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Convex splitting is a powerful technique in quantum information theory usedin proving the achievability of numerous information-processing protocols suchas quantum state redistribution and quantum network channel coding. In thiswork, we establish a one-shot error exponent and a one-shot strong converse forconvex splitting with trace distance as an error criterion. Our results showthat the derived error exponent (strong converse exponent) is positive if andonly if the rate is in (outside) the achievable region. This leads to newone-shot exponent results in various tasks such as communication over quantumwiretap channels, secret key distillation, one-way quantum message compression,quantum measurement simulation, and quantum channel coding with sideinformation at the transmitter. We also establish a near-optimal one-shotcharacterization of the sample complexity for convex splitting, which yieldsmatched second-order asymptotics. This then leads to stronger one-shot analysisin many quantum information-theoretic tasks.

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