Quantum Information Theory
A.Y. 2024/2025
Learning objectives
The course illustrates the physical origin of information theory and provides notions of modern quantum mechanics, with emphasis on implementations in atomic and quantum-optical systems. It also illustrates the most recent development of quantum information theory and the possible implementations of new protocols for transmission and manipulation of information.
Expected learning outcomes
Students will learn:
1. how to recognize information as a physical resource, with examples where the quantum nature of physical systems improve performances;
2. how to characterize entanglement of bipartite systems;
3. how to characterize nonlocality of physical systems and how to write Bell inequalities;
4. how to apply the notion of quantum estimation theory to find ultimate bound to precision of quantum measurements;
5. how to describe and quantify quantum enhancement in teleportation, dense coding, quantum cryptography and quantum metrology;
6. he/she will able to state the theorems of Naimark, Kraus and Shannon, and will be able to provide a mathematical proof of the first two.
1. how to recognize information as a physical resource, with examples where the quantum nature of physical systems improve performances;
2. how to characterize entanglement of bipartite systems;
3. how to characterize nonlocality of physical systems and how to write Bell inequalities;
4. how to apply the notion of quantum estimation theory to find ultimate bound to precision of quantum measurements;
5. how to describe and quantify quantum enhancement in teleportation, dense coding, quantum cryptography and quantum metrology;
6. he/she will able to state the theorems of Naimark, Kraus and Shannon, and will be able to provide a mathematical proof of the first two.
Lesson period: Second semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course cannot be attended as a single course. Please check our list of single courses to find the ones available for enrolment.
Course syllabus and organization
Single session
Responsible
Lesson period
Second semester
Course syllabus
1. Density matrix, operator-valued measures, quantum operations. Naimark
and Kraus-Sudarshan theorems. Qubit and Bloch-sphere.
2. No-cloning theorem. Information-disturbance tradeoff in quantum
mechanics.
3. Locality and realism: Bell's and CHSH inequalities.
Hidden variables models. Nonlocality tests.
4. Entanglement: Schmidt decomposition, entropy. LOCC operations and
PPT conditions. Separability and decoherence. Entanglement measures.
5. Applicatons of entanglement: teleportation, dense coding,
high-precision measurements, binary communication, cryptography.
6. Distillations and concentration of entanglement.
7. Quantum hypothesis testing: Bayes and Neyman-Pearson criteria.
Optimal POVM and applications.
8. Quantum estimation theory: local and global estimation. Fisher
information, quantum Cramer-Rao bound and optical estimation of
parameters.
9. Classical communication theory: mutual information and Shannon's theorems.
Quantum communication theory: Holevo bound and Schumacher's theorem.
and Kraus-Sudarshan theorems. Qubit and Bloch-sphere.
2. No-cloning theorem. Information-disturbance tradeoff in quantum
mechanics.
3. Locality and realism: Bell's and CHSH inequalities.
Hidden variables models. Nonlocality tests.
4. Entanglement: Schmidt decomposition, entropy. LOCC operations and
PPT conditions. Separability and decoherence. Entanglement measures.
5. Applicatons of entanglement: teleportation, dense coding,
high-precision measurements, binary communication, cryptography.
6. Distillations and concentration of entanglement.
7. Quantum hypothesis testing: Bayes and Neyman-Pearson criteria.
Optimal POVM and applications.
8. Quantum estimation theory: local and global estimation. Fisher
information, quantum Cramer-Rao bound and optical estimation of
parameters.
9. Classical communication theory: mutual information and Shannon's theorems.
Quantum communication theory: Holevo bound and Schumacher's theorem.
Prerequisites for admission
- Non relativistic quantum mechanics.
- Linear algebra
- Group theory.
- Linear algebra
- Group theory.
Teaching methods
Attendance: strongly advised.
Lectures: traditional, frontal lectures.
Lectures: traditional, frontal lectures.
Teaching Resources
Lecture notes available on Ariel + recorded lectures.
Other material:
M. Nielsen, E. Chuang
Quantum Computation and Quantum Information
(Cambridge University Press, 2000)
I. Bengtsson, K. Zyczkowski
Geometry of Quantum States
(Cambridge University Press, 2006)
A. Peres
Quantum Theory: concepts and methods
(Kluwer Academic, Dordrecht, 1993)
R. Puri
Mathematical Methods of quantum optics
(Springer, Berlin, 2005)
J. Preskill
Course Information for Physics 219
Other material:
M. Nielsen, E. Chuang
Quantum Computation and Quantum Information
(Cambridge University Press, 2000)
I. Bengtsson, K. Zyczkowski
Geometry of Quantum States
(Cambridge University Press, 2006)
A. Peres
Quantum Theory: concepts and methods
(Kluwer Academic, Dordrecht, 1993)
R. Puri
Mathematical Methods of quantum optics
(Springer, Berlin, 2005)
J. Preskill
Course Information for Physics 219
Assessment methods and Criteria
Oral exams to assess the understanding of the fundamental concepts, the ability of using them to solve problems, and the acquisition of working knowledge about the mathematical methods.
Professor(s)
Reception:
By appointment only (upon agreement by email)
LITA building, room A5/C11