Scrambling and quantum feedback in a nanomechanical system

The question of how swiftly entanglement spreads over a system has attracted vital interest. In this regard, the out-of-time-ordered correlator (OTOC) is quantitative measure spreading process. Particular interest concerns propagation quantum correlations in lattice systems, e.g., spin chains. seminal paper Roberts et al. (J. High Energy Phys. 03:051, 2015), concept OTOC’s radius was introduced. OTOC defines front line reached by spread entanglement. Beyond operators commute. present work, we propose model two nanomechanical systems coupled with nitrogen-vacancy (NV) center spins. Oscillators are to each other directly, while NV spins not. Therefore, correlation between may arise only through feedback exerted from first oscillator and transferred second via direct coupling. Thus, nonzero quantifies strength feedback. We show that cannot exert on classical nonlinear oscillators. also discuss inherently case linear harmonic indirectly coupling verify limit oscillator, vanishes.