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 communication in the field of Quantum Technologies, in the various interdisciplinary aspects. 
• Learning skills – Acquiring skills allowing the continuous upgrade of the knowledge in the field, by accessing a research environment and specialized literature.

Main goals are:

• Learning basic conceptual and operational tools
  (basic concepts of quantum mechanics for information processing and communication, both for representation and dynamics; main physical systems used to detect quantum coherent effects and to process quantum information, from solid-state nanodevices to atomic and photonic architectures; basic examples of quantum protocols)
• Know a bit about what’s going on in current fundamental and applied research
• Develop new skill and competencies
  (overview of theoretical techniques; ability to explore the use of quantum mechanics in different physical contexts of Quantum Technologies; ability to judge the state of the art and relative progress; acquire a basis to decide they you want to work in this field and come up with their own idea of how to do an interesting project)

1. Representation of quantum systems (12+2 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 (12+2 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 (6+2 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 (4 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 (2 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.

• L'esame orale standard comprende: (a) esposizione di un argomento a scelta del candidato, concordato in anticipo col docente; (b) esposizione di un argomento scelto dal candidato tra tre proposti dal docente, di diversa difficoltà. Il superamento dell'esame dipende dalla prova (a) mentre la (b) determina la valutazione.
• A richiesta dello studente, e previo il consenso del docente, la prova (a) può essere sostituita da un elaborato che comprenda un calcolo analitico o numerico che lo studente dovrà sviluppare in maniera indipendente ma assistita.     
• La valutazione è operata tenendo conto di: pertinenza delle risposte rispetto alle domande formulate; livello di comprensione dei contenuti esposti; accuratezza nell'esposizione dei calcoli; capacità di collegamento con altri temi dell'insegnamento (o di insegnamenti precedenti) e di riportare esempi; proprietà di linguaggio e chiarezza espositiva.

Le domande di seguito riportate non costituiscono un elenco esaustivo ma rappresentano solo alcuni esempi

- Derivare l'algebra di SU(2);

- Spazi di Liouville ed esempi di basi

- Derivare l'espressione esplicita di funzioni di operatori nilpotenti, idempotenti e di matrici di Pauli.

- Quantizzazione in circuiti mesoscopici

- Relazione tra U(2) e SU(2)

- Sistemi composti, fattorizzazione, operatori (gate) entangling 

- Soluzioni formali per la dinamica

- Oscillazioni coerenti e oscillazioni di Rabi

- Trasformazioni di gauge e trasformazioni untarie dipendenti dal tempoù

- Sistemi bipartiti: entanglement

- Sistemi bipartiti: misura

- Sistemi bipartiti: decoerenza