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SUMMARY:Quantum Conditional States\, Bayes' Rule\, and State Compatibility
  - Matthew Leifer (UCL)
DTSTART:20110303T141500Z
DTEND:20110303T151500Z
UID:TALK29111@talks.cam.ac.uk
CONTACT:Ashley Montanaro
DESCRIPTION:Quantum theory is a noncommutative generalization of classical
  probability theory. In the classical theory\, conditional probability pla
 ys an important role in both theory and applications\, but its quantum\nco
 unterpart is conspicuous by its absence. In this talk\, I will introduce t
 he formalism of quantum conditional states\, which is essentially just a c
 hange of notation that makes the equations of \nstandard quantum theory lo
 ok closer to their classical counterparts. This makes it easier to general
 ize classical concepts\, and has the \nadvantage that it unifies the treat
 ment of quantum dynamics with the treatment of correlations between quantu
 m systems. Conditional states allow for a quantum generalization of Bayes'
  rule\, which has appeared multiple times in the quantum information/found
 ations literature\, albeit in a disguised form. Examples of the quantum Ba
 yes' rule include: the relationship between retrodictive states and predic
 tive POVMs in the retrodictive quantum formalism of Pegg et. al. (generali
 zed to include \nbiased sources)\, the rule for updating the state of a re
 mote system after a measurement\, the ``almost optimal error correction'' 
 of Knill and Barnum\, and the ``pretty good'' measurement of Hausladen and
  \nWootters. As an application of the formalism\, I present a novel justif
 ication for the Brun-Finklestein-Mermin criterion for state \ncompatibilit
 y that would be acceptable to a Quantum Bayesian who thinks that quantum s
 tates represent subjective degrees of belief.\n
LOCATION:MR13\, Centre for Mathematical Sciences
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