Ge–Li–Lu–Zhou factor-two constrained commutator conjecture

Let $\mathbb{K}=\mathbb{R}$ or $\mathbb{K}=\mathbb{C}$, and let $B,B_2,\ldots,B_m\in M(n,\mathbb{K})$. Let $B^*$ denote the conjugate transpose and let $[A,B]=AB-BA$. Assume

$$\operatorname{tr}(B_\alpha B_\beta^*)=0$$

for every $2\leq\alpha\ne\beta\leq m$. Ge–Li–Lu–Zhou conjecture. Then

$$\sum_{\alpha=2}^{m}\|[B,B_\alpha]\|^2\leq\left(2\max_{2\leq\alpha\leq m}\|B_\alpha\|^2+\sum_{\alpha=2}^{m}\|B_\alpha\|^2\right)\|B\|^2.$$

The source describes this as another equivalent form of the fundamental Lu–Wenzel conjecture, apparently stronger in appearance but with a factor of $2$ in the bound; no resolution status is supplied.