Physics 4999E Study Guide - Final Guide: Mark Naimark, Operator Theory, Partial Trace

• School: Western University
• Department: Physics
• Course: Physics 4999E
• Professor: john stockholm

Document Summary

Cs 766/qic 820 theory of quantum information (fall 2011) The following theorem expresses a fundamental relationship between ordinary measurements and projective measurements. It is known as naimark"s theorem, although one should under- stand that it is really a simple, nite-dimensional case of a more general theorem known by the same name that is important in operator theory. Theorem: the two names refer to the same individual, mark naimark, whose name has been transliterated in these two different ways. Let x be a complex euclidean space, let be a measurement on x , and let y = c . There exists a linear isometry a u (x , x y ) such that. : pos (x ) for every a . De ne a l (x , x y ) as. (a) = 1x , so a is a linear isometry, and a (1x ea,a)a = (a) for each a as required.