Davis, R. I. A.; Delbourgo, R.; Jarvis, P. D. Integrity bases for local invariants of composite quantum systems. Addendum: ”Covariance, correlation and entanglement”. (English) Zbl 0953.81008 J. Phys. A, Math. Gen. 33, No. 19, 3723-3725 (2000). Summary: 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 \[ F(q)=1+ q+ 4q^2+ 6q^3+ 16q^4+ 23q^5+ 52q^6+ 77q^7+ 150q^8+ 224q^9+ 396q^{10}+ 583q^{11}+ O(q^{12}). \] Factorization of such series leads in principle to the identification of an integrity basis of algebraically independent invariants. This Addendum replaces Appendix B of our recent paper [J. Phys. A, Math. Gen. 33, 1895-1914 (2000)] which is incorrect. Cited in 1 Document MSC: 81P15 Quantum measurement theory, state operations, state preparations 81P05 General and philosophical questions in quantum theory Keywords:unitary group branchings; S-function plethysms; generating functions Citations:Zbl 0991.69335 PDFBibTeX XMLCite \textit{R. I. A. Davis} et al., J. Phys. A, Math. Gen. 33, No. 19, 3723--3725 (2000; Zbl 0953.81008) Full Text: DOI arXiv