# New techniques for bounding stabilizer rank

@article{Lovitz2021NewTF, title={New techniques for bounding stabilizer rank}, author={Benjamin Lovitz and Vincent Steffan}, journal={ArXiv}, year={2021}, volume={abs/2110.07781} }

In this work, we present number-theoretic and algebraic-geometric techniques for bounding the stabilizer rank of quantum states. First, we refine a number-theoretic theorem of Moulton to exhibit an explicit sequence of product states with exponential stabilizer rank but constant approximate stabilizer rank, and to provide alternate (and simplified) proofs of the best-known asymptotic lower bounds on stabilizer rank and approximate stabilizer rank, up to a log factor. Second, we find the first…

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