The Unification Conjecture for mutual free information and free entropy

Let $x_1,\ldots,x_n$ and $y_1,\ldots,y_n$ be self-adjoint operators in a $\mathrm{II}_1$-factor $(\mathscr{A},\tau)$, such that $\chi(x_1,\ldots,x_n)$, $\chi(y_1,\ldots,y_n)$, and $\chi(x_1,\ldots,x_n,y_1,\ldots,y_n)$ are all finite.

Unification Conjecture. The mutual free information satisfies

$$i^\ast(W^\ast(x_1,\ldots,x_n):W^\ast(y_1,\ldots,y_n))=-\chi(x_1,\ldots,x_n,y_1,\ldots,y_n)+\chi(x_1,\ldots,x_n)+\chi(y_1,\ldots,y_n).$$

This is part of the broader question of whether the microstates and non-microstates free entropies agree in general. The source states that both this identity and $\chi=\chi^\ast$ are unknown, so the conjecture remains open.