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SUMMARY:Spectral methods for quantum Markov chains - Oleg Szehr (Technisch
 e Universität München)
DTSTART:20140227T141500Z
DTEND:20140227T151500Z
UID:TALK49940@talks.cam.ac.uk
CONTACT:William Matthews
DESCRIPTION:Quantum Markov chains constitute a natural quantum-mechanical 
 generalization of the concept of a Markov chain and are used to model the 
 evolution of certain quantum systems.\nBoth in the classical and quantum c
 ontext many applications require estimates that quantify convergence time 
 and stability of the chain.\nWe develop a powerful framework that yields s
 uch estimates in terms of the spectrum of the transition map.\nThe methods
  employed are new even to the well studied theory of classical Markov chai
 ns.\nThe key observation is to relate the original problem of bounding a f
 unction of a transition map of a Markov chain to a Nevanlinna-Pick interpo
 lation problem in Wiener algebra.\nWe provide an introduction to an operat
 or theoretic approach to the Nevanlinna-Pick problem employing Ando's Theo
 rem and other strong results from the theory of Hilbert function spaces.
LOCATION:MR4\,  Centre for Mathematical Sciences\, Wilberforce Road\, Camb
 ridge
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