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CATEGORIES:CQIF Seminar
SUMMARY:Unifying typical entanglement and coin tossing: on
randomization in probabilistic theories - Oscar D
ahlsten (University of Oxford/National University
of Singapore)
DTSTART;TZID=Europe/London:20111117T141500
DTEND;TZID=Europe/London:20111117T151500
UID:TALK33269AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/33269
DESCRIPTION:It is well-known that pure quantum states are typi
cally almost maximally entangled\, and thus have c
lose to maximally mixed subsystems. We consider wh
ether this is true for probabilistic theories more
generally\, and not just for quantum theory. We d
erive a formula for the expected purity of a subsy
stem in any probabilistic theory for which this qu
antity is well-defined. It applies to typical enta
nglement in pure quantum states\, coin tossing in
classical probability theory\, and randomization i
n post-quantum theories\; a simple generalization
yields the typical entanglement in (anti)symmetric
quantum subspaces. The formula is exact and simpl
e\, only containing the number of degrees of freed
om and the information capacity of the respective
systems. It allows us to generalize statistical ph
ysics arguments in a way which depends only on coa
rse properties of the underlying theory. The proof
of the formula generalizes several randomization
notions to general probabilistic theories. This in
cludes a generalization of purity.
LOCATION:MR4\, Centre for Mathematical Sciences
CONTACT:Paul Skrzypczyk
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