BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//talks.cam.ac.uk//v3//EN
BEGIN:VTIMEZONE
TZID:Europe/London
BEGIN:DAYLIGHT
TZOFFSETFROM:+0000
TZOFFSETTO:+0100
TZNAME:BST
DTSTART:19700329T010000
RRULE:FREQ=YEARLY;BYMONTH=3;BYDAY=-1SU
END:DAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:+0100
TZOFFSETTO:+0000
TZNAME:GMT
DTSTART:19701025T020000
RRULE:FREQ=YEARLY;BYMONTH=10;BYDAY=-1SU
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
CATEGORIES:Peter Whittle Lecture
SUMMARY:An afternoon of talks exploring the links between
classical information theory\, probability\, stati
stics and their quantum counterparts. - Reinhard W
erner (Hannover)\, Fernando Brandao (Microsoft Re
search)\, Robert Koenig (TU Munich)\, Renato Renn
er (ETH Zurich)
DTSTART;TZID=Europe/London:20150128T140000
DTEND;TZID=Europe/London:20150128T181000
UID:TALK57434AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/57434
DESCRIPTION:An afternoon of talks exploring the links between
classical information theory\, probability\, stati
stics and their quantum counterparts.\n\n*2.00pm
Reinhard Werner (Hannover): Quantum Walks*\n\nLik
e random walks\, quantum walks are dynamical syste
ms on a lattice with a discrete time step. In con
trast to their classical counterparts\, however\,
they are reversible\, unitary processes. They mov
e faster\, i.e.\, with a limiting speed\, rather t
han proportional to the square root of the number
of steps. I will sketch a proof of the basic limi
t formula\, and give a large deviation estimate fo
r speeds outside the propagation region. Under tim
e-dependent but translation invariant noise the wa
lk typically slows down to the classical\, diffusi
ve scaling\, whereas with space dependent but stat
ionary disorder (in one dimension) one gets Anders
on localization\, i.e.\, no propagation at all. Th
is phenomenon is also typical for quasi-periodic w
alks\, like walks in an external electric field. F
inally\, I will discuss the recurrence of walks in
a scenario\, where the return to the initial stat
e is monitored by repeated measurements. It turns
out that recurrence has a straightforward characte
rization in terms of the spectrum of the unitary w
alk operator.\n\n\n\n\n*2.55pm Fernando Brandao (M
icrosoft Research\, Seattle): Hypothesis Testing a
nd Stein's Lemma for Quantum Systems*\n\nI will di
scuss quantum generalisations of hypothesis testin
g\, in particular of the well-known Stein's Lemma\
; the latter shows that the relative entropy is th
e optimal rate in asymmetric hypothesis testing be
tween two probability measures. I will discuss ext
ensions of the quantum version of Stein's lemma or
iginally proven by Hiai and Petz in 1991 and show
their relevance to the theory of quantum entanglem
ent.\n\n\n3.50 Coffee Break\n\n*4.20pm Robert Koe
nig (TU Munich) : Entropy Power Inequalities*\n\nT
he classical entropy power inequality\, originally
proposed by Shannon\, is a powerful tool in multi
-user information theory. In this talk\, I review
some of the history of this inequality\, as well a
s Shannon’s original application: such inequalitie
s provide bounds on the capacities of additive noi
se channels. I then introduce a quantum entropy p
ower inequality which lower bounds the output entr
opy as two independent signals combine at a beamsp
litter. In turn\, such inequalities provide upper
bounds on the classical capacity of additive boson
ic noise channels.\nThis is based on joint work wi
th Graeme Smith.\n\n\n*5.15 pm Renato Renner (ETH
Zurich) : Approximate Markov Chains*\n\nThree rand
om variables\, A\, B\, and C\, are said to satisfy
the Markov chain property if A and C are indepen
dent of each other conditioned on B. The degree to
which this property holds is related to an inform
ation-theoretic measure\, known as the “conditiona
l mutual information”. More precisely\, it can be
shown that the Markov chain property holds approx
imately if and only if the mutual information betw
een A and C conditioned on B is small. In my talk\
, I will explain how this statement can be extende
d 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
CONTACT:HoD Secretary\, DPMMS
END:VEVENT
END:VCALENDAR