



01893nas a2200145   4500008004100000245006300041210006300104260001300167490000800180520147500188100001401663700002001677700001301697856003701710       2020                        eng d00aEfficiently computable bounds for magic state distillation0 aEfficiently computable bounds for magic state distillation  c3/6/20200 v1243 a<p>Magic state manipulation is a crucial component in the leading approaches to realizing scalable, fault-tolerant, and universal quantum computation. Related to magic state manipulation is the resource theory of magic states, for which one of the goals is to characterize and quantify quantum &quot;magic.&quot; In this paper, we introduce the family of thauma measures to quantify the amount of magic in a quantum state, and we exploit this family of measures to address several open questions in the resource theory of magic states. As a first application, we use the min-thauma to bound the regularized relative entropy of magic. As a consequence of this bound, we find that two classes of states with maximal mana, a previously established magic measure, cannot be interconverted in the asymptotic regime at a rate equal to one. This result resolves a basic question in the resource theory of magic states and reveals a fundamental difference between the resource theory of magic states and other resource theories such as entanglement and coherence. As a second application, we establish the hypothesis testing thauma as an efficiently computable benchmark for the one-shot distillable magic, which in turn leads to a variety of bounds on the rate at which magic can be distilled, as well as on the overhead of magic state distillation. Finally, we prove that the max-thauma can outperform mana in benchmarking the efficiency of magic state distillation.&nbsp;</p>1 aWang, Xin1 aWilde, Mark, M.1 aSu, Yuan  uhttps://arxiv.org/abs/1812.10145