Integrity bases for local invariants of composite quantum systems. Addendum: ”Covariance, correlation and entanglement”. (English) Zbl 0953.81008

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.


81P15 Quantum measurement theory, state operations, state preparations
81P05 General and philosophical questions in quantum theory


Zbl 0991.69335
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