Transition from quantum to classical dynamics in weak measurements and reconstruction of quantum correlation

The ability to track and control the dynamics of a quantum system is the key to quantum technology. Despite its central role, the quantitative reconstruction of the dynamics of a single quantum system from the macroscopic data of the associated observable remains a problem. We consider this problem in the context of weak measurements of a single nuclear carbon spin in a diamond with an electron spin as a meter at room temperature, which is a well-controlled and understandable bipartite quantum system. In this work, based on a detailed theoretical analysis of the model of the experiment, we study the relationship between the statistical properties of the macroscopic readout signal of the spin of a single electron and the quantum dynamics of the spin of a single nucleus, which is characterized by a parameter associated with the strength of the measurement. We determine the parameter of measurement strength in separate experiments and use it to reconstruct the quantum correlation. We control the validity of our approach applying the Leggett-Garg test.