  In this paper we propose a scheme for quasi-perfect state transfer in a
network of dissipative harmonic oscillators. We consider ideal sender and
receiver oscillators connected by a chain of nonideal transmitter oscillators
coupled by nearest-neighbor resonances. From the algebraic properties of the
dynamical quantities describing the evolution of the network state, we derive a
criterion, fixing the coupling strengths between all the oscillators, apart
from their natural frequencies, enabling perfect state transfer in the
particular case of ideal transmitter oscillators. Our criterion provides an
easily manipulated formula enabling perfect state transfer in the special case
where the network nonidealities are disregarded. By adjusting the common
frequency of the sender and the receiver oscillators to be out of resonance
with that of the transmitters, we demonstrate that the sender's state tunnels
to the receiver oscillator by virtually exciting the nonideal transmitter
chain. This virtual process makes negligible the decay rate associated with the
transmitter line on the expenses of delaying the time interval for the state
transfer process. Apart from our analytical results, numerical computations are
presented to illustrate our protocol.
