We describe explicitly the algebra of polynomial functions on the Hilbert space of four-qubit states that are invariant under the group $\mathrm{SL}(2,C{)}^4$ 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.

• Received 31 December 2002

DOI:https://doi.org/10.1103/PhysRevA.67.042303