# Giuseppe Marmo

- Cátedras de Excelencia
- Cátedras de excelencia 2016
- Giuseppe Marmo

### Giuseppe Marmo - Universita di Napoli Federico II, Italy

Prof. Marmo has been full professor of physics at the University Federico II at Naples since 1986. He has made significant scientific contributions on theoretical and mathematical physics, among others, to the theory of non-Abelian monopoles, to the no-interaction theorem in relativistic particle dynamics, to the inverse problem in the calculus of variations and to the classical and quantum theory of bi-Hamiltonian systems. Recently he has contributed to the study of the geometrical structure of the space of quantum states in connection with the characterisation of separability and entanglement for composite systems. He has also contributed to the formulation of nonlinear coherent states for deformed oscillators and to the foundations of Quantum Tomography. Currently he is working on the geometry of Quantum Information Theory that constitutes the core of the presented research proposal. He has published more than 300 papers on these and other topics in the most prestigious specialised international journals and is a member of various editorial committees.

**Research stay at UC3M: **DEPARTMENT OF MATHEMATICS (NOV 2016 - MAY 2017)

The geometrization of Quantum Mechanics and the quantum Fisher-Rao metric.

In addition to the study of operator algebras, Lie-Jordan algebras and reduction procedures, quantum states and their evolution, all of this devoted to discuss foundational properties of quantum mechanics, we would like to focus here on the tomographic picture of quantum mechanics along with the geometrical formulation ofquantum mechanics to develop a quantum information geometry.

Braunstein and Caves found measurements that optimally resolve neighboring quantum states and characterized their degree of distinguishability in terms of a Riemannian metric, the so called Fisher-Rao quantum metric. Under this focus, the probabilistic aspects of quantum mechanics would be developed in the direction pointed by the geometrization program of Quantum Mechanics sketched above. In the particular instance of pure states, the Fisher-Rao metric coincides with the Fubini-Study metric connections, curvature, geodesics, Jacobi endomorphisms, all of them aimed at investigating complexity problems.