In this work, we investigate the role of functionals of generalized fidelity measures in deriving quantum speed limits (QSLs) within a geometric approach. We establish a general theoretical framework and show that, once a specific generalized fidelity is selected, the resulting Margolus-Levitin and Mandelstam-Tamm QSLs for both unitary and nonunitary (Lindblad-type) dynamics depend solely on the chosen fidelity measure. We prove that any monotone, differentiable reparametrization of the chosen fidelity yields exactly the same Margolus-Levitin and Mandelstam-Tamm-type QSL, rendering the QSLs invariant under such transformations and thereby unifying fidelity- and metric-induced geometric formulations. This result highlights the limitations of improving QSLs through functional transformations of fidelity and indicates that genuine improvements must arise from alternative fidelity definitions. We further show that several QSLs reported in the literature are encompassed by our framework and discuss possible extensions based on other generalized fidelity measures beyond those explicitly analyzed. In addition, we consider the damped Jaynes-Cummings model as a concrete physical setting to explore the behavior of the QSLs discussed in this work and analyze their regime-dependent features.

We investigate the dynamics of a two-dimensional Sznajd model in which a third ideological position emerges spontaneously from local interactions between agents. Starting from random initial conditions, we observe that this emergent position arises solely as a result of the interaction dynamics, and not from predefined agent states. We analyze the system's behavior as a function of social apathy, modeled as the fraction of nonparticipating agents, and identify a critical apathy threshold that separates distinct regimes of opinion dominance. To quantify the interplay between disorder and structure in the system, we employ the complexity-entropy plane. This analysis reveals that the system is robust to asymmetries in initial conditions; its macroscopic behavior remains qualitatively unchanged. Furthermore, we find that statistical complexity reaches a maximum near the transition region, highlighting the emergence of rich collective dynamics characterized by abrupt topological changes parametrized by apathy.

In this work we apply a procedure based on the quantum imaginary time evolution method to solve the unitdisk maximum independent set problem. Numerical simulations are performed for instances of six-, eight-, and ten-qubit graphs. We find that the failure probability of the procedure is relatively small and rapidly decreases with the number of shots. In addition, a theoretical upper bound for the failure probability of the procedure is obtained.

In this work we apply a procedure based on the quantum imaginary time evolution method to solve the unit-disk maximum independent set problem. Numerical simulations were performed for instances of 6, 8 and 10-qubits graphs. We have found that the failure probability of the procedure is relatively small and rapidly decreases with the number of shots. In addition, a theoretical upper bound for the failure probability of the procedure was obtained.

We investigate bounds in the transmission of classical information through quantum systems. Our focus lies in the generalized Holevo theorem, which provides a single-letter Holevo-like inequality from arbitrary quantum distance measures. Through the introduction of the alpha-z-R & eacute;nyi relative entropies, which comprise known relevant quantities such as the R & eacute;nyi relative entropy and the sandwiched R & eacute;nyi relative entropy, we establish the Holevo-R & eacute;nyi inequality. This result leads to a quantum bound for the alpha-mutual information, suggesting new insights into communication channel performance and the fundamental limits for reliability functions in memoryless multi-letter communication channels.

The Jensen–Shannon divergence has been successfully applied as a segmentation tool for symbolic sequences, that is to separate the sequence into subsequences with the same symbolic content. In this work, we propose a method, based on the Jensen–Shannon divergence, for segmentation of what we call quantum generated sequences, which consist in symbolic sequences generated from measuring a quantum system. For one-qubit and two-qubit systems, we show that the proposed method is adequate for segmentation.

We analyze two ways to obtain distinguishability measures between quantum maps by employing the square root of the quantum Jensen-Shannon divergence, which forms a true distance in the space of density operators. The arising measures are the transmission distance between quantum channels and the entropic channel divergence. We investigate their mathematical properties and discuss their physical meaning. Additionally, we establish a chain rule for the entropic channel divergence, which implies the amortization collapse, a relevant result with potential applications in the field of discrimination of quantum channels and converse bounds. Finally, we analyze the distinguishability between two given Pauli channels and study exemplary Hamiltonian dynamics under decoherence.

Divergences or similarity measures between probability distributions have become a very useful tool for studying different aspects of statistical objects, such as time series, networks, and images. Notably, not every divergence provides identical results when applied to the same problem. Therefore, it seems convenient to have the widest possible set of divergences to be applied to the problems under study. Besides this choice, an essential step in the analysis of every statistical object is the mapping of each one of their representing values into an alphabet of symbols conveniently chosen. In this work, we choose the family of divergences known as the Burbea-Rao centroids (BRCs). For the mapping of the original time series into a symbolic sequence, we work with the ordinal pattern scheme. We apply our proposals to analyze simulated and real time series and to real textured images. The main conclusion of our work is that the best BRC, at least in the studied cases, is the Jensen-Shannon divergence, besides the fact that it verifies some interesting formal properties.

