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CATEGORIES:CQIF Seminar
SUMMARY:Strong subadditivity of entropy: when is it (nearl
y) saturated? - Andreas Winter (University of Bris
tol)
DTSTART;TZID=Europe/London:20110210T141500
DTEND;TZID=Europe/London:20110210T151500
UID:TALK26333AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/26333
DESCRIPTION:Strong subadditivity of the quantum entropy (Lieb\
, Ruskai 1973) is the fundamental inequality\, use
d over and over again in quantum information and m
any-body physics. It states that for any state rho
on three parties A\, B\, C\,\n\nI(A:C|B) := S(AB)
+S(BC)-S(B)-S(ABC) >=0. (SSA)\n\nIn joint work w
ith Hayden\, Jozsa and Petz\, we had clarified the
structure of states saturating SSA. I will review
this result\, which in particular implies that fo
r such states\, rho_AC has to be separable. What c
an be said about the case when I(A:C|B) is "small"
? After reviewing the situation in the classical c
ase\, i formulate a general form for a conjectured
stronger subadditivity relation. Its simplest for
m turns out to be false. However\, if some version
of it holds\, this would have very interesting co
nsequences: it would imply that rho_AC is k-extend
ible\, where k is an anti-monotonic function of\nI
(A:C|B). This would extend and complement results
by Brandao\, Christandl and Yard (arXiv:1011.2751)
regarding the faithfulness of squashed entangleme
nt.\n\nThis talk is work in progress with Ke Li.
LOCATION:MR13\, Centre for Mathematical Sciences
CONTACT:Ashley Montanaro
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