Extracting Randomness from "Magic" States*

Magic is a fundamental description of the non-classicality of quantum states and plays a crucial role in fault-tolerant quantum computation. Many constructions in quantum information science rely on ensembles of random unitaries or states, prompting intense study on the topic of randomness within the context of the field. In this presentation, we show that there is a direct mathematical relationship between the magic of a multiqubit pure state and the randomness of the post-measurement ensemble obtained from measuring out subsystems of this state. Here, we quantify randomness using the framework of approximate state 2-designs and present compelling numerical evidence that our result extends to higher-order approximate state designs as well. To illustrate the relationship between magic and randomness, we numerically simulate subsystem measurements on the output of a random Clifford circuit initialized to a product state and show how the randomness of the resulting ensemble depends on the magic of the circuit's initial state. Our results further demonstrate how magic states act as a quantum resource, and suggest a practical method for leveraging magic to generate approximate state designs.