Reznick's Positivstellensatz and applications to quantum information theory

par M. Alexander Müller-Hermes (Université Lyon 1)

mardi 5 nov. 2019, 11:30 → 13:30 Europe/Paris

Salle du conseil du LIP 394 Nord (ENS Lyon)

In his solution of Hilbert’s 17th problem Artin showed that any positive definite polynomial in several variables can be written as the quotient of two sums of squares. Later Reznick showed that the denominator in Artin’s result can always be chosen as an N-th power of a specific quadratic form and gave explicit bounds on N. By using concepts from quantum information theory (such as partial traces and an identity due to Chiribella) we present a simpler proof of a complex version of this result and we will mention applications to quantum information theory.