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SUMMARY:Attempting to reverse the irreversible in quantum physics - Mark W
 ilde (Louisiana State University)
DTSTART:20150106T110000Z
DTEND:20150106T120000Z
UID:TALK56960@talks.cam.ac.uk
CONTACT:William Matthews
DESCRIPTION:Some mathematical consequences of the postulates of quantum ph
 ysics are several entropy inequalities established in the 1970s\, such as 
 the strong subadditivity of quantum entropy and the monotonicity of quantu
 m relative entropy under physical processes. These entropy inequalities ar
 e statements of irreversibility and thus have been connected to thermodyna
 mics and to establishing optimality of communication protocols in quantum 
 information theory. Strong subadditivity is the statement that the entropy
  sum of two individual systems is larger than entropy sum of their union a
 nd intersection. Monotonicity of quantum relative entropy is the statement
  that the relative entropy between two quantum states does not increase af
 ter they each undergo the same physical process. These inequalities\, alon
 g with joint convexity of relative entropy and concavity of conditional qu
 antum entropy\, are all known to be equivalent to each other\, and thus we
  can say that together they constitute a fundamental law of quantum inform
 ation theory. In this talk\, I will highlight recent progress on the "reco
 very problem\," that is\, how well can we try to reverse an irreversible p
 hysical process\, or\, can we refine our understanding of this fundamental
  law of quantum information theory? In particular\, after giving some back
 ground\, I will focus the discussion on a "remainder term" for monotonicit
 y of quantum relative entropy and I will also show how the aforementioned 
 entropy inequalities are equivalent to each other even with remainder term
 s present. This is joint work with Kaushik Seshadreesan\, Marius Lemm\, an
 d Mario Berta from arXiv:1403.6102\, arXiv:1410.1441\, arXiv:1410.1443\,  
 arXiv:1412.0333\, arXiv:1412.4067.\n
LOCATION:MR12\,  Centre for Mathematical Sciences\, Wilberforce Road\, Cam
 bridge
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