Perfect tensors describe highly entangled quantum states that have attracted
particular attention in the fields of quantum information theory and quantum
gravity. In loop quantum gravity, the natural question arises whether SU(2)
invariant tensors, which are fundamental ingredients of the basis states of
spacetime, can also be perfect. In this work, we present a number of general
constraints for the layout of such invariant perfect tensors (IPTs) and further
describe a systematic and constructive approach to check the existence of an
IPT of given valence. We apply our algorithm to show that no qubit encoding of
valence 4 and 6 can be described by an IPT and close a gap to prove a no-go
theorem for invariant perfect qubit encodings.
