Unitary-equivalence conjecture for three-copy SIC estimation fidelity

Let $\mathscr{A}$ and $\mathscr{B}$ be SICs in dimension $3$, and let $F(\mathscr{A}^{\otimes 3})$ and $F(\mathscr{B}^{\otimes 3})$ denote their three-copy estimation fidelities. SIC fidelity conjecture. Two SICs in dimension $3$ can achieve the same three-copy estimation fidelity if and only if they are unitarily equivalent. This conjecture proposes that three-copy estimation fidelity distinguishes the unitary-equivalence classes of SICs in dimension $3$, resolving whether inequivalent SICs have different operational implications; the supplied text gives numerical evidence but no resolution.