Partially smoothed information measures

Abstract

Smooth entropies are a tool for quantifying resource trade-offs in (quantum) information theory and cryptography. In typical bi- and multi-partite problems, however, some of the sub-systems are often left unchanged and this is not reflected by the standard smoothing of information measures over a ball of close states. We propose to smooth instead only over a ball of close states which also have some of the reduced states on the relevant sub-systems fixed. This partial smoothing of information measures naturally allows to give more refined characterizations of various information-theoretic problems in the one-shot setting. In particular, we immediately get asymptotic second-order characterizations for tasks such as privacy amplification against classical side information or classical state splitting. For quantum problems like state merging the general resource trade-off is tightly characterized by partially smoothed information measures as well.

v3: published version

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Cited by in corpus (9)

• Tight Exponential Analysis for Smoothing the Max-Relative Entropy and for Quantum Privacy Amplification
• Moderate deviation expansion for fully quantum tasks
• Thermodynamic Implementations of Quantum Processes
• Channel Simulation: Finite Blocklengths and Broadcast Channels
• One-shot quantum state redistribution and quantum Markov chains
• Reliability Function of Quantum Information Decoupling via the Sandwiched Rényi Divergence
• On the Second-Order Asymptotics of the Partially Smoothed Conditional Min-Entropy & Application to Quantum Compression
• One-Shot Distributed Source Simulation: As Quantum as it Can Get
• One-shot Multiple Access Channel Simulation