| Speaker: | Alexey Bondal (Kavli IPMU) |
|---|---|
| Title: | Pure mathematics in foundations of quantum information theory |
| Date (JST): | Wed, Nov 26, 2025, 15:30 - 17:00 |
| Place: | Lecture Hall |
| Abstract: |
Heisenberg indeterminacy principle is based on complementarity of coordinate and impulse. Complementary observables in a finite dimensional Hilbert space lead to the notion of Mutually Unbiased Bases (MUB). The classification of MUB attracts a lot of attention in Quantum Information Theory, because they are ubiquitous in Quantum Computers, Quantum Tomography, Quantum Criptography, etc. Still the problem is widely open. The proof of the existence a 4-dimensional family of MUB’s in dimension 6 (joint work with I. Zhdanovskiy) is heavily based on Algebraic Geometry. We will discuss the relation of the MUB problem with the classification of orthogonal decompositions of Lie algebra sl(n,C) and with Winnie the Pooh problem. We will give an interpretation in terms of representation theory of Temperley-Lieb like algebras of graphs, and outline how this leads to a noncommutative version of perverse sheaves. We describe the set of MUB’s as the critical locus of a potential, a Laurent polynomial. The Symplectic Geometry behind this description and Mirror Symmetry of the potential will be discussed. |
