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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Unions\, intersections and a one shot quantum join
t typicality lemma - Pranab Sen (Tata Institute of
Fundamental Research)
DTSTART;TZID=Europe/London:20180726T090000
DTEND;TZID=Europe/London:20180726T094500
UID:TALK108385AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/108385
DESCRIPTION:A fundamental tool to prove inner bounds in
classical network information theory is the so-cal
led `conditional joint typicality lemma'\;. In
addition to the lemma\, one often uses unions and
intersections of typical sets in the inner bound a
rguments without so much as giving them a second t
hought. These arguments fail spectacularly in the
quantum setting. This bottleneck shows up in the f
act that so-called `simultaneous decoders'\;\,
as opposed to `successive cancellation decoders
9\;\, are known for very few channels in quantum n
etwork information theory.
In this talk w
e shall see how to overcome the bottleneck by prov
ing for the first time a one-shot quantum joint ty
picality lemma with robust union and intersection
properties. To do so we develop two novel tools&nb
sp\; in quantum information theory\, which we call
tilting and smoothing\, which should be of indepe
ndent interest.
Our joint typicality lemm
a allows us to construct simultaneous quantum deco
ders for many multiterminal quantum channels and g
ives a \; powerful tool to extend many results
in classical network information theory to the on
e-shot quantum setting. We shall see a glimpse of
this in the talk by constructing a one shot simult
aneous decoder for the quantum multiple access cha
nnel with an arbitrary number of senders. Our one<
br> shot rates reduce to the known optimal rates w
hen restricted to the asymptotic iid setting\, whi
ch were previously obtained by successive cancella
tion and time sharing.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:INI IT
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