  We investigate the role of Segal's Gamma-spaces in the context of classical
and quantum information, based on categories of finite probabilities with
stochastic maps and density matrices with quantum channels. The information
loss functional extends to the setting of probabilistic Gamma-spaces considered
here. The Segal construction of connective spectra from Gamma-spaces can be
used in this setting to obtain spectra associated to certain categories of
gapped systems.
