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SUMMARY:Unions\, intersections and a one shot quantum joint typicality lem
 ma - Pranab Sen (Tata Institute of Fundamental Research)
DTSTART:20180726T080000Z
DTEND:20180726T084500Z
UID:TALK108385@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:<span>A fundamental tool to prove inner bounds in classical ne
 twork information theory is the so-called `conditional joint typicality le
 mma&#39\;. In addition to the lemma\, one often uses unions and intersecti
 ons of typical sets in the inner bound arguments without so much as giving
  them a second thought. These arguments fail spectacularly in the quantum 
 setting. This bottleneck shows up in the fact that so-called `simultaneous
  decoders&#39\;\, as opposed to `successive cancellation decoders&#39\;\, 
 are known for very few channels in quantum network information theory.<br>
  <br> In this talk we shall see how to overcome the bottleneck by proving 
 for the first time a one-shot quantum joint typicality lemma with robust u
 nion and intersection properties. To do so we develop two novel tools&nbsp
 \; in quantum information theory\, which we call tilting and smoothing\, w
 hich should be of independent interest.<br> <br> Our joint typicality lemm
 a allows us to construct simultaneous quantum decoders for many multitermi
 nal quantum channels and gives a&nbsp\; powerful tool to extend many resul
 ts in classical network information theory to the one-shot quantum setting
 . We shall see a glimpse of this in the talk by constructing a one shot si
 multaneous decoder for the quantum multiple access channel with an arbitra
 ry number of senders. Our one<br> shot rates reduce to the known optimal r
 ates when restricted to the asymptotic iid setting\, which were previously
  obtained by successive cancellation and time sharing.</span><br><br><br><
 br>
LOCATION:Seminar Room 1\, Newton Institute
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