  Trapped atomic ions enable a precise quantification of the flow of
information between internal and external degrees of freedom by employing a
non-Markovianity measure [H.-P. Breuer et al., Phys. Rev. Lett. 103, 210401
(2009)]. We reveal that the nature of projective measurements in quantum
mechanics leads to a fundamental, nontrivial bias in this measure. We observe
and study the functional dependence of this bias to permit a demonstration of
applications of local quantum probing. An extension of our approach can act as
a versatile reference, relevant for understanding complex systems.
