Explore a lecture on product mixing, quantum separation, and comfortable juntas in the context of the special unitary group. Delve into Gowers' problem of determining the largest subset of SU_n with specific product properties. Examine the product mixing conjecture and its implications for quantum communication protocols. Learn about a groundbreaking result that completely solves the product-mixing problem, providing sharp bounds for subsets of SU_n with Haar measure exceeding e^(-cn^(1/3)). Understand how this solution immediately yields an upper bound for Gowers' problem and its significance in the field of quantum mathematics and communication.
Overview
Syllabus
Product Mixing, Quantum Separation, and Comfortable Juntas
Taught by
Simons Institute