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Integrity bases for local invariants of composite quantum systems

2000
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Journal of Physics A: Mathematical and General
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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

doi:10.1088/0305-4470/33/19/408
fatcat:q6unptaxdbhdrfab42ij246iaa