Non-Markovian Quantum Memory in a Hybrid NV Center--Mechanical Mode System: BLP and RHP Characterization of Spin--Phonon Coupling Effects

We investigate non-Markovian quantum memory in a negatively charged nitrogen-vacancy (NV) center strain-coupled to a quantized mechanical mode. From the spin-1 NV Hamiltonian and the C_3v spin--strain interaction, we derive an effective qubit--phonon model with transverse exchange and longitudinal phase-modulation couplings. The open dynamics is described by a GKSL master equation, and memory in the reduced qubit channel is characterized using trace-distance backflow for the orthogonal reference pair │±〉= (│0〉± │-1〉) / √2 and the Rivas--Huelga--Plenio (RHP) CP-divisibility criterion. At resonance, the reference-pair BLP backflow follows transverse > hybrid > longitudinal, whereas the extrapolated RHP quantity follows hybrid > transverse >> longitudinal. Adding g_z / ω_m = 0.10 to the transverse baseline g⊥ / ω_m = 0.20 reduces the reference-pair backflow by 8.61% while increasing the RHP quantity by approximately 78.65%. This opposite response is traced to the distinct roles of coherent exchange and longitudinal phase modulation in distinguishability recovery and full-channel CP-indivisibility. The same ordering contrast persists over the sampled detuning interval, whereas thermal occupation can modify the BLP hierarchy and induce isolated noninvertibility of the reduced dynamical map for some exchange-containing regimes. Numerical validation and convergence tests confirm the robustness of the principal resonance result and delineate the validity of the inverse-based RHP construction.