While the total number of ideal measurement outcomes, modelled by \(P_{m}\), must be identical to the dimension of the Hilbert space (ignoring the technical complication of degeneracy), this is no lon...While the total number of ideal measurement outcomes, modelled by \(P_{m}\), must be identical to the dimension of the Hilbert space (ignoring the technical complication of degeneracy), this is no longer the case for the POVM described by \(E_{m}\); there can be more or fewer measurement outcomes, depending on the physical details of the measurement apparatus.
