Finite and Profinite Quantum Systems

This monograph provides an introduction to finite quantum systems, a field at the interface between quantum information and number theory, with applications in quantum computation and condensed matter physics.

The first major part of this monograph studies the so-called 'qubits' and 'qudits', systems with periodic finite lattice as position space. It also discusses the so-called mutually unbiased bases, which have applications in quantum information and quantum cryptography. Quantum logic a...