Anno Accademico 2022/2023

  • Docente: Pierbiagio Pieri
  • Crediti formativi: 6
  • SSD: FIS/02
  • Lingua di insegnamento: Inglese
  • Moduli: Pierbiagio Pieri (Modulo 1) Lorenzo Piroli (Modulo 2)
  • Modalità didattica: Convenzionale - Lezioni in presenza (Modulo 1) Convenzionale - Lezioni in presenza (Modulo 2)
  • Campus: Bologna
  • Corso: Laurea Magistrale in Physics (cod. 9245)

Conoscenze e abilità da conseguire

At the end of the course, the student will become confident with the intrinsic and specific properties of states of a quantum system, acquiring knowledge about: the notion of entanglement and its manifestation through correlations existing in quantum matter; the quantum nature of light and its interaction with atoms. The student will be able to interpret some notable quantum phenomena involved in the manipulation of atoms and electromagnetic radiation, in order to study modern quantum information and computation theory.


Despite being more than a century old, many aspects of quantum mechanics still leave students puzzled because of their counter-intuitive predictions with respect to our classical experience.

Such “unusual” behaviour is due to the properties and the kind of information that “quantum states” can hold.

  • Module 1: Quantum states of atoms and light (P. Pieri - 28h)
  • Quantum theory of light; electromagnetic oscillator, Fock states
  • Coherent states: theory and properties, squeezed states
  • Atoms in e.m. field; dipole approximation; the Rabi and Jaynes-Cummings models
  • Some notions on macroscopic quantum-coherent phenomena: introduction to superfluidity and superconductivity; explanation of basic phenomenology in terms of macroscopic wave function; BEC with ultracold gases
  • Module 2: Quantum information & entanglement ( - 20h)

    • States and ensembles: Density matrices. Schmidt decomposition

    • Quantum measurements: projective-valued measures (PVM) and positive operator-valued measures (POVM)

    • Quantum evolution: Quantum instruments. Completely positive trace-preserving maps. Kraus representation. Examples: amplitude damping, dephasing, depolarizing channels

    • Entanglement theory: EPR and Bell inequalities, entanglement measures

    • Entanglement as a resource: Dense coding, teleportation, quantum key distribution


Entanglement, quantum information and quantum computation

1) Michael A. Nielsen, Isaac L. Chuang, Quantum Computation and Quantum Information, ‎Cambridge University Press

2) Mark M. Wilde, Quantum Information Theory, Cambridge University Press

Quantum states of atoms and light

1) Lecture notes available on the repository virtuale.unibo.it

2) Christopher C. Gerry, Peter L. Knight, Introductory Quantum Optics, Cambridge University Press, Cambridge (2005)

3) Ulf Leonhardt, Measuring the Quantum State of Light, Cambridge University Press, Cambridge (1997)

Metodi didattici

Lecture-based teaching

Modalità di verifica e valutazione dell'apprendimento

Oral exam.

It consists of (at least) two questions, one for each part of the program.

Students should demonstrate to be familiar and have a good understanding of the different subjects.

They will be asked to both present an introduction to the main general topics and to prove more specific results, making connections among the different parts of the syllabus.

The organization of the presentation and a rigorous scientific language will be also considered for the formulation of the final grade.

The “cum laude” honor will be granted to students who demonstrate a personal and critical rethinking of the subject.

According to the general rules of the University, students will be allowed to reject the grade only once, but they can withdraw at any time during the exam.

Strumenti a supporto della didattica

Most of the material is available on-line in the university repository.

Orario di ricevimento

Consulta il sito web di Pierbiagio Pieri

Consulta il sito web di Lorenzo Piroli


Istruzione di qualità

L'insegnamento contribuisce al perseguimento degli Obiettivi di Sviluppo Sostenibile dell'Agenda 2030 dell'ONU.