  Electron spin states of solid-state defects such as Nitrogen- and
Silicon-vacancy {\em color centers} in diamond are a leading quantum-memory
candidate for quantum communications and computing. Via open-quantum-systems
modeling of spin-phonon coupling -- the major contributor of decoherence -- at
a given temperature, we derive the time dynamics of the density operator of an
electron-spin qubit. We use our model to corroborate experimentally-measured
decoherence rates. We further derive the temporal decay of distillable
entanglement in spin-spin entangled states heralded via photonic Bell-state
measurements. Extensions of our model to include other decoherence mechanisms,
e.g., undesired hyperfine couplings to the neighboring nuclear-spin
environment, will pave the way to a rigorous predictive model for engineering
artificial-atom qubits with desirable properties.
