Zhang's quasisymmetric modulus conjecture

For $Z\in\mathbb{M}_d$, let $|Z|_{\mathrm{qsym}}$ denote the quasisymmetric modulus used in Zhang's conjecture. For $A,B\in\mathbb{M}_d$, there are unitaries $U,V\in\mathbb{M}_d$. Zhang's quasisymmetric modulus conjecture.

$$|A+B|_{\mathrm{qsym}}\le\sqrt{2}\left(U|A|_{\mathrm{qsym}}U^*+V|B|_{\mathrm{qsym}}V^*\right).$$

This is described as a related strong conjecture proposed by Zhang; the supplied text gives no resolution status.