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SUMMARY:Unifying typical entanglement and coin tossing: on randomization i
 n probabilistic theories - Oscar Dahlsten (University of Oxford/National U
 niversity of Singapore)
DTSTART:20111117T141500Z
DTEND:20111117T151500Z
UID:TALK33269@talks.cam.ac.uk
CONTACT:Paul Skrzypczyk
DESCRIPTION:It is well-known that pure quantum states are typically almost
  maximally entangled\, and thus have close to maximally mixed subsystems. 
 We consider whether this is true for probabilistic theories more generally
 \, and not just for quantum theory. We derive a formula for the expected p
 urity of a subsystem in any probabilistic theory for which this quantity i
 s well-defined. It applies to typical entanglement in pure quantum states\
 , coin tossing in classical probability theory\, and randomization in post
 -quantum theories\; a simple generalization yields the typical entanglemen
 t in (anti)symmetric quantum subspaces. The formula is exact and simple\, 
 only containing the number of degrees of freedom and the information capac
 ity of the respective systems. It allows us to generalize statistical phys
 ics arguments in a way which depends only on coarse properties of the unde
 rlying theory. The proof of the formula generalizes several randomization 
 notions to general probabilistic theories. This includes a generalization 
 of purity.
LOCATION:MR4\, Centre for Mathematical Sciences
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