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CATEGORIES:CQIF Seminar
SUMMARY:Quantum Conditional States\, Bayes' Rule\, and Sta
te Compatibility - Matthew Leifer (UCL)
DTSTART;TZID=Europe/London:20110303T141500
DTEND;TZID=Europe/London:20110303T151500
UID:TALK29111AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/29111
DESCRIPTION:Quantum theory is a noncommutative generalization
of classical probability theory. In the classical
theory\, conditional probability plays an importan
t role in both theory and applications\, but its q
uantum\ncounterpart is conspicuous by its absence.
In this talk\, I will introduce the formalism of
quantum conditional states\, which is essentially
just a change of notation that makes the equations
of \nstandard quantum theory look closer to their
classical counterparts. This makes it easier to g
eneralize classical concepts\, and has the \nadvan
tage that it unifies the treatment of quantum dyna
mics with the treatment of correlations between qu
antum systems. Conditional states allow for a quan
tum generalization of Bayes' rule\, which has appe
ared multiple times in the quantum information/fou
ndations literature\, albeit in a disguised form.
Examples of the quantum Bayes' rule include: the r
elationship between retrodictive states and predic
tive POVMs in the retrodictive quantum formalism o
f Pegg et. al. (generalized to include \nbiased so
urces)\, the rule for updating the state of a remo
te system after a measurement\, the ``almost optim
al error correction'' of Knill and Barnum\, and th
e ``pretty good'' measurement of Hausladen and \nW
ootters. As an application of the formalism\, I pr
esent a novel justification for the Brun-Finkleste
in-Mermin criterion for state \ncompatibility that
would be acceptable to a Quantum Bayesian who thi
nks that quantum states represent subjective degre
es of belief.\n
LOCATION:MR13\, Centre for Mathematical Sciences
CONTACT:Ashley Montanaro
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