  We characterize the non-commutative Aleksandrov--Clark measures and the
minimal realization formulas of contractive and, in particular, isometric
non-commutative rational multipliers of the Fock space. Here, the full Fock
space over $\mathbb{C} ^d$ is defined as the Hilbert space of square--summable
power series in several non-commuting formal variables, and we interpret this
space as the non-commutative and multi-variable analogue of the Hardy space of
square--summable Taylor series in the complex unit disk. We further obtain
analogues of several classical results in Aleksandrov--Clark measure theory for
non-commutative and contractive rational multipliers.
  Non-commutative measures are defined as positive linear functionals on a
certain self-adjoint subspace of the Cuntz--Toeplitz algebra, the unital
$C^*-$algebra generated by the left creation operators on the full Fock space.
Our results demonstrate that there is a fundamental relationship between NC
Hardy space theory, representation theory of the Cuntz--Toeplitz and Cuntz
algebras, and the emerging field of non-commutative rational functions.
