Anatole Khelif is a teacher-researcher and lecturer specializing in mathematical logic. He is an alumnus of the École normale supérieure, rue d’Ulm. For several years now, he has been leading a seminar on categorical logic. He is interested in the links between logic and category theory, geometry and probability theory. He is also interested in theoretical physics, working with Marc Lachieze-Rey. Anatole Khelif has also organized the SIC (Séminaire itinérant de catégories) on several occasions. He supervised Christophe Chalons’ thesis on “ludic degrees”. For him, logic is a very schematic attempt to describe how our brains work.

Precisely the quantum connection allows quantum teleportation which is not the teleportation of Star Trek. In fact, this connection does not allow information to be transmitted faster than light. We propose an initial classification of “connection strengths” called “playful degrees”. The strongness of two connections is compared by the following way : a connection is weaker than an other if we can reduce the first to the second by a “playful reduction“. They can range from no connection to the perfect transmission of information. We will study interesting classes of connections: trivial connections, FMQ connections which can be reduced from a quantum entanglement, ”casino harmless” connexions which can’t send ”probabilistic information” and stronger connections. We will give definitions, examples and counter-examples.