Quantum information theory, the entropy bound, and mathematical rigor in physics

The fundamental role of the entropy bound, I less than or equal to S(<(rho)over bar>) - (S) over bar(rho), is illustrated through its use in determining the information capacities of quantum systems and the ultimate accuracy Limits of precision quantum measurements, leading to a discussion on the relevance of mathematical rigor in the treatment of physics problems. The history of this bound is also reviewed.