David Rasmussen Lolck

Self-testing results allow us to characterize measurements and states in a quantum device from classical output probabilities in a nonlocal game. However, there is some variation in how the individual self- testing statements are stated and proven, including whether they apply robustly or assume purity of the state or protectiveness of the measurements. We investigate these differences, and as one of our main results show that if the reference strategy of a given game has full Schmidt rank, the notions of self-testing strategies using either mixed or pure states coincide. Additionally, we show by example that not all types of self-testing statements are equivalent: We both provide an example of a nonlocal game which is an exact, but not a robust, self-test, and an example of another game which does not self-test any state.