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.
From: Mario Berta [view email]
[v1]
Sun, 15 Jul 2018 23:28:18 UTC (23 KB)
[v2]
Thu, 23 Aug 2018 07:38:18 UTC (25 KB)
[v3]
Thu, 2 Jul 2026 12:36:15 UTC (31 KB)
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