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CATEGORIES:CQIF Seminar
SUMMARY:Attempting to reverse the irreversible in quantum
physics - Mark Wilde (Louisiana State University)
DTSTART;TZID=Europe/London:20150106T110000
DTEND;TZID=Europe/London:20150106T120000
UID:TALK56960AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/56960
DESCRIPTION:Some mathematical consequences of the postulates o
f quantum physics are several entropy inequalities
established in the 1970s\, such as the strong sub
additivity of quantum entropy and the monotonicity
of quantum relative entropy under physical proces
ses. These entropy inequalities are statements of
irreversibility and thus have been connected to th
ermodynamics and to establishing optimality of com
munication protocols in quantum information theory
. Strong subadditivity is the statement that the e
ntropy sum of two individual systems is larger tha
n entropy sum of their union and intersection. Mon
otonicity of quantum relative entropy is the state
ment that the relative entropy between two quantum
states does not increase after they each undergo
the same physical process. These inequalities\, al
ong with joint convexity of relative entropy and c
oncavity of conditional quantum entropy\, are all
known to be equivalent to each other\, and thus we
can say that together they constitute a fundament
al law of quantum information theory. In this talk
\, I will highlight recent progress on the "recove
ry problem\," that is\, how well can we try to rev
erse an irreversible physical process\, or\, can w
e refine our understanding of this fundamental law
of quantum information theory? In particular\, af
ter giving some background\, I will focus the disc
ussion on a "remainder term" for monotonicity of q
uantum relative entropy and I will also show how t
he aforementioned entropy inequalities are equival
ent to each other even with remainder terms presen
t. This is joint work with Kaushik Seshadreesan\,
Marius Lemm\, and 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\, Wilberf
orce Road\, Cambridge
CONTACT:William Matthews
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