Strong converse Exponents of Partially Smoothed Information Measures

TL;DR

This paper determines the exact strong converse exponents for partially smoothed information measures in quantum information theory, revealing differences between pure and classical states and applying these results to various quantum tasks.

Contribution

It provides the first precise characterization of strong converse exponents for these measures, highlighting their non-uniformity across different quantum states.

Findings

Strong converse exponents differ between pure and classical states.

Derived exponents for quantum data compression and randomness extraction.

Determined the exponent for classical privacy amplification.

Abstract

Partially smoothed information measures are fundamental tools in one-shot quantum information theory. In this work, we determine the exact strong converse exponents of these measures for both pure quantum states and classical states. Notably, we find that the strong converse exponents based on trace distance takes different forms between pure and classical states, indicating that they are not uniform across all quantum states. Leveraging these findings, we derive the strong converse exponents for quantum data compression, intrinsic randomness extraction, and classical state splitting. A key technical step in our analysis is the determination of the strong converse exponent for classical privacy amplification, which is of independent interest.