Continuous functions as quantum operations: A probabilistic approximation

FREYTES, HECTOR CARLOS;LEDDA, ANTONIO;SERGIOLI, GIUSEPPE

2010-01-01

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Abstract

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.