Strict separation of Minimax and Maximin lower bounds for vector Gaussian rate-distortion with trace distortion

The vector Gaussian rate-distortion problem with variable side information under trace distortion, denoted ${\textsc{RDTr}}$, is considered together with its Minimax and Maximin lower bounds. Strict-separation conjecture. There exists an instance of the ${\textsc{RDTr}}$ such that the Minimax lower bound is strictly greater than the Maximin lower bound, and hence greater than the Enhanced-Enhancement lower bound and the ${\textsc{ELB}}$. The claim would show that the Minimax lower bound is genuinely stronger than the other listed lower bounds for at least one instance of the trace-distortion problem; the source does not state whether such an instance has been established.