Laboratoire d'Informatique de Grenoble

Abstract

Interactive theorem provers are tools that permit users to produce formal mathematical proofs. These tools have been used to guarantee that highly non-trivial proofs are indeed correct, and, in some cases, have permitted the detection of gaps in already published proofs.
In this talk we investigate how interactive theorem provers can be used in the context of quantum computing, by formalizing fundamental notions from this domain. More precisely, we present a formalization of projective measurements in Isabelle/HOL, along with the formal construction of the projective measurement associated with a given observable. We also formalize local joint probability distributions and the CHSH inequality, which permits to prove that there is no local hidden-variable theory for quantum mechanics.