A lower bound on the quantum query complexity of read-once functions
<|reference_start|>A lower bound on the quantum query complexity of read-once functions: 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'' of initially coherently superposed inputs in the query register, having different values of the function. The number of queries is bounded by comparing the required total amount of decoherence of a judiciously selected set of input-output pairs to an upper bound on the amount achievable in a single query step. We use an extension of this result to general weights on input pairs, and general superpositions of inputs.<|reference_end|>
@article{barnum2002a,
    title={A lower bound on the quantum query complexity of read-once functions},
    author={Howard Barnum, Michael Saks},
    journal={arXiv preprint arXiv:quant-ph/0201007},
    year={2002},
    archivePrefix={arXiv},
    eprint={quant-ph/0201007},
    primaryClass={quant-ph cs.CC}
}