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Let $\mathbf m=(x_1,\ldots,x_n)$ be the maximal graded ideal of$S:=K[x_1,\ldots,x_n]$. We prove that $\operatorname{qdepth}(\mathbf m^t)\leq\left\lceil \frac{n}{t+1} \right\rceil$, for any $t\geq 1$, and, moreover, that$\operatorname{qdepth}(\mathbf m^t) = \left\lceil \frac{n}{t+1} \right\rceil$in the cases (i) $t\leq 2$, (ii) $t\geq n-1$ and (iii) $n\leq (t+1)(t+3)$.

Quasi depth of powers of the maximal graded ideal