Quantum inequalities and quantum entropy
In this course, I will introduce quantum inequalities related to quantum entropy in quantum information theory. Quantum inequalities will include a wide class of entropic inequalities and trace inequalites, such as strong subadditivity of von Neumann entroy, data processing inequalities, Lieb's concavity theorem, Golden-Thompson inequality, etc. Quantum Brascamp-Lieb inequalities and quantum Brascamp-Lieb dualities will also be discussed.
Lecturer
Date
3rd April ~ 3rd July, 2024
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Wednesday | 13:30 - 16:40 | A3-4-301 | ZOOM 05 | 293 812 9202 | BIMSA |
Prerequisite
linear algebra, calculus
Reference
1. E. A. Carlen, Trace inequalities and quantum entropy: An introductory course, 2009
2. E. H. Lieb, Convex trace functions and the Wigner-Yanase-Dyson conjecture, Adv. Math. 1973
3. E. H. Lieb, M. B. Ruskai, Proof of the strong subadditivity of quantum-mechanical entropy, J. Math. Phys. 1973
4. E. A. Carlen, E. H. Lieb, Brascamp-Lieb inequalities for non-commutative intergration, Documenta Math., 2008
5. M. Berta1, D. Sutter, M. Walter, Quantum Brascamp–Lieb dualities, Commun. Math. Phys. 2023
2. E. H. Lieb, Convex trace functions and the Wigner-Yanase-Dyson conjecture, Adv. Math. 1973
3. E. H. Lieb, M. B. Ruskai, Proof of the strong subadditivity of quantum-mechanical entropy, J. Math. Phys. 1973
4. E. A. Carlen, E. H. Lieb, Brascamp-Lieb inequalities for non-commutative intergration, Documenta Math., 2008
5. M. Berta1, D. Sutter, M. Walter, Quantum Brascamp–Lieb dualities, Commun. Math. Phys. 2023
Audience
Undergraduate
, Advanced Undergraduate
, Graduate
Video Public
No
Notes Public
No
Language
Chinese