Quantum Stochastics and Quantum Learning

Recent advancements in quantum technology, such as quantum computing, communication and metrology have created renewed interest in the probabilistic and statistical challenges posed by quantum information theory. While the fundamental principles of detecting and processing statistical signals remain the same, the statistical inference and information-theoretic bounds in quantum models deviate from their classical counterparts due to the unique nature of quantum probability. As a result, findings often differ in non-trivial ways.

This seminar aims to explore stochastic problems arising from quantum systems in a unified way, beginning with the foundational principles of quantum probability. Topics will include , but are not limited to, quantum statistical estimation and hypothesis testing, quantum limit theorems and quantum information geometry.

The lectures on quantum learning theory (learning, certification, and tomography) and tensor norms are based on lecture notes of John Wright and lecture notes of Ion Nechita respectively.

Lecture Slides

• Lecture 1 (05/09/24): Quantum Stochastics. Slides.

• Lecture 2 (12/09/24): Introduction to Quantum Mechanics (by Prerthan Munireternam). Slides.

• Lecture 3 (19/09/24): Testing Quantum Hypothesis. Slides.

• Lecture 4 (26/09/24): Quantum Estimation I. Slides.

• Lecture 5 (03/10/24): Quantum Noise and Operations (by Prerthan Munireternam). Slides.

• Lecture 6 (10/10/24): Quantum Estimation II. Slides.

• Lecture 7 (17/10/24): Quantum Estimation III. Slides.

• Lecture 8 (24/10/24): Introduction to Quantum Information Theory (by Prerthan Munireternam). Slides.

• Lecture 9 (07/11/24): Random Matrices in Quantum Information Theory (by Xiaoyu Dong). Slides.

• Lecture 10 (28/11/24): Convergence Rates in the Cushen-Hudson Quantum Central Limit Theorem (by Milad M. Goodarzi).  Slides.

• Lecture 11 (06/03/25): Quantum Learning I. Slides.

• Lecture 12 (13/03/25): Quantum Learning II. Slides.

• Lecture 13 (20/03/25): Quantum Learning III. Slides.

• Lecture 14 (27/03/25): Quantum State Certification. Slides.

• Lecture 15 (03/04/25): Quantum Tomography I. Slides.

• Lecture 16 (08/05/25): Quantum Tomography II. Slides.

• Lecture 17 (15/05/25): Quantum Tomography III. Slides.

• Lecture 18 (05/06/25): Tensor norms and quantum entanglement I (by Rathindra Nath Karmakar). Notes.

• Lecture 19 (12/06/25): Tensor norms and quantum entanglement II (by Rathindra Nath Karmakar). Notes.

• Lecture 20 (26/06/25): Tensor norms and quantum entanglement III (by Rathindra Nath Karmakar). Notes.