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IEEE European Symposium on Security and Privacy Workshops (EuroS&PW)

QQIF: Quantum Quantitative Information Flow (invited paper)

Arthur Américo, Pasquale Malacaria

Published Sep 1, 2020• 2 citations
Publisher

Abstract

The field of Quantitative Information Flow (QIF) is concerned with quantifying information leakage in systems. This work generalises the QIF framework to the quantum setting, having as foundations the recently developed g-leakage framework. Next, some recent results of the field of quantum statistical decision are presented and translated in terms of the "quantum" g-leakage framework, including a recently developed quantum generalisation of the Coriasceous Theorem, an important result for QIF.

DOI
10.1109/eurospw51379.2020.00042

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The field of Quantitative Information Flow (QIF) is concerned with quantifying information leakage in systems. This work generalises the QIF framework to the quantum setting, having as foundations the recently developed g-leakage framework. Next, some recent results of the field of quantum statistical decision are presented and translated in terms of the "quantum" g-leakage framework, including a recently developed quantum generalisation of the Coriasceous Theorem, an important result for QIF.
The field of quantitative information flow (QIF) is concerned with measuring and controlling information leakage in computational systems, aiming to assess and improve their security. Much effort has been put into developing a mathematical framework for QIF, the standard approach being to model systems as monolithic infomation theoretic channels. However, many real-life systems can be best described by a collection of interacting channels instead. This motivates us to investigate the behaviour of channel compositions under the QIF framework. The channel compositions we study capture typical ways in which parts interact in real-world systems. Among other results, we derive relations between the information leakage of compositions and that of their components, establish whether we may substitute a component with a safer one without compromising the security of the whole, and model two anonymity protocols from the literature: the Dining Cryptographers and the Crowds.
We present a framework for quantifying information flow within general quantum processes. For this purpose, we introduce the signaling power of quantum channels and discuss its relevant operational properties. This function supports extensions to higher-order maps, enabling the evaluation of information flow in general quantum causal networks and processes with indefinite causal order. Furthermore, our results offer a rigorous approach to information dynamics in open systems that applies also in the presence of initial system-environment correlations, and allows for the distinction between classical and quantum information backflow.
The advantages of quantum information processing are in many cases obtained as consequences of quantum interactions, especially for computational tasks where two-qubit interactions are essential. In this work, we establish the framework of analyzing and quantifying loss or gain of information on a quantum system when the system interacts with its environment. We show that the information flow, the theoretical method of characterizing (non-)Markovianity of quantum dynamics, corresponds to the rate of the minimum uncertainty about the system given quantum side information. Thereafter, we analyze the information exchange among subsystems that are under the performance of quantum algorithms, in particular, the amplitude amplification algorithms where the computational process relies fully on quantum evolution. Different realizations of the algorithm are considered, such as (i) quantum circuits, (ii) analog computation, and (iii) adiabatic computation. It is shown that, in all the cases, our formalism provides insight into the process of amplifying the amplitude from the information flow or leakage on the subsystems.
Information flow is the branch of security that studies the leakage of information due to correlation between secrets and observables. Since in general such correlation cannot be avoided completely, it is important to quantify the leakage. The most followed approaches to defining appropriate measures are those based on information theory. In particular, one of the most successful approaches is the recently proposed ggg-leakage framework, which encompasses most of the information-theoretic ones. A problem with ggg-leakage, however, is that it is defined in terms of a minimization problem, which, in the case of large systems, can be computationally rather heavy. In this paper we study the case in which the channel associated to the system can be decomposed into simpler channels, which typically happens when the observables consist of multiple components. Our main contribution is the derivation of bounds on the (multiplicative version of) ggg-leakage of the whole system in terms of the ggg-leakages of its components. We also consider the particular cases of min-entropy leakage and of parallel channels, generalizing and systematizing results from the literature. We demonstrate the effectiveness of our method and evaluate the precision of our bounds using examples.
We develop a unified dynamical-spectral framework for equilibration in isolated quantum systems based on a subspace coarse-graining approach. Central to our formulation is the Leakage Fidelity Function (LFF), defined as the probability that a unitarily evolving state escapes the support of its initial subspace. This quantity provides a direct, operational measure of information flow and memory loss without invoking ensemble assumptions or perturbative arguments. We derive universal bounds on temporal fluctuations of the LFF, in terms of the spectral gap structure and the square of the effective dimension, evincing that large spectral delocalization suppresses fluctuations and guarantees equilibration on average. By introducing spectral power distributions and associated entropic measures, we establish a quantitative link between phase mixing, gap participation, and dynamical stability. We further investigate the equilibration timescale by connecting the LFF to quantum speed limits, thereby revealing the average time required for equilibration. Our results provide a state-dependent, geometrically transparent perspective on how spectral complexity and subspace information leakage jointly govern irreversibility in closed quantum many-body systems.
This paper introduces the concept of Quantum Complexity Flow (QCF), a novel framework for understanding and quantifying complexity within multi-body quantum systems. The central premise of QCF is that complexity isn't a fixed, inherent property but rather a dynamic flow – denoted as [JC] – that governs the evolution of quantum states. This flow represents the rate and direction of complexity propagation, influenced by the interactions between particles. The theoretical framework presented here aims to provide a more nuanced approach to describing quantum systems, particularly those exhibiting intricate entanglement and correlated behavior. The paper lays the groundwork for a new field of study, potentially holding significant implications for understanding fundamental quantum phenomena and could be a candidate for consideration in the pursuit of a Nobel Prize. Further development of QCF will involve refining the mathematical formalism and exploring its applications in various quantum systems.