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SUMMARY:An afternoon of talks exploring the links between classical inform
 ation theory\, probability\, statistics and their quantum counterparts. - 
 Reinhard Werner (Hannover)\, Fernando  Brandao (Microsoft Research)\,  Rob
 ert Koenig (TU Munich)\, Renato Renner (ETH Zurich)
DTSTART:20150128T140000Z
DTEND:20150128T181000Z
UID:TALK57434@talks.cam.ac.uk
CONTACT:HoD Secretary\, DPMMS
DESCRIPTION:An afternoon of talks exploring the links between classical in
 formation theory\, probability\, statistics and their quantum counterparts
 .\n\n*2.00pm  Reinhard Werner  (Hannover): Quantum Walks*\n\nLike random w
 alks\, quantum walks are dynamical systems on a lattice with a discrete ti
 me step.  In contrast to their classical counterparts\, however\, they are
  reversible\, unitary processes.  They move faster\, i.e.\, with a limitin
 g speed\, rather than proportional to the square root of the number of ste
 ps.  I will sketch a proof of the basic limit formula\, and give a large d
 eviation estimate for speeds outside the propagation region. Under time-de
 pendent but translation invariant noise the walk typically slows down to t
 he classical\, diffusive scaling\, whereas with space dependent but statio
 nary disorder (in one dimension) one gets Anderson localization\, i.e.\, n
 o propagation at all. This phenomenon is also typical for quasi-periodic w
 alks\, like walks in an external electric field. Finally\, I will discuss 
 the recurrence of walks in a scenario\, where the return to the initial st
 ate is monitored by repeated measurements. It turns out that recurrence ha
 s a straightforward characterization in terms of the spectrum of the unita
 ry walk operator.\n\n\n\n\n*2.55pm Fernando Brandao (Microsoft Research\, 
 Seattle): Hypothesis Testing and Stein's Lemma for Quantum Systems*\n\nI w
 ill discuss quantum generalisations of hypothesis testing\, in particular 
 of the well-known Stein's Lemma\; the latter shows that the relative entro
 py is the optimal rate in asymmetric hypothesis testing between two probab
 ility measures. I will discuss extensions of the quantum version of Stein'
 s lemma originally proven by Hiai and Petz in 1991 and show their relevanc
 e to the theory of quantum entanglement.\n\n\n3.50  Coffee Break\n\n*4.20p
 m Robert Koenig (TU Munich) : Entropy Power Inequalities*\n\nThe classical
  entropy power inequality\, originally proposed by Shannon\, is a powerful
  tool in multi-user information theory. In this talk\, I review some of th
 e history of this inequality\, as well as Shannon’s original application
 : such inequalities provide bounds on the capacities of additive noise cha
 nnels.  I then introduce a quantum entropy power inequality which lower bo
 unds the output entropy as two independent signals combine at a beamsplitt
 er. In turn\, such inequalities provide upper bounds on the classical capa
 city of additive bosonic noise channels.\nThis is based on joint work with
  Graeme Smith.\n\n\n*5.15 pm Renato Renner (ETH Zurich) : Approximate Mark
 ov Chains*\n\nThree random variables\, A\, B\, and C\, are said to satisfy
  the Markov chain property if  A and C are independent of each other condi
 tioned on B. The degree to which this property holds is related to an info
 rmation-theoretic measure\, known as the “conditional mutual information
 ”.  More precisely\, it can be shown that the Markov chain property hold
 s approximately if and only if the mutual information between A and C cond
 itioned on B is small. In my talk\, I will explain how this statement can 
 be extended to the more general setting where A\, B\, and C are arbitrary 
 quantum systems. \n\n\n\n\n
LOCATION:MR15  Centre for Mathematical Sciences
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