Stabilizer R\'enyi entropy

TL;DR

This paper introduces a new, easily computable measure of quantum nonstabilizerness called stabilizer R'enyi entropy, linking it to quantum chaos and providing an experimental measurement protocol.

Contribution

It proposes a novel R'enyi entropy-based measure of quantum magic, demonstrating its advantages and connections to chaos and experimental feasibility.

Findings

The measure effectively quantifies nonstabilizerness.

It is computationally simpler than existing measures.

Maximal nonstabilizerness relates to quantum chaos.

Abstract

We introduce a novel measure for the quantum property of nonstabilizerness - commonly known as "magic" - by considering the R\'enyi entropy of the probability distribution associated to a pure quantum state given by the square of the expectation value of Pauli strings in that state. We show that this is a good measure of nonstabilizerness from the point of view of resource theory and show bounds with other known measures. The stabilizer R\'enyi entropy has the advantage of being easily computable because it does not need a minimization procedure. We present a protocol for an experimental measurement by randomized measurements. We show that the nonstabilizerness is intimately connected to out-of-time-order correlation functions and that maximal levels of nonstabilizerness are necessary for quantum chaos.