QUANTUM INFORMATION AND FOUNDATIONS

The course introduces concepts and techniques of advanced quantum mechanics, from theoretical foundations to applications in "Quantum Technologies". The course is centred on quantum bipartite systems, the founding concept for the study of quantum "mysteries" as entanglement, decoherence and measurement. Applied to quantum dynamics of electrons and photons in coherent systems/architectures, these phenomena provide the paradigm of quantum computation and communication.

• Knowledge and understanding – Knowledge of the main ideas and theoretical/numerical techniques for the study of the dynamics of complex quantum systems. Knowledge of the working principles of state-of-the-art physical systems.

• Applying knowledge and understanding – Ability in the application of basic theoretical techniques and approximations in the analysis/simulation of dynamical processes in quantum systems. Ability in familiarizing themselves with new opportunities offered by Quantum Technologies.  

• Marking judgements - Ability in making choices concerning the education process and the thesis. Ability in developing personal interpretations of physical phenomena. Ability in evaluating potentialities offered by Quantum Technologies for post-degree academic or industrial jobs.

• Communication skills – Ability in communicate in the field of Quantum Technologies, in the various interdisciplinary aspects. 

• Learning skills – Acquiring skills which allow the continuous upgrade of the knowledge in the field, by accessing a research environment and specialized literature.

Corses of quantum mechanics and "Advanced quantum Mechanics", condensed matter physics and "Solid-state physics", elements of statistical mechanics, linear algebra and functional spaces. We also suggest attending the courses of   "Superconductivity and superfluidity" e di "Mesoscopic and Topological materials" which however are not strictly propedeutical.

Attending the lectures is warmly suggested

1. Representation of quantum systems (4 h)

   Quantum bits, composite systems; physical systems (photons, nuclear spin, confined atoms, artificial atoms based on semiconductors/superconductors, cavities); algebra in Hilbert spaces and applications to quantum networks; examples; classical and quantum computation (seminar)

2. Quantum dynamics (4 h)

   Time evolution operator; pulsed dynamics; Heisenberg and von Neumann equation and their phenomenological generalization to relaxation and dephasing; quantum systems in oscillatory fields; time-dependent unitary transformations (rotating frame, adiabatic frame, geometric phases)

3. Bipartite and multipartite systems (4 h)

   Density matrix; quantum measurement and von Neumann model; applications (superdense coding, no-cloning theorem, cryptography, quantum teleportation)  Entanglement; EPR paradox and Bell inequality (seminar).

4. Coherent nanosystems (0 h) (two or three of the following topics)

   NMR molecules in liquids; photons and atoms in cavities; artificial atoms and circuit QED; trapped ions and cold atoms; nanomechanical and nanoelectromechanical systems; topological excitations in condensed matter.

5. Selected topic (3 h) (seminar, one of the following topics)

   New quantum technologies for measurement and sensing; open quantum systems; introduction to quantum information; introduction to quantum thermodynamics; introduction to quantum control theory.

[1] M. Nielsen and I. Chuang. Quantum Computation and Quantum Information. Cambridge University Press, Cambridge, 2010.

[2] S. Haroche and J.M. Raimond, Exploring the Quantum: Atoms, Cavities and Photons, Oxford, 2006.

[3] G. Falci, Quantum Foundations and Technologies: lecture notes & slides

[4] G. Chen, D. A. Church, B.-G. Englert, C. Henkel, B. Rohwedder, M. O. Scully, and M. S. Zubairy. Quantum Computing Devices: Principles, Designs and Analysis. Chapman and Hall/CRC, 2007.

[5] C. P. Williams and S. H. Clearwater, Explorations in Quantum Computing, Springer Verlag, New York, 1998.

[6] G. Benenti, G. Casati, D. Rossini, Principles of Quantum Computation and Information: a comprehensive textbook, World Scientific, 2019