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SUMMARY:Strong subadditivity of entropy: when is it (nearly) saturated? - 
 Andreas Winter (University of Bristol)
DTSTART:20110210T141500Z
DTEND:20110210T151500Z
UID:TALK26333@talks.cam.ac.uk
CONTACT:Ashley Montanaro
DESCRIPTION:Strong subadditivity of the quantum entropy (Lieb\, Ruskai 197
 3) is the fundamental inequality\, used over and over again in quantum inf
 ormation and many-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 with Hayden\, Jozsa and Petz\, we had clarified the structu
 re of states saturating SSA. I will review this result\, which in particul
 ar implies that for such states\, rho_AC has to be separable. What can be 
 said about the case when I(A:C|B) is "small"? After reviewing the situatio
 n in the classical case\, i formulate a general form for a conjectured str
 onger subadditivity relation. Its simplest form turns out to be false. How
 ever\, if some version of it holds\, this would have very interesting cons
 equences: it would imply that rho_AC is k-extendible\, 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 faithfuln
 ess of squashed entanglement.\n\nThis talk is work in progress with Ke Li.
LOCATION:MR13\, Centre for Mathematical Sciences
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