  We examine the physical manifestations of exceptional points and passage
times in a two-level system which is subjected to quantum measurements and
which admits a non-Hermitian description. Using an effective Hamiltonian acting
in the two-dimensional space spanned by the evolving initial and final states,
the effects of highly precise quantum measurements in which the monitoring
device interferes significantly with the evolution dynamics of the monitored
two-level system is analysed. The dynamics of a multipartite system consisting
of the two-level system, a source of external potential and the measurement
device is examined using correlation measures such as entanglement and
non-classical quantum correlations. Results show that the quantum correlations
between the monitored (monitoring) systems is considerably decreased
(increased) as the measurement precision nears the exceptional point, at which
the passage time is half of the measurement duration. The results indicate that
the underlying mechanism by which the non-classical correlations of quantum
systems are transferred from one subsystem to another may be better revealed
via use of geometric approaches.
