We establish a lower bound of $\Omega{(\sqrt{n})}$ on the bounded-error quantum query complexity of read-once Boolean functions, providing evidence for the conjecture that $\Omega(\sqrt{D(f)})$ is a lower bound for all Boolean functions.Our technique extends a result of Ambainis, based on the idea that successful computation of a function requires ``decoherence'' ... more >>>

In Direct Sum problems [KRW], one tries to show that for a given computational model, the complexity of computing a collection $F = \{f_1(x_1), \ldots f_l(x_l)\}$ of finite functions on independent inputs is approximately the sum of their individual complexities. In this paper, by contrast, we study the diversity of ... more >>>