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CATEGORIES:CQIF Seminar
SUMMARY:Quantum theory from simple physical principles for
single systems - Howard Barnum (University of New
Mexico)
DTSTART;TZID=Europe/London:20150305T141500
DTEND;TZID=Europe/London:20150305T151500
UID:TALK57643AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/57643
DESCRIPTION:We describe simple physically and informationally
meaningful principles that give rise to the quantu
m description of finite-dimensional systems terms
of density matrices and positive operator-valued m
easures.\n\nThe first three principles characteriz
e finite dimensional formally real Jordan-algebrai
c systems: real\, complex\, and quaternionic quant
um theory\, plus systems whose state spaces are ba
lls\, and one exceptional\ncase. The principles ar
e (1) a generalized spectral decomposition\, (2) a
high degree of symmetry\, and (3) that there is n
o irreducible three (or more) path interference.
We'll explore the physical\nimplications of the pr
inciples\, individually and in various combination
s.\n\nComplex quantum theory then follows from "lo
cal tomography": that the state of a composite sys
tem be determinable from the statistics (including
correlations) of local observables. But one may
obtain quantum theory without considering composit
e systems\, by requiring (4)\n"energy observabilit
y": the generators of reversible dynamics are obse
rvables.\n\nDropping (3) might allow systems enjoy
ing many properties of quantum physics\, but exhib
iting higher-order interference\; we'll discuss pr
operties of such theories\, in particular whether
they support good notions of entropy and a reasona
ble statistical mechanics\, and whether they are p
ossible candidates for new physics encompassing qu
antum theory as a limiting case.\n\nTime permittin
g\, the possibility and properties of composites o
f systems satisfying (1-3) (Jordan-algebraic syste
ms) will be discussed.
LOCATION:MR4\, Centre for Mathematical Sciences\, Wilberfo
rce Road\, Cambridge
CONTACT:William Matthews
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