Lecture 1: Introduction to Semidefinite Programming

Lecture notes can be found here.

Recorded lecture can be found here.

Topics covered: Definitions, nomenclature, basic examples, weak duality, and Slater's theorem for strong duality.

Application: Finding the minimum energy of a Hamiltonian.

Lecture 2: Semidefinite programs for nice problems and popular functions

Lecture notes can be found here.

Recorded lecture can be found here.

Topics covered: Quantum state discrimination/exclusion, trace distance, the fidelity function, proving nontrivial properties using SDPs, Kitaev's diamond norm (this is included at the beginning of the next lecture's video).

Lecture 3: Studying quantum cryptography via semidefinite programming

Lecture notes can be found here.

Recorded lecture can be found here.

Topics covered: The impossibility of quantum bit-commitment, the possibility of unforgeable quantum money.

Lecture 4: Separability testing and quantum relative entropy*

Lecture notes can be found here.

Recorded lecture can be found here.

Topics covered: Symmetric extensions, quantum entropy and relative entropy.

*Erratum: There are two common ways of defining quantum entropies, using logarithms base 2 and base e. Some of the quantities in this lecture are defined for the base e version. Note that it does not change the math very much, since the two definitions only differ by a constant. Please note this if you plan on using these notes as a reference to solve anything numerically (or analytically).

Lecture 5: Nonlocality

Lecture notes can be found here.

Recorded lecture can be found here.

Topic covered: NPA hierarchy for quantum correlations.