  We discuss the structure of decoherence-free subsystems for a bosonic channel
affected by collective depolarization. A single use of the channel is defined
as a transmission of a pair of bosonic modes. Collective depolarization
consists in a random linear U(2) transformation of the respective mode
operators, which is assumed to be identical for $N$ consecutive uses of the
channel. We derive a recursion formula that characterizes the dimensionality of
available decoherence-free subsystems in such a setting.
