**Research**

Mathematical aspects of identifying entangled quantum states (entanglement witnesses, nonlinear entanglement criteria, spin squeezing inequalities)

Methods for the experimental creation and detection of entanglement in quantum optical systems (photonic systems, spin squeezing in cold atomic ensembles, optical lattices of cold atoms)

Multi-particle singlet states in cold gases (see link at Morgan W. Mitchell's group)

Multi-particle entanglement of Dicke states

Scalable state tomography (Permutationally Invariant Quantum Tomography)

Application of entangled quantum states for quantum metrology (e.g., differential magnetometry with cold atomic ensembles)

Quantum Fisher Information and its relation to multipartite entanglement

Foundations of quantum theory (Bell inequalities and local hidden variable models)

1.
Polytope of separable states for the Optimal Spin Squeezing
Inequalities. [Figure from Phys. Rev. Lett. 99, 25045 (2007);
Phys. Rev. A 79, 042334 (2009).]

2. Setup generating a four-qubit symmetric Dicke state with two excitations with parametric down-conversion in a BBO crystal, linear optical elements and detectors. [Figure from Phys. Rev. Lett. 98, 063604 (2007).]

3. Results of Permutationally Invariant Tomography in a four-photon experiment [Figure from Phys. Rev. Lett. 105, 250403 (2010).]

4. Multipartite entanglement in Dicke states created with cold gases [Figure from Phys. Rev. Lett. 112, 155304 (2014). ]

5. Bipartite entanglement in Dicke states created with cold gases [Figure from Science 360, 416 (2018).]