# Is the Pusey-Barrett-Rudolph (PBR) theorem only applicable in two dimensions?

Yes, the argument given in that paper is completely general and applies to pairs of states in Hilbert spaces of arbitrary dimension. The choose two linearly independent vectors and look at the two-dimensional *subspace* generated by these vectors. They do *not* assume that the Hilbert space itself is two-dimensional. In fact, they they say this explicitly:

These states span a two-dimensional subspace of the Hilbert space. We can restrict attention to this subspace and from hereon, without loss of generality, treat the systems as qubits.

This is a perfectly standard approach to theorems in linear algebra that is used all the time. We use it in QM very often too, e.g. when we diagonalize operators simultaneously, where we fix the eigenvalue for one of them (i.e., we restrict the attention to one of its eigenspaces) and study the eigenvalues of the other one.