Quantum memory and scrambling from the perspective of a classical neural network

TL;DR

This paper introduces a modified concept of quantum memory for time-dependent systems, compares it with OTOC, and demonstrates its study in realistic systems using neural networks, revealing faster oscillations and higher sensitivity.

Contribution

It extends quantum memory analysis to realistic, time-dependent systems and employs neural networks to predict quantum correlations, highlighting differences from OTOC.

Findings

Quantum memory shows faster oscillations than OTOC.

Quantum memory does not equilibrate over time.

Neural networks can predict quantum memory and OTOC results.

Abstract

Entropic uncertainty relations are universal quantifiers of fundamental uncertainties of quantum measurements and are widely discussed in the quantum metrology literature. Quantum memory is a phenomenon related to the specific type of quantum correlations that allows for reducing fundamental uncertainties of quantum measurements. In the present work, the modified concept of quantum memory for time-dependent problems is proposed. We compare the time-dependent formulation of quantum memory with the out-of-time-ordered correlator (OTOC). Quantum memory is a rigorous mathematical concept that requires demanding calculations. Thus, until now, quantum memory has been discussed mainly for simple model systems and stationary problems. In the present work, we demonstrate that quantum memory can also be studied for realistic and physically relevant systems, e.g., the atomic helical spin chain, as well as the emergence and propagation of quantum correlations in time. We found that quantum memory manifests faster oscillations in time than OTOC and does not equilibrate. Furthermore, an artificial neural network is trained and asked to predict results for OTOC and quantum memory. These results show that quantum memory is more sensitive than OTOC in terms of broken inversion symmetry and the nonreciprocal effect.