  Extensive theoretical and experimental investigations on multipartite systems
close to an avoided energy-level crossing reveal interesting features such as
the extremisation of entanglement. Conventionally, the estimation of
entanglement directly from experimental observation involves either one of two
approaches: Uncertainty-relation-based estimation that captures the linear
correlation between relevant observables, or rigorous but error-prone quantum
state reconstruction on tomograms obtained from homodyne measurements. We
investigate the behaviour, close to avoided crossings, of entanglement
indicators that can be calculated directly from a numerically-generated
tomogram. The systems we study are two generic bipartite continuous-variable
systems: a Bose-Einstein condensate trapped in a double-well potential, and a
multi-level atom interacting with a radiation field. We also consider a
multipartite hybrid quantum system of superconducting qubits interacting with
microwave photons. We carry out a quantitative comparison of the indicators
with a standard measure of entanglement, the subsystem von Neumann entropy
(SVNE). It is shown that the indicators that capture the nonlinear correlation
between relevant subsystem observables are in excellent agreement with the
SVNE.
