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Integrity bases for local invariants of composite quantum systems

RIA Davis·R Delbourgo·PD Jarvis
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Abstract

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.

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RIA Davis, R Delbourgo, PD Jarvis. 2000-03-13. Integrity bases for local invariants of composite quantum systems. https://doi.org/10.1088/0305-4470%2F33%2F19%2F408

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