For the "greater-than" problem in Yao's 2-party communication complexity model, Alice receives $X$ and Bob receives $Y$, and they need to decide whether $X>Y$.

I recently listened to an (online) seminar talk where the speaker mentioned that it is known that any randomized $k$-round protocol that computes "greater-than" requires $\Omega\left(\frac{(\log n)^{1/k}}{k^2}\right)$ bits.

Unfortunately, I didn't get to ask the speaker about where this result appeared and I didn't have any luck searching for it online. Is there a reference where I could find the proof for this round-communication trade-off?

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    $\begingroup$ An $\Omega(\log n)$ lower bound already holds for any round. It should be $\Omega(n^{1/k}k^{-2})$ and it was proved here. (See this answer by sagnik) $\endgroup$ – Willard Zhan Mar 12 at 20:17

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