Semidefinite Programming as a Tool for Quantum Information
Part II: Reformulations, seesaw algorithms, and SDP hierarchies
Presented at Qalypso 2026 Summer School: Quantum Optimisation Techniques & Physics of Computation (Valletta, Malta, 2026).
Course date: 4 September 2026.
– Part I of this course at Qalypso 2026 Summer School (Lectures I and II) was given by Marco Túlio Quintino. The materials are available on his website: Lecture I: What is an SDP? and Lecture II: Dual certificates, strong duality, and numerical SDPs.
→ See my own lecture notes for the first part of the course here (PDF).
This course explores how semidefinite programming (SDP) can be used to tackle quantum information problems that do not initially appear to be SDPs. We first examine how changes of variables and analytical reformulations turn problems involving measurement incompatibility and quantum channel discrimination into SDPs. We then consider approximation methods: seesaw algorithms for finding achievable strategies, and outer approximations and SDP hierarchies for establishing impossibility proofs. Case studies include channel discrimination without memory, the search for the most incompatible measurements, and entanglement detection through the hierarchy of symmetric extensions.
Course materials
View or download the slides (PDF)
