  Topological phases are often characterized by special edge states confined
near the boundaries by an energy gap in the bulk. On raising temperature, these
edge states are lost in a clean system due to mobile thermal excitations.
Recently however, it has been established that disorder can localize an
isolated many body system, potentially allowing for a sharply defined
topological phase even in a highly excited state. Here we show this to be the
case for the topological phase of a one dimensional magnet with quenched
disorder, which features spin one-half excitations at the edges. The time
evolution of a simple, highly excited, initial state is used to reveal quantum
coherent edge spins. In particular, we demonstrate, using theoretical arguments
and numerical simulation, the coherent revival of an edge spin over a time
scale that grows exponentially bigger with system size. This is in sharp
contrast to the general expectation that quantum bits strongly coupled to a
'hot' many body system will rapidly lose coherence.
