The State Space of a Pair of Spin-1/2 Particles

The state space of a quantum mechanical systemconsisting of more than one particle exhibits someunusual features giving rise to interesting phenomena,such as the Einstein–Rosen–Podolsky paradox.In order to get a feel for the structure of such a statespace, it is useful to study the spin component of apair of spin-1/2 particles, whose associated state spaceis clearly the simplest example occurring within the context of quantum mechanical systems ofmore than one particle. In a series of papers R.Horodecki et al. did just that and they found somebeautiful results, which are certainly of interest tothe mathematical physicist. In the present note, ina different context and using somewhat different methodsof proof, we rederive some of the results obtained byHorodecki. Furthermore, using these methods we are able to prove some additional resultswhich to our knowledge have never beenpublished.