Complementarity in Finite Quantum Mechanics and Computer-Aided Computations of Complementary Observables

Abstract

Mathematical formulation of Bohr’s complementarity principle leads to the concepts of mutually unbiased bases in Hilbert spaces and complementary quantum observables. In this paper, we consider algebraic structures associated with these concepts and their applications to constructive quantum mechanics. We also briefly discuss some computer-algebraic approaches to the problems under consideration and propose an algorithm for solving one of them.