Exact trace-distance strong converse exponent for quantum soft covering

Determine the exact strong converse exponent of quantum soft covering under the trace-distance criterion, extending the existing lower bound to a matching characterization.

Background

The paper establishes the exact strong converse exponent for quantum soft covering when approximation error is measured by the sandwiched Rényi divergence over the full data-processing range of orders. It notes that, under trace distance, Cheng and Gao have established only a lower bound on the strong converse exponent. Consequently, the exact trace-distance exponent for quantum soft covering remains 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