Second-Order Characterizations via Partial Smoothing

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Conference Proceeding
IEEE International Symposium on Information Theory - Proceedings, 2019, 2019-July pp. 937 - 941
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© 2019 IEEE. Smooth entropies are a tool for quantifying resource trade-offs in information theory and cryptography. However, in typical multi-partite problems 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. As a consequence, we can derive 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.
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