We give a strong direct sum theorem for computing $XOR \circ g$. Specifically, we show that the randomized query complexity of computing the XOR of $k$ instances of $g$ satisfies $\bar{R}_\varepsilon(XOR \circ g)=\Theta(\bar{R}_{\varepsilon/k}(g))$. This matches the naive success amplification bound and answers a question of Blais and Brody.

As a consequence of our strong direct sum theorem, we give a total function $g$ for which $R(XOR \circ g) = \Theta(k\log(k)R(g))$, answering an open question from Ben-David et al.