Continuous Functions as Quantum Operations: a probabilistic   approximation
  In this note we propose a version of the classical Stone-Weierstrass theorem in the context of quantum operations, by introducing a particular class of quantum operations, dubbed polynomial quantum operations. This result permits to interpret from a probabilistic point of view, and up to a certain approximation, any continuous function from the real cube [0; 1]^n to the real interval [0; 1] as a quantum operation. 
Hector Freytes, Antonio Ledda, Giuseppe Sergioli
quant-ph