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SUMMARY:Negative Probabilities\, Fine's Theorem and Quantum Histories - Jo
 nathan J. Halliwell (Imperial College London)
DTSTART:20140612T133000Z
DTEND:20140612T143000Z
UID:TALK53000@talks.cam.ac.uk
CONTACT:William Matthews
DESCRIPTION:Many situations in quantum theory and other areas of physics l
 ead to quasi-probabilities which seem to be physically useful but can be n
 egative. The interpretation of such objects is not at all clear. In this p
 aper\, we show that quasi-probabilities naturally fall into two qualitativ
 ely different types\, according to whether their non-negative marginals ca
 n or cannot be matched to a non-negative probability. The former type\, wh
 ich we call viable\, are qualitatively similar to true probabilities\, but
  the latter type\, which we call non-viable\, may not have a sensible inte
 rpretation. Determining the existence of a probability matching given marg
 inals is a non-trivial question in general. In simple examples\, Fine's th
 eorem indicates that inequalities of the Bell and CHSH type provide criter
 ia for its existence. A simple proof of Fine's theorem is given.  Our resu
 lts have consequences for the linear positivity condition of Goldstein and
  Page in the context of the histories approach to quantum theory. Although
  it is a very weak condition for the assignment of probabilities it fails 
 in some important cases where our results indicate that probabilities clea
 rly exist. Some implications for the histories approach to quantum theory 
 are discussed.
LOCATION:MR3\,  Centre for Mathematical Sciences\, Wilberforce Road\, Camb
 ridge
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