Characterizing Initial Correlations via Spectroscopy

In the presence of initial correlations, quantum evolution cannot be described in terms of completely positive trace preserving maps. Such initial correlations can arise due to strong coupling between the system and environment and inform the applicability of important results in physics, such as the quantum regression formula. Therefore it is vital to characterize these correlations for a better understanding of the system and proper quantum control.

Taking inspiration from correlated spectroscopy, we demonstrate a method to determine the correlation between the system and the environment. Our spectroscopic method extracts information about the initial correlations from the system by benefiting from the system - environment interactions. We apply this formalism to Nitrogen-Vacancy centers in diamonds interacting with photonic modes of a cavity.