  Quantum noise is ubiquitous to quantum systems as they incessantly interact
with their surroundings and results in degrading useful resources such as
coherence for single quantum systems and quantum correlations for multipartite
systems. Given the importance of these resources in various quantum information
processing protocols, it is of utmost importance to characterize how
deteriorating is a particular noise scenario (quantum channel) in reference to
a certain resource? Here we develop a theory of coherence breaking channels for
single quantum systems. Any quantum channel on a single quantum system will be
called a coherence breaking channel if it is an incoherent channel and maps any
state to an incoherent state. We explicitly and exhaustively characterize these
coherence breaking channels. Moreover, we define the coherence breaking indices
for incoherent quantum channels and present various examples to elucidate this
concept. We further introduce the concept of coherence sudden death under noisy
evolutions and make an explicit connection of the phenomenon of coherence
sudden death with the coherence breaking channels and the coherence breaking
indices together with various suggestive examples. Furthermore, for higher
dimensional Hilbert spaces, we establish the typicality of the dynamics of
coherence under any incoherent quantum channel exploiting the concentration of
measure phenomenon.
