Detecting entanglement is important to verify required resources for the implementation of quantum-enabled strategies in quantum information and metrology. Testing whether a given state is entangled or not, however, is a highly challenging problem. The complexity is further enhanced in multipartite systems. We study the structure of entanglement among multiple quantum systems with discrete, continuous and hybrid variables. In many cases it is possible to to detect entanglement by quantifying the state's metrological sensitivity. We further study new methods for the efficient generation of entanglement in experiments.

• Z. Ren, W. Li, A. Smerzi, M. Gessner, Phys. Rev. Lett. 126, 080502 (2021).

• M. Fadel and M. Gessner, Phys. Rev. A 102, 012412 (2020).

• Z. Qin et al., npj Quantum Information 5, 3 (2019).

• M. Gessner, L. Pezzè, and A. Smerzi, Phys. Rev. A 95, 032326 (2017).

• M. Gessner, L. Pezzè, and A. Smerzi, Quantum 1, 17 (2017).

• M. Gessner, L. Pezzè, and A. Smerzi, Phys. Rev. A 94, 020101(R) (2016).

Steering is a stronger form of quantum correlations that can only be found in some entangled states. These correlations have applications in one-sided device independent protocols of quantum communication. We are interested in understanding these correlations from the perspective of quantum metrology and to develop sharper tools that allow us to reveal their presence in more complicated many-body states.

• B. Yadin, M. Fadel, M. Gessner, Nat. Commun. 12, 2410 (2021).

Entanglement is usually very fragile under incoherent evolutions. Under some conditions, however, entanglement can be preserved even though the purity decreases. This phenomenon can be explained geometrically for two qubits, but an exhaustive understanding in the multipartite case is still lacking.

• E. G. Carnio, A. Buchleitner, and M. Gessner, New J. Phys. 18, 073010 (2016).

• E. G. Carnio, A. Buchleitner, and M. Gessner, Phys. Rev. Lett. 115, 010404 (2015).

Besides entanglement, other forms of quantum correlations or coherent phenomena are relevant for specific applications of quantum information theory. Some correlations such as nonlocality or steering, are stronger than entanglement, other nonclassical features such as discord and coherence are weaker. Purity can be identified as the most elementary resource for nonclassical phenomena.

• M. Gessner and A. Smerzi, EPJ Quantum Technology 6, 4 (2019).

• A. Streltsov, H. Kampermann, S. Wölk, M. Gessner, and D. Bruß, New J. Phys. 20, 053058 (2018).

• Y. Li, M. Gessner, W. Li, and A. Smerzi, Phys. Rev. Lett. 120, 050404 (2018).

• M. Gessner, E.-M. Laine, H.-P. Breuer, and J. Piilo, Phys. Rev. A 85, 052122 (2012).