Unitary group branchings appropriate to the calculation of local invariants of density matrices of composite quantum systems are formulated using the method of $S$-function plethysms. From this, the generating function for the number of invariants at each degree in the density matrix can be computed. For the case of two two-level systems the generating function is $F(q) = 1 + q + 4q^{ 2} + 6 q^{ 3} + 16 q^{ 4} + 23 q^{ 5} + 52 q^{ 6} + 77 q^{ 7} + 150 q^{ 8} + 224 q^{ 9} + 396 q^{ 10} + 583 q^{ 11}+ O(q^{ 12})$. Factorisation of such series leads in principle to the identification of an integrity basis of algebraically independent invariants. This note replaces Appendix B of our paper\cite{ us} J Phys { \bf A33} (2000) 1895-1914 (\texttt{ quant-ph/0001076}) which is incorrect.
Categories: quant-ph