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SUMMARY:Metrics on quantum channels: issues\, fixes\, applications - Andre
 as Winter\, Universitat Autònoma de Barcelona
DTSTART:20180222T141500Z
DTEND:20180222T151500Z
UID:TALK95653@talks.cam.ac.uk
CONTACT:Steve Brierley
DESCRIPTION:The diamond norm on superoperators (aka completely bounded nor
 m' in the Heisenberg picture) provides a natural\, operationally well-moti
 vated\, and computable metric on quantum channels (cptp maps). In particul
 ar\, it quantifies the optimal bias in hypothesis testing between two chan
 nels\, it is given by a semidefinite programme\, and it enjoys a number of
  good mathematical properties. It furthermore provides the natural setting
  when discussing continuity of channel capacities. In some situations\, ho
 wever\, notably in infinite dimension\, the diamond norm is too strong to 
 be reasonably applicable. This can be illustrated with simple Bosonic chan
 nels. Inspired by communication theory\, i propose a definition of diamond
  norm with an energy constraint (with respect to a given  Hamiltonian)\, a
 nd show that this allows for a resolution of most of the issues of the dia
 mond norm\, while retaining its good properties. As an application\, i sho
 w how to prove the continuity of Bosonic quantum channel capacities (C\, Q
 \, P\, etc) with an energy constraint at the input.\n\n[Based on arXiv:171
 2.10267]
LOCATION:MR15\, Centre for Mathematical Sciences\, Wilberforce Road\, Camb
 ridge
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