Tight One-Shot Analysis for Convex Splitting with Applications in Quantum Information Theory

Understand

Convex splitting is a powerful technique in quantum information theory used in proving the achievability of numerous information-processing protocols such as quantum state redistribution and quantum network channel coding.

• In this work, we establish a one-shot error exponent and a one-shot strong converse for convex splitting with trace distance as an error criterion.
• Our results show that the derived error exponent (strong converse exponent) is positive if and only if the rate is in (outside) the achievable region.
• This leads to new one-shot exponent results in various tasks such as communication over quantum wiretap channels, secret key distillation, one-way quantum message compression, quantum measurement simulation, and quantum channel coding with side information at the transmitter.