复合量子系统局域不变量的完整性基
Integrity bases for local invariants of composite quantum systems
摘要：
利用$S$ -函数体积法，构造了适用于计算复合量子系统密度矩阵定域不变量的酉群分支。由此，可以计算密度矩阵中每个度处的不变量的数量的生成函数。对于两个二能级系统的情况，生成函数是$F(q) = 1 + q + 4q^{2} + 6 q^{3} + 16 q^{4} + 23 q^{5} + 52 q^{6} + 77 q^{7} + 150 q^{8} + 224 q^{9} + 396 q^{10} + 583 q^{11}+ O(q^{12})$。因式分解等系列导致原则上确定的代数独立的不变量的完整性基础。本注释取代了我们的论文\cite{us} J Phys { \bf A33}（2000）1895-1914（\texttt{quant-ph/0001076}）的附录B，该附录不正确。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
