Laboratoire de Physique Théorique
Toulouse - UMR 5152

One of the defining properties of quantum mechanics is the existence of incompatible observables, of which the observables of position and momentum are a well-known example. In this talk, we will connect the problem of determining whether a given set of measurements is compatible to the inclusion of free spectrahedra. Free spectrahedra are objects arising in convex optimization. After a short introduction to the theory of free spectrahedra, we show how results from algebraic convexity can be used to quantify the degree of incompatibility of binary quantum measurements. In particular, this new connection will allow to completely characterize the case in which the dimension of the quantum system is exponential in the number of measurements.