Researchers have developed a new theoretical approach to distinguish whether two states of a many-body quantum system belong to different topological classes. The methodology is based on expressing a "strange correlator" —a recent tool for quantum topological discrimination— as a function of Kirkwood-Dirac quasiprobabilities (KDQs). KDQs offer a first-principles representation of two-time quantum correlators, enabling a detailed analysis of topological properties.

The connection between strange correlators and KDQs reveals that the former can be interpreted as weak values of an observable. This observable is capable of transforming an initial trivial state into a topologically non-trivial one. This interpretation has led to the proposal of a quantum topology "witness," which can be measured by observing the prior and subsequent effects of a sudden quench in a many-body system. Such a sudden quench is precisely the type of transformation that induces a transition between trivial and topological phases.

The work also proposes an interferometric protocol for topological discrimination, exploiting schemes that allow for the complete reconstruction of KDQs. This protocol is evaluated on a probe quantum state, whose main features are detailed in the study. The implementation of such measurement schemes and the reconstruction of KDQs opens the door to the experimental characterization of quantum state topology, which is crucial for the development of quantum computing and topological materials.