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.


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