  It is known that a macroscopic quantum superposition (MQS), when it is
exposed to environment, decoheres at a rate scaling with the separation of its
component states in phase space. This is more or less consistent with the well
known proposition that a more macroscopic quantum state is reduced more quickly
to a classical state in general. Effects of initial mixedness, however, on the
subsequent decoherence of MQSs have been less known. In this paper, we study
the evolution of a highly mixed MQS interacting with an environment, and
compare it with that of a pure MQS having the same size of the central distance
between its component states. Although the decoherence develops more rapidly
for the mixed MQS in short times, its rate can be significantly suppressed
after a certain time and becomes smaller than the decoherence rate of its
corresponding pure MQS. In an optics experiment to generate a MQS, our result
has a practical implication that nonclassicality of a MQS can be still
observable in moderate times even though a large amount of noise is added to
the initial state.
