QLunch: Owidiusz Makuta

Speaker: Owidiusz Makuta, Center for Theoretical Physics, Polish Academy of Sciences

Title: From anticommuting operators to PPT entangled states 

Abstract: In this talk, I will present the results of our work focused on a group of hermitian, unitary operators that either mutually commute or anticommute. To start, I will discuss how, using a graph theory, we can uncover the underlying structure of these operators, based solely on their commutation/anticommutation relations. This, in turn, allows us to easily compute an upper bound on the sum of expected values (or their squares) of these operators. Interestingly, this has a multitude of applications such as computing geometric measures of entanglement for stabilizer subspaces and finding the largest eigenvalues of some simple Hamiltonians. Most importantly, this result can be used to construct an entanglement witness capable of detecting PPT (positive partial transpose) entanglement, as well as PPT entangled states themselves.