In this work we study the reduced density matrices of sublattices of fermionic, bosonic and spin lattice models. Firstly, we consider fermionic and bosonic lattice models, and we show that the reduced density matrix associated with a sublattice coincides with the state obtained by applying the maximum entropy principle under suitably chosen constraints. Secondly, for informationally incomplete scenarios, we considered spin lattice models. We study the performance of the MaxEnt method for estimating the reduced density matrix of sublattices of the lattice system. We find that the performance of the MaxEnt estimation improves not only with the number of measured observables (as expected), but also with the lattice length. In these cases, the MaxEnt solution can be considered, not as an exact solution, but as a good estimator. (C) 2022 Elsevier B.V. All rights reserved.

Jensen–Shannon divergence is an important distinguishability measure between probability distributions that finds interesting applications within the context of Information Theory. In particular, this classical divergence belongs to a remarkable class of divergences known as Csiszár or f-divergences. In this paper we analyze the problem of obtaining a distance measure between two quantum states starting from the classical Jensen–Shannon divergence between two probability distributions. Considering the Jensen–Shannon divergence as a Csiszár divergence, we first focus on the problem of distinguishability between two pure quantum states. We find a quantum version of the classical Jensen–Shannon divergence that differs from the previously introduced Quantum Jensen–Shannon Divergence. The two quantum versions of Jensen–Shannon divergence have different interpretations within the framework of Quantum Information Theory. Whereas the former quantum version of Jensen–Shannon divergence can be interpreted as the Holevo bound, the alternative quantum version obtained in this work equals the accessible information. Furthermore, we obtain a monoparametric family of metrics between two quantum pure states. Finally, we extend this family of metrics to the case of mixed quantum states by means of the concept of purification.

Given a physical system to define a suitable measurement process on it constitutes one of the most crucial and challenging issues in physics. According to the particular theory under consideration, taking measurements has more or fewer subtleties but one ubiquitous concept for every physical theory is the uncertainty. In quantum mechanics, it is possible to identify a fundamental unpredictability given by Heisenberg uncertainty relations and the indistinguishability of quantum states, together with a practical uncertainty related to unavoidable errors in the measurement process. Considering only these fundamental ties, the estimation of unknown values of physical magnitudes has well-defined precision limits. The Cramer-Rao bound is a cornerstone for the analysis of these restrictions and an irreplaceable tool to determine the most accurate measurement procedures. On the quantum side, there exist quantum correlations known as entanglement and quantum discord which bring new ways to overcome the classical precision limits. Quantum metrology is a relatively young emerging area whose main aim is to study how to improve parameter estimation theory by using quantum correlations present in multipartite systems.

The main aim of this work is to investigate the relation between the freezing of Quantum Discord and the behavior of the actual quantum correlations present in bipartite quantum states. In order to accomplish this objective, we use first the Fano representation of two-qubit states from which we can identify a correlation matrix containing the information about the classical and quantum correlations present in the bipartite quantum state. From the behavior of the elements of the correlation matrix before and after making measurements on one of the subsystems, we identify the classical and quantum correlations present in these bipartite states. Then, we use this correlation matrix as a tool to analyze the phenomenon of non-dissipative decoherence in two-qubit states with maximally mixed marginals in typical dynamic scenarios where freezing of standard Quantum Discord takes place. We find that under some initial conditions where freezing of quantum discord occurs, some quantum correlations instead may not remain constant. In order to further explore into these results we also compute for the first time a recently introduced non-commutativity measure of quantum correlations (NCMQC) to analyze the behavior of quantum correlations under the same scenarios of non-dissipative decoherence. In complete agreement with the results obtained by means of the correlation matrix, our results also show that quantum correlations, as measured by NCMQC, do not freeze. Thus, our results put at stake the usual interpretation that the freezing of Quantum Discord is equivalent to the freezing of the physical quantum correlations themselves. We conclude from our study that freezing of quantum discord may not always be identified as equivalent to the freezing of the actual quantum correlations. Thus, the identification of freezing of quantum discord as a useful resource for tasks of quantum information processing is called into question.

