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

Signatures of avoided energy-level crossings in entanglement indicators obtained from quantum tomograms