The interaction of information and control has been a topic of interest to system
theorists that can be traced back at least to the 1950’s when the fields of communications, control,
and information theory were new but developing rapidly. Recent advances in our understanding of
this interplay have emerged from work on the dynamical effect of state quantization together with
results connecting communication channel data rates and system stability. Although this work has
generated considerable interest, it has been centrally concerned with the relationship between control
system performance and feedback information processing rates while ignoring the complexity (i.e. the
cost of information processing). The concepts of communication and computation complexity of a
controlled dynamical system based on digitized information lie in what is largely an uncharted area.
In our recent work an attempt was made to explore this area by introducing a new measure of
communication complexity for a two-player distributed control system. This complexity is named
control communication complexity (CCC). It is based on the communication complexity concept
defined in distributed computing and seeks to connect the complexity of information exchange over
finite bandwidth channels with the control system dynamics. The purpose of the present paper is
to extend the study of control communication complexity to an interesting class of continuous-time
control systems that have appeared in the recent literature dealing with quantum communication
and control systems. An interesting aspect of this extension is that it brings together heretofore
independent research themes that have been prominent in the research career of Roger Brockett.