Geometric Phases In Weak Measurements

We explore a natural extension of the Abelian geometric phase factor in sequences of incomplete measurements to include high dimensional quantum states in the weak measurement scenario. To achieve the goal, we focus on sequential weak measurements of non-commuting projectors and combine the idea of weak measurements and the notion of a non-Abelian geometric phase. In this way, we find that the non-Abelian geometric phase in the weak measurement scenario can be useful to gain information about the space of states and the connection between them, favorable to reproducing the overlap matrix and the Wilson Loop