In a quantum system coupled with a non-Markovian environment, quantum information may flow out of or in to the system. Measuring quantum information flow and its sensitivity to perturbations is important for a better understanding of open quantum systems and for the implementation of quantum technologies. Information gets shared between a quantum system and its environment by means of system-environment correlations (SECs) that grow during their interaction. We design a nuclear magnetic resonance (NMR) experiment to directly observe the evolution of the SECs and use the second moment of their distribution as a natural metric for quantifying the flow of information. In a second experiment, by accounting for the environment dynamics, we study the sensitivity of the shared quantum information to perturbations in the environment. The metric used in this case is the out-of-time-order correlation function (OTOC). By analyzing the decay of the OTOC as a function of the SEC spread, instead of the evolution time, we are able to demonstrate its exponential behavior.The development of quantum technologies is obstructed by the loss of quantum properties caused by interactions with the environment that lead to decoherence [1][2][3][4][5]. Quantum information is shared with the environment by means of systemenvironment correlations (SECs) [6][7][8]. In the case of interactions with a non-Markovian environment, the SECs may lead to the flow of quantum information back to the system [9, 10]. Interferences arising from this backflow may be catastrophic to quantum information processes taking place in the system. The purpose of this work is to investigate the growth of the SECs as a function of time and to gauge how susceptible they are to perturbations in the environment. An open question with respect to the latter point is whether environment perturbations can be used to reduce information backflow.Our experiment is well-equipped to directly measure correlations between the system and the environment. It builds upon solid-state nuclear magnetic resonance (NMR) methods that have been employed to detect multiple-quantum coherences in homonuclear many-body systems [11][12][13][14][15][16][17][18][19]. These methods have recently been used for the investigation of multiple-quantum coherences in ion traps [20,21]. A change in the encoding basis has allowed for the observation of multispin dynamics of correlation growth during the free induction decay experiment [14,16]. Here, we extend these methods to composite heteronuclear systems to measure the growth of correlations with the environment.We consider a central spin model, which consists of a single spin-1/2 interacting with environment spins of another spin species that may also be coupled [22][23][24][25]. Quantum information initially resides in the central spin and is later shared with the environment in the form of multi-spin SECs. * Email: mniknam@uwaterloo.ca NMR techniques make it possible to separate the systemenvironment evolution from the internal evolution of the enviro...
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