Probing the Quantum Nature of Stochastic Spin Flip Dynamics in Nitrogen-Vacancy Centers via Nondemolition Quasiprobability Negativity

Stochastic spin flips in solid-state systems under longitudinal relaxation leads to apparent dephasing and loss of coherent information while such dynamics originate from quantum interactions between the system and its environment. Quantum nondemolition measurements enable a noninvasive reconstruction of temporal correlations in a quantum system, where the resulting quasiprobability distribution can exhibit negative regions that provide a necessary and sufficient signature of macrorealism violation while inherently satisfying no-signaling-in-time conditions. In this work, we extend the ND-quasiprobability framework to open quantum systems described by Kraus operators and apply it to Nitrogen nuclear spin flip-flop dynamics in nitrogen-vacancy (NV) centers in diamond under longitudinal relaxation. We derive a generalized form of the ND-quasiprobability distribution for stochastic spin-flip processes and show that, while its classical contribution remains normalized, the quantum contribution can produce negative regions that cannot be explained by classical stochastic models. By analyzing symmetry and normalization conditions, we identify parameter regimes in which negativity emerges as a signature of nonclassical behavior. Our results indicate that nuclear spin flip-flop dynamics in NV centers intrinsically retain quantum features and provide an experimentally accessible pathway for distinguishing quantum trajectories from classical noise in solid-state spin platforms.