We built a new set of suitable measures of correlations for bipartite quantum states based upon a recently introduced theoretical framework [Bussandri et al. in Quantum Inf. Proc. 18:57, 2019]. We applied these measures to examine the behavior of correlations in two-qubit states with maximally mixed marginals independently interacting with non-dissipative decohering environments in different dynamical scenarios of physical relevance. In order to get further insight about the physical meaning of the behavior of these correlation measures we compared our results with those obtained by means of well-known correlation measures such as quantum mutual information and quantum discord. On one hand, we found that the behaviors of total and classical correlations, as assessed by means of the measures introduced in this work, are qualitatively in agreement with the behavior displayed by quantum mutual information and the measure of classical correlations typically used to calculate quantum discord. We also found that the optimization of all the measures of classical correlations depends upon a single parameter and the optimal value of this parameter turns out to be the same in all cases. On the other hand, regarding the measures of quantum correlations used in our studies, we found that in general their behavior does not follow the standard quantum discord D . As the quantification by means of standard quantum discord and the measures of quantum correlations introduced in this work depends upon the assumption that total correlations are additive, our results indicate that this property needs a deeper and systematic study in order to gain a further understanding regarding the possibility to obtain reliable quantifiers of quantum correlations within this additive scheme.

We present a generalization of the Holevo theorem through distance measures between quantum states, showing that each of these leads to an alternative Holevo theorem. This result involves two quantities: the distance-based Holevo quantity and the generalized accessible information Id. Additionally, we consider three distinguishability notions relevant to quantum cryptography, applying the resulting new inequalities to qubits ensembles. For some well-known distinguishability notion, we show that for any ensemble of two qubits the generalized quantities—Id and —are equal. On the other hand, by using a paradigmatic example, we show that the quantities corresponding to the Bures distance captures not only the non-commutativity of the ensemble but also its purity.

In this work, we developed a general approach to the problem of detecting and quantifying different types of correlations in bipartite quantum systems. Our method is based on the use of distances between quantum states and processes. We rely upon the premise that total correlations can be separated into classical and quantum contributions due to their different nature. In addition, according to recently discussed criteria, we determined the requirements to be satisfied by distances in order to generate correlation measures physically well behaved. The proposed measures allow us to quantify quantum, classical and total correlations. Besides the well-known case of relative entropy, we introduce some additional examples of distances which can be used to build bona fide quantifiers of correlations.

Se hace en este trabajo una aproximación conceptual a la noción de gauge introducida por Hermann Weyl, contextualizada en su origen clásico en la segunda década del siglo XX, con un breve comentario sobre su posterior inserción en la mecánica cuántica de la década siguiente, cuando el área estaba consolidándose. Considerando que es conveniente dar para ello un ámbito adecuado en el que es importante atender al estilo de pensamiento de su autor, se presenta un breve perfil del mismo. Se atiende a sus intereses físicos y filosóficos sin dejar de lado su principal tarea profesional como matemático. El punto de vista adoptado sugiere que no es posible comprender en su integridad el pensamiento de este autor si no se contemplan sus facetas relacionadas con estos tres grandes campos disciplinares. Aunque este objetivo en su plenitud escapa por su extensión y sutilezas a este trabajo, se supone que una aproximación introductoria al caso histórico puede contribuir a una mejor comprensión de su alcance posterior, tal como aparece en las numerosas aplicaciones de este concepto en investigaciones contemporáneas vinculadas con la física de partículas elementales.

Since its conception 90 years ago, the quantum uncertainty principle introduced by Werner Heisenberg lies behind most important features of quantum physics, and its implications have an impact that goes far beyond the physics community. This book focuses on the quantum uncertainty principle, providing an up-to-date examination of recent developments of its applications in quantum information theory. The book brings together several renowned experts working in the foundations of quantum mechanics and quantum information theory. The authors provide different approaches to the study of uncertainty relations and other fundamental aspects of the quantum formalism. Topics addressed include entanglement and Bell inequalities, the application of entropic information measures to the study of uncertainty inequalities, the characterization of deep learning networks in the context of adiabatic quantum computation, and the study of general properties of the set of quantum states. The content of this book will surely benefit both experienced and new researchers specializing in quantum information theory and the foundations of quantum mechanics.

The VII Conference on Quantum Foundations: 90 years of uncertainty (https://sites [...].

We study a version of the generalized (h, ϕ)-entropies, introduced by Salicrú et al. [M. Salicrú et al., Commun. Stat. Theory Method. 22, 2015 (1993)], for a wide family of probabilistic models that includes quantum and classical statistical theories as particular cases. We extend previous works by exploring how to define (h, ϕ)-entropies in infinite dimensional models.

Jensen–Shannon divergence is a well known multi-purpose measure of dissimilarity between probability distributions. It has been proven that the square root of this quantity is a true metric in the sense that, in addition to the basic properties of a distance, it also satisfies the triangle inequality. In this work we extend this last result to prove that in fact it is possible to derive a monoparametric family of metrics from the classical Jensen–Shannon divergence. Motivated by our results, an application into the field of symbolic sequences segmentation is explored. Additionally, we analyze the possibility to extend this result into the quantum realm.