 
Summary: Mathematics
and
Statistics
COLLOQUIUM
Doug Farenick
University of Regina
Extremal Quantum
Measurements
Friday, October 14, 2011
3:30 p.m.
Classroom Building 417
Abstract:This is a report on work done in collaboration with former UofR stu
dents Sarah Plosker and Jerrod Smith.
It is a standard and important fact of real analysis that the set of all Borel
probability measures on a (locally) compact Hausdorff sample space is a convex
(and weak*compact) set whose extreme points are precisely the Dirac measures
(that is, measures whose mass is concentrated at a single point). What is the
situation for probability measures whose values are quantum effects? The answer
appears to be known to theoretical physicists in the case of finite sample spaces.
The first theorem I present describes the extremal positive operatorvalued mea
