Are there different orderings of the fifteen SU(4) generators in common use?


I've recently performed certain analyses (Archipelagos of Total Bound and Free Entanglement) pertaining to eq. (50) in Separable Decompositions of Bipartite Mixed States , that is

\begin{equation} \label{rhoAB} \rho_{AB}^{(1)}=\frac{1}{2 \cdot 4} \textbf{1} \otimes \textbf{1} +\frac{1}{4} (t_1 \sigma_1 \otimes \lambda_1+t_2 \sigma_2 \otimes \lambda_{13}+t_3 \sigma_3 \otimes \lambda_3), \end{equation}

"where $t_{\mu} \neq 0$, $t_{\mu} \in \mathbb{R}$, and $\sigma_i$ and $\lambda_{\nu}$ are SU(2) and SU(4) generators, respectively."

Subsequent analyses (which I could detail)--concerning certain entanglement constraints employed in the two studies--lead me to speculate whether or not there is a possible ambiguity in the specific identification of the three $4 \times 4$ matrices ($\lambda$'s).

I, of course, had to use a specific set of three in my analyses--but, at this point, I'd just as soon leave matters "wide open" and not "bias" matters, if possible.

If there is possible ambiguity (which I presently suspect) perhaps good practice should dictate that the specific ordering employed be explicitly identified.

Paul B. Slater

Posted 2020-01-19T15:35:10.877

Reputation: 789

No answers