SIC-POVMs and algebraic number theory
John Yard, Institute for Quantum Computing
SIC-POVMs (Symmetric Informationally Complete Positive Operator-Valued Measures) are certain extremal rank-1 projective measurements corresponding to maximal sets of complex equiangular lines as well as to minimal complex projective 2-designs. They are conjectured to exist in every finite-dimensional complex Hilbert space as orbits of generalized Pauli groups.
Post-Quantum Key Exchange for the Internet and the Open Quantum Safe Project
Douglas Stebila, McMaster University
Most public key cryptography algorithms used on the Internet are based on mathematical problems which could be broken by large-scale quantum computers. This motivates the field of post-quantum cryptography, which aims to construct public key cryptosystems that are believed to be secure even against quantum computers. Since a future quantum computer could retroactively break the confidentiality of today's communications, it is important to begin transitioning public key encryption and key exchange to quantum-resistant algorithms.