Key points are not available for this paper at this time.
We describe explicitly the algebra of polynomial functions on the Hilbert space of four-qubit states that are invariant under the group SL (2, C) ^4 of stochastic local quantum operations assisted by classical communication. From this description, we obtain a closed formula for the hyperdeterminant in terms of low degree invariants.
Luque et al. (2003) studied this question.