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arXiv:2604.25663 · Annalen der Physik

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

Dimitrios Maroulakos, Andrzej Wal, Marcin Kowalik, Czesław Jasiukiewicz, Rohit Kumar Shukla, Sunil K. Mishra, Levan Chotorlishvili

quant-phSubmitted Apr 28, 2026• Announced Apr 29, 2026• 4 citations
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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.

Journal reference
journal : Annalen der Physik,volume 538, pages e00560, year 2026
DOI
10.1002/andp.202500560

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Abstract We quantify the role of scrambling in quantum machine learning. We characterize a quantum neural network’s (QNNs) error in terms of the network’s scrambling properties via the out-of-time-ordered correlator (OTOC). A network can be trained by minimizing a loss function. We show that the loss function can be bounded by the OTOC. We prove that the gradient of the loss function can be bounded by the gradient of the OTOC. This demonstrates that the OTOC landscape regulates the trainability of a QNN. We show numerically that this landscape is flat for maximally scrambling QNNs, which can pose a challenge to training. Our results pave the way for the exploration of quantum chaos in quantum neural networks.
This tutorial article introduces the physics of quantum information scrambling in quantum many-body systems. The goals are to understand how to precisely quantify the spreading of quantum information and how causality emerges in complex quantum systems. We introduce a general framework to study the dynamics of quantum information, including detection and decoding. We show that the dynamics of quantum information is closely related to operator dynamics in the Heisenberg picture, and, under certain circumstances, can be precisely quantified by the so-called out-of-time-ordered correlator (OTOC). The general behavior of the OTOC is discussed based on several toy models, including the Sachdev-Ye-Kitaev model, random circuit models, and Brownian models, in which the OTOC is analytically tractable. We introduce numerical methods, including exact diagonalization and tensor network methods, to calculate the OTOC for generic quantum many-body systems. We also survey current experimental schemes for measuring the OTOC in various quantum simulators. Published by the American Physical Society 2024
Entropic uncertainty relations quantify the limits on the predictability of quantum measurements. When the measured system is correlated with a quantum memory, these limits are described by the memory-assisted entropic uncertainty relation (MA-EUR). We examine the behavior of MA-EUR when the memory qubit undergoes noisy dynamics implemented via high-order controlled processes, namely, the quantum switch and the quantum time-flip. We consider a setting in which the control qubit is the very system on which the measurements are performed, while the target qubit serves as a noisy quantum memory. Focusing on Pauli channels, we show that feeding them into the quantum switch and the quantum time-flip can significantly reduce the total entropic uncertainty as compared to their direct application. Our results reveal that indefinite causal order and input-output direction can serve as resources to mitigate the effects of noise in the context of MA-EUR and its applications.
The uncertainty principle is one of the comprehensive and fundamental concept in quantum theory. This principle states that it is not possible to simultaneously measure two incompatible observatories with high accuracy. Uncertainty principle has been formulated in various form. The most famous type of uncertainty relation is expressed based on the standard deviation of observables. In quantum information theory the uncertainty principle can be formulated using Shannon and von Neumann entropy. Entropic uncertainty relation in the presence of quantum memory is one of the most useful entropic uncertainty relations. Due to their importance and scalability, solid state systems have received considerable attention nowadays. In this work we will consider a quantum dot system as a solid state system. We will study the quantum correlation and quantum memory assisted entropic uncertainty in this typ of system. We will show that the temperature in of quantum dot system can affect the quantum correlation and entropic uncertainty bound. It will be observed that the entropic uncertainty bound decreases with decreasing temperature and quantum correlations decreases with increasing the temperature.
How violently do two quantum operators disagree? Different fields of physics feature different measures of incompatibility: (i) In quantum information theory, entropic uncertainty relations constrain measurement outcomes. (ii) In condensed matter and high-energy physics, the out-of-time-ordered correlator (OTOC) signals scrambling, the spread of information through many-body entanglement. We unite these measures, deriving entropic uncertainty relations for scrambling. The entropies are of distributions over weak and strong measurements' possible outcomes. Weakness causes the OTOC quasiprobability (a nonclassical generalization of a probability, in terms of which the OTOC decomposes) to govern terms in the uncertainty bound. Scrambling strengthens the bound, we show, in numerical simulations of a spin chain. Beyond scrambling, we derive entropic uncertainty relations satisfied by commonly performed weak-measurement experiments. We unveil a physical significance of common quasiprobabilities and weak values (conditioned expectation values): as governing terms in entropic uncertainty bounds.