Strong modular Zauner's conjecture for Hilbert C*-modules

Let $\mathcal{A}$ be a unital C*-algebra with the invariant basis number property or let $\mathcal{A}$ be a W*-algebra. For $d\in\mathbb{N}$, consider unit inner product frames in the standard module $\mathcal{A}^d$, with $\frac{1}{d+1}$-equiangularity meaning that mutual inner-product products equal $\frac{1}{d+1}$. Strong modular Zauner's conjecture. For every $d\in\mathbb{N}$, there exists a $\frac{1}{d+1}$-equiangular unit inner product frame $\{\tau_j\}_{j=1}^{d^2}$ for $\mathcal{A}^d$, equivalently a tight frame with unit diagonal inner products and

$$\langle\tau_j,\tau_k\rangle\langle\tau_k,\tau_j\rangle=\frac{1}{d+1},\qquad 1\leq j,k\leq d^2,\ j\neq k.$$

The extra algebraic hypotheses define the strong form of the modular extension of Zauner's conjecture. The supplied text does not state whether this form is open, solved, or refuted.