  Models of quantum disentanglement are developed for nanometer-scale molecular
charge qubits (MCQs). Two MCQs, $A$ and $B$, are prepared in a Bell state and
separated for negligible $A$-$B$ interactions. Interactions between the local
environment and each MCQ unravels $A$-$B$ entanglement during coherent
system+environment evolution. Three models are used for dynamics: (1) a
previously-developed, numerical model, in which both $AB$ and environment
$\mathcal{E}$ are modeled explicitly; (2) an exact, semi-analytic model, in
which only the dynamics of $AB$ are calculated, and (3) an approximate model
developed from the semi-analytic model and assumptions about randomness in
$\mathcal{E}$. In the approximate model, the non-zero coherences of the density
operator for $AB$ decay with a Gaussian time dependence. This provides a time
scale for system dynamics in the exact models as well. This time scale is
related directly to the strength of AB-$\mathcal{E}$ interaction. This time
scale describes cases where environmental interaction with one target MCQ is
dominant, generalizing a previous time scale applicable only when both MCQs
have roughly the same strength of interaction with the local environment.
Entanglement is measured using two-qubit correlation functions, the dynamics of
which are used to demonstrate the effectiveness of the time scale. The
early-time decay of coherences and the loss of entanglement is
well-characterized as Gaussian, a behavior that Markovian models for memoryless
environments cannot capture. The approximate Gaussian model may be used to
describe the dynamics of MCQ disentanglement under the influence of
environments modeled here, as well as other environments where randomness is
present.
