacy amplification and discusses differences between general converses and ensemble converses that assume specific hash‑family restrictions (e.g., strongly 2‑universal).

Prior results have shown stronger ensemble converses under such restrictions, but it is not clear whether those exponents represent the true strong converse when general hash functions are permitted. The authors articulate a conjectural separation, motivating further investigation.