  The situation of two independent observers conducting measurements on a joint
quantum system is usually modelled using a Hilbert space of tensor product
form, each factor associated to one observer. Correspondingly, the operators
describing the observables are then acting non-trivially only on one of the
tensor factors. However, the same situation can also be modelled by just using
one joint Hilbert space, and requiring that all operators associated to
different observers commute, i.e. are jointly measurable without causing
disturbance. The problem of Tsirelson is now to decide the question whether all
quantum correlation functions between two independent observers derived from
commuting observables can also be expressed using observables defined on a
Hilbert space of tensor product form. Tsirelson showed already that the
distinction is irrelevant in the case that the ambient Hilbert space is of
finite dimension. We show here that the problem is equivalent to the question
whether all quantum correlation functions can be approximated by correlation
function derived from finite-dimensional systems. We also discuss some physical
examples which fulfill this requirement.
