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SUMMARY:The compositional structure of multipartite quantum entanglement -
  Bob Coecke (Oxford)
DTSTART:20100422T131500Z
DTEND:20100422T141500Z
UID:TALK23307@talks.cam.ac.uk
CONTACT:Jonathan
DESCRIPTION:Multipartite quantum states constitute a (if not the) key reso
 urce for quantum computations and protocols.  However obtaining a generic\
 , structural understanding of entanglement in N-qubit systems is still lar
 gely an open problem.  Here we show that multipartite quantum entanglement
  admits a compositional structure.  The two SLOCC-classes of genuinely ent
 angled 3-qubit states\, the GHZ-class and the W-class\, exactly correspond
  with the two kinds of commutative Frobenius algebras on C^2\, namely `spe
 cial' ones and `anti-special' ones.  Within the graphical language of symm
 etric monoidal categories\, the distinction between `special' and `anti-sp
 ecial' is purely topological\, in terms of `connected' vs. `disconnected'.
   These GHZ and W Frobenius algebras form the primitives of a graphical ca
 lculus which is expressive enough to generate and reason about representat
 ives of arbitrary N-qubit states. This calculus induces a generalised grap
 h state paradigm for measurement-based quantum computing\, and refines  th
 e graphical calculus of complementary observables due to Duncan and one of
  the authors [ICALP'08]\, which has already shown itself to have many appl
 ications and admit automation.  \n\nReference: Aleks Kissinger and Bob Coe
 cke\, ICALP 2010\, http://arxiv.org/abs/1002.2540
LOCATION:MR11\, Centre for Mathematical Sciences
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