Mutual information fluctuations and non-stabilizerness in random circuits

TL;DR

This paper reveals a direct relationship between non-stabilizerness and information scrambling in random quantum circuits, linking quantum resource theory with entanglement phase transitions and providing insights into quantum process simulation.

Contribution

It establishes an analytical and numerical connection between non-stabilizerness and mutual information fluctuations in random circuits, advancing understanding of quantum resources and information dynamics.

Findings

Non-stabilizerness is proportional to mutual information fluctuations.

Fluctuations decrease as non-stabilizerness increases, aiding phase transition detection.

The work links quantum resource theory with information scrambling and entanglement transitions.

Abstract

The emergence of quantum technologies has brought much attention to the characterization of quantum resources as well as the classical simulatability of quantum processes. Quantum resources, as quantified by non-stabilizerness, have in one theoretical approach been linked to a family of entropic, monotonic functions. In this work, we demonstrate both analytically and numerically a simple relationship between non-stabilizerness and information scrambling using the fluctuations of an entropy-based quantifier. Specifically, we find that the non-stabilizerness generated by a random quantum circuit is proportional to fluctuations of mutual information. Furthermore, we explore the role of non-stabilizerness in measurement-induced entanglement phase transitions. We find that the fluctuations of mutual information decrease with increasing non-stabilizerness yielding potentially easier identification of the transition point. Our work establishes a key connection between quantum resource theory, information scrambling and measurement-induced entanglement phase transitions.