Resource theory of quantum scrambling

TL;DR

This paper develops a resource theory framework for quantum scrambling, introducing measures for entanglement and magic scrambling, and applies it to explain experiments and bound decoding fidelity.

Contribution

It introduces a novel resource theory of quantum scrambling with two new monotones, linking theoretical measures to experimental and operational tasks.

Findings

Resource monotones explain recent experimental observations of magic.

Monotones bound decoding fidelity in black hole decoding protocols.

Operational interpretation of scrambling resource measures.

Abstract

Quantum scrambling refers to the spread of local quantum information into the many degrees of freedom of a quantum system. In this work, we introduce a resource theory of scrambling which incorporates two mechanisms, "entanglement scrambling" and "magic scrambling". We introduce two resource monotones called the Pauli growth and the OTOC (out-of-time-ordered correlator) magic for these two mechanisms, respectively. We use our resource theory to explain recent experimental observations of magic. We also show that both resource monotones can be used to bound the decoding fidelity in Yoshida's black hole decoding protocol. These applications provide an operational interpretation of the resource monotones defined in this work.