C8538 - QUANTUM INFORMATION THEORY

Learning outcomes

At the end of the course the student will have become familiar with the modern language of quantum information theory and with the concept of entanglement, both as a property of quantum matter and as an operational resource. During the course the student will learn about several applications of quantum information ideas, ranging from quantum communication and teleportation protocols, to quantum metrology and quantum simulation.

Course contents

This course provides an introduction to standard ideas in quantum information theory, covering applications to quantum optics and light-matter interactions, together with glimpses into quantum computation theory and quantum technologies.. The course is divided into two modules: Module 1 provides an introduction to quantum information concepts, ideas, and techniques, while Module 2 focuses on quantum optics and light-matter interactions.

Module 1: Entanglement, quantum information and quantum computation (24h)

• States and ensembles: Density matrices. Schmidt decomposition
• Quantum measurements: projective-valued measures (PVM) and positive operator-valued measures (POVM)
• Quantum evolution: Quantum channels and operations. CPT maps. Kraus and Stinesrping representations. Examples.
• Entanglement theory: EPR and Bell inequalities, entanglement measures
• Elements of Quantum Shannon Theory
• Entanglement as a resource. Local operations and classical communication. Dense coding, teleportation, quantum key distribution
• Elements of Quantum Computing

Module 2: Quantum states of atoms and light (24h)

• 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; AC Stark effect
• Wigner-Weisskopf theory of spontaneous emission

Readings/Bibliography

Lecture notes will be available on-line in the university repository. In addition, the following references will be useful

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) Steck, Quantum and Atom Optics, available at: https://atomoptics.uoregon.edu/~dsteck/teaching/quantum-optics/

Teaching methods

Lecture-based teaching

Assessment methods

Oral exam.

It consists of (at least) two questions, one for each module of the course. For the first module, one of the two questions will be an exercise, similar to those solved in class or given as homework during the course.

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.

Students with Specific Learning Disabilities (SLD) or temporary/permanent disabilities are advised to contact the University Office responsible in a timely manner (https://site.unibo.it/studenti-con-disabilita-e-dsa/en ). The office will be responsible for proposing any necessary accommodations to the students concerned. These accommodations must be submitted to the instructor for approval at least 15 days in advance, and will be evaluated in light of the learning objectives of the course.

Teaching tools

Lecture notes will be available on-line in the university repository

Office hours

See the website of Marcello Dalmonte

See the website of Lorenzo Piroli