  This paper is concerned with open quantum systems whose dynamic variables
have an algebraic structure, similar to that of the Pauli matrices for
finite-level systems. The Hamiltonian and the operators of coupling of the
system to the external bosonic fields depend linearly on the system variables.
The fields are represented by quantum Wiener processes which drive the system
dynamics according to a quasilinear Hudson-Parthasarathy quantum stochastic
differential equation whose drift vector and dispersion matrix are affine and
linear functions of the system variables. This setting includes the
zero-Hamiltonian isolated system dynamics as a particular case, where the
system variables are constant in time, which makes them potentially applicable
as a quantum memory. In a more realistic case of nonvanishing system-field
coupling, we define a memory decoherence time when a mean-square deviation of
the system variables from their initial values becomes relatively significant
as specified by a weighting matrix and a fidelity parameter. We consider the
decoherence time maximization over the energy parameters of the system and
obtain a condition under which the zero Hamiltonian provides a suboptimal
solution. This optimization problem is also discussed for a direct energy
coupling interconnection of such systems.
