  This paper is concerned with open quantum harmonic oscillators (OQHOs)
described by linear quantum stochastic differential equations. This framework
includes isolated oscillators with zero Hamiltonian, whose system variables
remain unchanged (in the Heisenberg picture of quantum dynamics) over the
course of time, making such systems potentially applicable as quantum memory
devices. In a more realistic case of system-environment coupling, we define a
memory decoherence horizon as a typical time for a mean-square deviation of the
system variables from their initial values to become relatively significant as
specified by a weighting matrix and a fidelity parameter. We consider the
maximization of the decoherence time over the energy and coupling matrices of
the OQHO as a memory system in its storage phase and obtain a condition under
which the zero Hamiltonian delivers a suboptimal solution. This optimization
problem is also discussed for an interconnection of OQHOs.
