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arXiv:2305.19334 · Quantum Science and Technology

Quantum scrambling via accessible tripartite information

Gabriele Lo Monaco, Luca Innocenti, Dario Cilluffo, Diana A. Chisholm, Salvatore Lorenzo, G. Massimo Palma

Published Apr 17, 2023• 10 citations
arXivHTMLPDF

Abstract

Abstract Quantum information scrambling (QIS), from the perspective of quantum information theory, is generally understood as local non-retrievability of information evolved through some dynamical process, and is often quantified via entropic quantities such as the tripartite information. We argue that this approach comes with a number of issues, in large part due to its reliance on quantum mutual informations, which do not faithfully quantify correlations directly retrievable via measurements, and in part due to the specific methodology used to compute tripartite informations of the studied dynamics. We show that these issues can be overcome by using accessible mutual informations, defining corresponding ‘accessible tripartite informations’, and provide explicit examples of dynamics whose scrambling properties are not properly quantified by the standard tripartite information. Our results lay the groundwork for a more profound understanding of what QIS represents, and reveal a number of promising, as of yet unexplored, venues for further research.

DOI
10.1088/2058-9565/accd92

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Abstract Quantum information scrambling (QIS), from the perspective of quantum information theory, is generally understood as local non-retrievability of information evolved through some dynamical process, and is often quantified via entropic quantities such as the tripartite information. We argue that this approach comes with a number of issues, in large part due to its reliance on quantum mutual informations, which do not faithfully quantify correlations directly retrievable via measurements, and in part due to the specific methodology used to compute tripartite informations of the studied dynamics. We show that these issues can be overcome by using accessible mutual informations, defining corresponding ‘accessible tripartite informations’, and provide explicit examples of dynamics whose scrambling properties are not properly quantified by the standard tripartite information. Our results lay the groundwork for a more profound understanding of what QIS represents, and reveal a number of promising, as of yet unexplored, venues for further research.
Abstract Quantum information scrambling (QIS) is a characteristic feature of several quantum systems, ranging from black holes to quantum communication networks. While accurately quantifying QIS is crucial to understanding many such phenomena, common approaches based on the tripartite information have limitations due to the accessibility issues of quantum mutual information, and do not always properly take into consideration the dependence on the encoding input basis. To address these issues, we propose a novel and computationally efficient QIS quantifier, based on a formulation of QIS in terms of quantum state discrimination. We show that the optimal guessing probability, which reflects the degree of QIS induced by an isometric quantum evolution, is directly connected to the accessible min-information , a generalized channel capacity based on conditional min-entropy, which can be cast as a convex program and thus computed efficiently. By applying our proposal to a range of examples with increasing complexity, we illustrate its ability to capture the multifaceted nature of QIS in all its intricacy.
Abstract Recent advances in quantum information science have shed light on the intricate dynamics of quantum many-body systems, for which quantum information scrambling is a perfect example. Motivated by considerations of the thermodynamics of quantum information, this perspective aims at synthesizing key findings from several pivotal studies and exploring various aspects of quantum scrambling. We consider quantifiers such as the out-of-time-ordered correlator (OTOC) and the quantum mutual information, their connections to thermodynamics, and their role in understanding chaotic vs . integrable quantum systems. With a focus on representative examples, we cover a range of topics, including the thermodynamics of quantum information scrambling, and the scrambling dynamics in quantum gravity models such as the Sachdev-Ye-Kitaev (SYK) model. Examining these diverse approaches enables us to highlight the multifaceted nature of quantum information scrambling and its significance in understanding the fundamental aspects of quantum many-body dynamics at the intersection of quantum mechanics and thermodynamics.
In this paper, we investigate the dynamics of a spin chain whose two end spins interact with two independent non-Markovian baths by using the non-Markovian quantum state diffusion (QSD) equation approach. Specifically, two issues about information scrambling in an open quantum system are addressed. The first issue is that tripartite mutual information (TMI) can quantify information scrambling properly via its negative value in a closed system, whether it is still suitable to indicate information scrambling in an open quantum system. We find that negative TMI is not a suitable quantifier of information scrambling in an open quantum system in some cases, while negative tripartite logarithmic negativity (TLN) is an appropriate one. The second one is that up to now almost all information scrambling in open quantum systems reported were focus on a Markovian environment, while the effect of a non-Markovian environment on information scrambling is still elusive. Our results show that the memory effect of an environment will be beneficial to information scrambling. Moreover, it is found that the environment is generally detrimental for information scrambling in the long-term, while in some cases it will be helpful for information scrambling in the short-term.
The quantum neural network is one of the promising applications for near-term noisy intermediate-scale quantum computers. A quantum neural network distills the information from the input wave function into the output qubits. In this Letter, we show that this process can also be viewed from the opposite direction: the quantum information in the output qubits is scrambled into the input. This observation motivates us to use the tripartite information-a quantity recently developed to characterize information scrambling-to diagnose the training dynamics of quantum neural networks. We empirically find strong correlation between the dynamical behavior of the tripartite information and the loss function in the training process, from which we identify that the training process has two stages for randomly initialized networks. In the early stage, the network performance improves rapidly and the tripartite information increases linearly with a universal slope, meaning that the neural network becomes less scrambled than the random unitary. In the latter stage, the network performance improves slowly while the tripartite information decreases. We present evidences that the network constructs local correlations in the early stage and learns large-scale structures in the latter stage. We believe this two-stage training dynamics is universal and is applicable to a wide range of problems. Our work builds bridges between two research subjects of quantum neural networks and information scrambling, which opens up a new perspective to understand quantum neural networks.
For the characterization of the dynamics in quantum many-body systems the question of how information spreads and becomes distributed over the constituent degrees of freedom is of fundamental interest. The delocalization of information under many-body dynamics has been dubbed scrambling, and out-of-time-order correlators were proposed to probe this behavior. In this work we investigate the time evolution of tripartite information as a natural operator-independent measure of scrambling, which quantifies to what extent the initially localized information can be recovered only by global measurements. Studying the dynamics of quantum lattice models with tunable integrability breaking, we demonstrate that in contrast to quadratic models generic interacting systems scramble information irrespective of the chosen partitioning of the Hilbert space, which justifies the characterization as a scrambler. Without interactions the dynamics of tripartite information in momentum space reveals unambiguously the absence of scrambling.
Quantum extreme learning machines (QELMs) leverage untrained quantum dynamics to efficiently process information encoded in input quantum states, avoiding the high computational cost of training more complicated nonlinear models. On the other hand, quantum information scrambling (QIS) quantifies how the spread of quantum information into correlations makes it irretrievable from local measurements. Here, we explore the tight relation between QIS and the predictive power of QELMs. In particular, we show efficient state estimation is possible even beyond the scrambling time, for many different types of dynamics — in fact, we show that in all the cases we studied, the reconstruction efficiency at long interaction times matches the optimal one offered by random global unitary dynamics. These results offer promising venues for robust experimental QELM-based state estimation protocols, as well as providing novel insights into the nature of QIS from a state estimation perspective.