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$B0J2<$NFbMF$G!"(BOxford$BBg3X$N(BJamie Vicary$B$5$s$N9V1i$rM=Dj$7$F$*$j$^$9!#(B $B7wO@$rMQ$$$?NL;R7W;;!&NL;R>pJs$N8&5f$K4X$9$kOCBj$G$9$,!"Hs@lLg2H$N(B $BJ}$bG0F,$KCV$$$F$*OC$7D:$-$^$9!#3'MM$N$4;22C$r$*BT$A$7$F$*$j$^$9!#(B
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$B9V1i<T(B Jamie Vicary $B;a(B (Dept. Computer Science, Univ. Oxford / Centre for Quantum Technologies, Univ. Singapore)
$BBjL\(B THE GEOMETRY OF QUANTUM AND CLASSICAL INFORMATION
$BF|;~(B 2013$BG/(B9$B7n(B12$BF|!JLZ!K(B11:00-12:00
$B>l=j(B $B5~ETBg3XAm9g8&5f#29f4[(B 4$B3,(B478$B9f<<(B http://www.kurims.kyoto-u.ac.jp/~hassei/map-2.jpg $B!J?tM}2r@O8&5f=jK\4[$G$O$"$j$^$;$s!"$4Cm0U2<$5$$!K(B
$B35MW(B Recent work has shown a beautiful connection between geometry and information flow, in both quantum and classical computer science. Diagrams involving points, lines and regions encode basic phenomena such as quantum measurement, entanglement creation, secret key preparation and encryption. Procedures such as quantum teleportation, quantum dense coding and encrypted communication can then be defined as equations between these diagrams, such that solutions to these equations in the correct 2-category correspond precisely to implementations of these algorithms in the ordinary sense. This work has many connections to other areas of mathematics and physics, such as topological quantum field theory, representation theory, and higher category theory, which I will briefly describe. All mathematical aspects will be introduced from scratch, so this talk should make sense to non-specialists.
$BLd9g$;(B $BD9C+@n???M!J5~ETBg3X?tM}2r@O8&5f=j!K(B<hassei at kurims.kyoto-u.ac.jp>
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