Presented by:
Mario Berta
Date:
Thursday 26th July 2018 - 11:00 to 11:45
Venue:
INI Seminar Room 1
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. However, for quantum systems
we can so far only give the asymptotic first-order expansion of these
quantities.
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