Learn about groundbreaking research in quantum state identity testing through this conference presentation from the 19th Theory of Quantum Computation Conference (TQC 2024). Explore the optimal solutions for determining whether n unknown quantum states are equal or unequal, with a focus on both one-sided and two-sided error regimes. Discover how the researchers utilize semi-definite programming and representation theory to develop an optimal test for any input distribution, introduce a novel G-test employing arbitrary subgroups, and present an approximation of the permutation test using classical permutation and Swap tests. Delve into the mathematical foundations of quantum state identity testing, building upon the established Swap test methodology while introducing new theoretical frameworks for more complex quantum state comparisons. The presentation, delivered by Harry Buhrman, Dmitry Grinko, Philip Verduyn Lunel, and Jordi Weggemans, offers valuable insights for researchers and students working in quantum information science and quantum computation. Read more