  We introduce the problem of stability verification of quantum sources which
are non-i.i.d.. The problem consists in ascertaining whether a given quantum
source is stable or not, in the sense that it produces always a desired quantum
state or if it suffers deviations. Stability is a statistical notion related to
the sparsity of errors. This problem is closely related to the problem of
quantum verification first proposed by Pallister et. al. [1], however, it
extends the notion of the original problem. We introduce a family of states
that come from these non-i.i.d. sources which we call a Markov state. These
sources are more versatile than the i.i.d. ones as they allow statistical
deviations from the norm instead of the more coarse previous approach. We prove
in theorem 1 that the Markov states are not well described with tensor products
over a changing source. In theorem 2 we further provide a lower bound on the
trace distance between two Markov states, or conversely, an upper bound on the
fidelity between these states. This is a bound on the capacity of determining
the stability property of the source, which shows that it is exponentially
easier to ascertain this with respect to n, the number of outcomes from the
source.
