Exact trace-distance strong converse exponent for quantum privacy amplification

Determine the exact strong converse exponent of quantum privacy amplification under the trace-distance criterion, extending the existing lower bounds to a matching characterization.

Background

The paper determines the exact strong converse exponent for quantum privacy amplification under the sandwiched Rényi divergence for orders greater than two and, together with prior work, discusses the full data-processing range. Under trace distance, however, the cited results provide only lower bounds. A matching upper bound and exact characterization for quantum privacy amplification therefore remain unresolved.

References

A natural next step is to determine the exact strong converse exponents of quantum soft covering and quantum privacy amplification under the trace distance. For quantum soft covering, Cheng and Gao established a lower bound on the strong converse exponent. For quantum privacy amplification, lower bounds were obtained by Shen, Gao, and Cheng and by Salzmann and Datta. These bounds provide only one side of the corresponding exponents, and exact characterizations under the trace distance remain open.

— Strong Converse Exponents of Quantum Soft Covering and Privacy Amplification  (2608.16452 - Li et al., 17 Aug 2026) in Section Conclusion