We establish a novel approach to probing spatially resolved multi-time correlation functions of interacting many-body systems, with scalable experimental overhead. Specifically, designing nonlinear measurement protocols for multidimensional spectra i
n a chain of trapped ions with single-site addressability enables us, e.g., to distinguish coherent from incoherent transport processes, to quantify potential anharmonicities, and to identify decoherence-free subspaces.
As one of the most striking features of quantum mechanics, quantum correlations are at the heart of quantum information science. Detection of correlations usually requires access to all the correlated subsystems. However, in many realistic scenarios
this is not feasible since only some of the subsystems can be controlled and measured. Such cases can be treated as open quantum systems interacting with an inaccessible environment. Initial system-environment correlations play a fundamental role for the dynamics of open quantum systems. Following a recent proposal, we exploit the impact of the correlations on the open-system dynamics to detect system-environment quantum correlations without accessing the environment. We use two degrees of freedom of a trapped ion to model an open system and its environment. The present method does not require any assumptions about the environment, the interaction or the initial state and therefore provides a versatile tool for the study of quantum systems.
