Geometry of the Schmidt decomposition and Hardy’s theorem

The Schmidt decomposition theorem allows us to express an entangled wave function of two quantum systems in a particularly simple form. The purpose of this paper is to describe a geometrical method of performing the Schmidt decomposition that complements the usual algebraic method. This geometrical method is worked out in detail for a pair of spin‐1/2 particles and its utility is illustrated by giving a simple discussion of several aspects of Hardy’s version of Bell’s theorem.