  A quantum system subjected to a strong continuous monitoring undergoes
quantum jumps. This very well known fact hides a neglected subtlety: sharp
scale-invariant fluctuations invariably decorate the jump process even in the
limit where the measurement rate is very large. This article is devoted to the
quantitative study of these remaining fluctuations, which we call spikes, and
to a discussion of their physical status. We start by introducing a classical
model where the origin of these fluctuations is more intuitive and then jump to
the quantum realm where their existence is less intuitive. We compute the exact
distribution of the spikes for a continuously monitored qubit. We conclude by
discussing their physical and operational relevance.
