2014/12/30 by Frank Roumen
Computer Science · Mathematics · #cs.LO #math.CT
paper · pdf · doi:10.4204/eptcs.171.12
published as EPTCS 171, 2014, pp. 132-144 · In Proceedings QPL 2013, arXiv:1412.7917
arxiv created 2014/12/30 · arxiv updated 2014/12/31
The most general type of measurement in quantum physics is modeled by a positive operator-valued measure (POVM). Mathematically, a POVM is a generalization of a measure, whose values are not real numbers, but positive operators on a Hilbert space. POVMs can equivalently be viewed as maps between effect algebras or as maps between algebras for the Giry monad. We will show that this equivalence is an instance of a duality between two categories. In the special case of continuous POVMs, we obtain two equivalent representations in terms of morphisms between von Neumann algebras.