Speakers: Matéo Spriet (LPP, Lille)

In the 80’s, Richard Feynman developed the idea that it could be possible to exploit some properties of quantum systems to build computers that are faster and more powerful than classical computers (i.e., those governed by the laws of classical physics). As any classical system can be seen as a quantum system with a great number of particles, it becomes crucial to be able to determine which systems are « purely quantum », so that one may hope to obtain a « quantum advantage ». I this talk, I will present a way to tackle this problem mathematically, by using the notion of quasiprobabilistic representation of quantum mechanics. I will start by describing the mathemathical models of classical and quantum physics: the former using random variables on symplectic manifolds,  the latter using operators on Hilbert spaces. A quasiprobabilistic representation is then a way to establish a partial correspondence between these two models. Such a representation allows in particular to single out a « classical fragment of quantum mechanics », which can be seen as a sub-part of quantum mechanics that cannot be used to achieve any quantum <a href="http://advantage.

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https://indico.math.cnrs.fr/event/16463/