Mathematical foundations of quantum theories: algebraic and geometric structures for the mathematical formulation of quantum mechanics. In particular, geometric Hamiltonian formulation of quantum theories w.r.t. the symplectic and Riemannian (Fubini-Study metric) structures in complex projective spaces.
Quantum information theory and quantum computing: application of the geometric formulation for the characterization of quantum information aspects (e.g. entanglement measures, entropy, quantum mutual information). Study of algorithms for adiabatic and gate-based quantum computers.
Hybrid quantum-classical algorithms: definition and characterization of hybrid algorithms for NISQ machines, in particular for solving optimization problems.
Quantum machine learning: techniques for implementing learning mechanisms in quantum machines.
Quantum cryptography: definition of quantum key distribution (QKD) protocols based on transmission of entangled states in device and semi-device independent scenarios. Security proofs and quantitative estimation of secret key rate.
Quantum logic: study of abstract structures for constructing out quantum logics from families of fuzzy sets.
