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SUMMARY:Chain rule for quantum relative entropies and their applications i
 n quantum information theory - Kun Fang\, DAMTP
DTSTART:20191024T131500Z
DTEND:20191024T141500Z
UID:TALK131584@talks.cam.ac.uk
CONTACT:Johannes Bausch
DESCRIPTION:The chain rule for the classical relative entropy ensures that
  the relative entropy between probability distributions on multipartite sy
 stems can be decomposed into a sum of relative entropies of suitably chose
 n conditional distributions on the individual systems. In this talk\, we w
 ill discuss similar chain rules for two different quantum relative entropi
 es\, that is\, the Umegaki relative entropy and the Belavkin-Staszewski (B
 S) relative entropy. These new chain rules admit important applications in
  the context of asymptotic quantum channel discrimination and quantum chan
 nel capacities. More precisely\, the chain rule for the Umegaki relative e
 ntropy allows us to solve an open problem in quantum channel discriminatio
 n that adaptive protocols cannot improve the error rate for asymmetric cha
 nnel discrimination compared to non-adaptive strategies. The chain rule fo
 r the BS relative entropy helps to sharpen single-letter converse bounds o
 n quantum channel capacities in a significant way.\n\nThis talk is based o
 n arXiv papers: 1909.05826 and 1909.05758.
LOCATION:MR9\,  Centre for Mathematical Sciences\, Wilberforce Road\, Camb
 ridge
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