  The Renyi entropy plays an essential role in quantum information theory. We
study the continuity estimation of the Renyi entropy. An inequality relating
the Renyi entropy difference of two quantum states to their trace norm distance
is derived. This inequality is shown to be tight in the sense that equality can
be attained for every prescribed value of the trace norm distance. It includes
the sharp Fannes inequality for von Neumann entropy as a special case.
