Why can states and measurement outcomes be represented as vectors?

Piero G. L. Mana

Published 2003-05-20, updated 2004-09-22Version 3

It is shown how, given a "probability data table" for a quantum or classical system, the representation of states and measurement outcomes as vectors in a real vector space follows in a natural way. Some properties of the resulting sets of these vectors are discussed, as well as some connexions with the quantum-mechanical formalism.