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For a fixed irrational $\theta>0$ with a prescribed irrationality measure function, we study the correlation $\int\limits_{1}^{X}\Delta\left(x\right)\Delta\left(\theta x\right)dx$, where $\Delta$ is the Dirichlet's Delta Function from the Divisor Problem. It is known that when $\theta$ have finite irrationality measure there's a decorrelation given in terms of its measure and a strong decorrelation is obtained at every positive irrational number, except, maybe, at the Liouville numbers. We prove that for the irrationals with a prescribed irrationality measure function $\psi$, a decorrelation can be obtained in terms of $\psi^{-1}$.

Quantum batteries are emerging as highly efficient energy storage devices that can exceed classical performance limits. Although there have been significant advancements in controlling these systems, challenges remain in stabilizing stored energy and minimizing losses due to inevitable environmental interaction. In this paper, we propose a protocol that employs selective weak measurements to protect quantum states from such influence and mitigate battery discharging. We establish thermodynamic constraints that allow this method to be implemented without disrupting the overall energy and ergotropy balance of the system. Our findings demonstrate that appropriately chosen measurement intensity can reduce unwanted discharging effects, thereby preserving ergotropy and improving the stability of quantum batteries. Additionally, we explore how weak measurements influence the coherent and incoherent components of ergotropy, providing new insights into the practical application of quantum coherence in energy storage technologies., Comment: 17 pages, 14 figures

Quantum metrology offers significant improvements in several quantum technologies. In this work, we propose a Gaussian quantum metrology protocol assisted by initial position-momentum correlations (PM). We employ a correlated Gaussian wave packet as a probe to examine the dynamics of Quantum Fisher Information (QFI) and purity based on PM correlations to demonstrate how to estimate the PM correlations and, more importantly, to unlock its potential applications such as a resource to enhance quantum thermometry. In the low-temperature regime, we find an improvement in the thermometry of the surrounding environment when the original system exhibits a non-null initial correlation (correlated Gaussian state). In addition, we explore the connection between the loss of purity and the gain in QFI during the process of estimating the effective environment coupling and its effective temperature.

Wave-particle duality is one of the most striking and counter-intuitive features of quantum mechanics, illustrating that two incompatible observables cannot be measured simultaneously with arbitrary precision. In this work, we experimentally demonstrate the equivalence of wave-particle duality and entropic uncertainty relations using orbital angular momentum (OAM) states of light. Our experiment utilizes an innovative and reconfigurable platform composed of few-mode optical fibers and photonic lanterns, showcasing the versatility of this technology for quantum information processing. Our results provide fundamental insights into the complementarity principle from an informational perspective, with implications for the broader field of quantum technologies., Comment: 9 pages, 5 figures

The monogamy of nonlocality is one the most intriguing and cryptographically significant predictions of quantum theory. The physical principle of information causality offers a promising means to understand and restrict the extent of nonlocality without invoking the abstract mathematical formalism of quantum theory. In this article, we demonstrate that the original bipartite formulation of information causality cannot imply non-trivial monogamy relations, thereby refuting the previous claims. Nevertheless, we show that the recently proposed multipartite formulation of information causality implies stronger-than-no-signaling monogamy relations. We use these monogamy relations to enhance the security of device-independent quantum key distribution against a no-signaling eavesdropper constrained by information causality., Comment: First draft, comments are welcome!

The superposition of causal order shows promise in various quantum technologies. However, the fragility of quantum systems arising from environmental interactions, leading to dissipative behavior and irreversibility, demands a deeper understanding of the possible instabilities in the coherent control of causal orders. In this work, we employ a collisional model to investigate the impact of an open control system on the generation of interference between two causal orders. We present the environmental instabilities for the switch of two arbitrary quantum operations and examine the influence of environmental temperature on each potential outcome of control post-selection. Additionally, we explore how environmental instabilities affect protocol performance, including switching between mutually unbiased measurement observables and refrigeration powered by causal order superposition, providing insights into broader implications., Comment: 7+8 pages, 3+7 figures

Hafnia-based ferroelectrics have become a valuable class of electronic functional materials at the nanoscale, showing great potential for next-generation memory and logic devices. However, more robust ferroelectric properties and better understanding of the polarization mechanisms are currently needed both in technology and science. Herein, we report the properties of oxygen-deficient Hf0.5Zr0.5O2 films with ultralarge remanent polarization (Pr) of 387 uC cm-2 at room temperature (1 kHz). Structure characterizations identify a new ferroelectric monoclinic Pc phase in these Hf0.5Zr0.5O2 films. The in-situ STEM measurements evidence polar displacements of the oxygen atoms, which move up and down in the Pc structure under applied DC bias fields, showing a huge displacement (1.6 A). DFT calculations optimized the Pc structure and also predicted a large polarization. The coexistence of the ferroelectric monoclinic (Pc) phases and orthorhombic (Pca21) is responsible for this superior ferroelectric properties. These findings are promising for hafnia-based ferroelectric applications in integrated ferroelectric devices, energy harvesting and actuators, etc.

Tuning searches are pivotal in High-Performance Computing (HPC), addressing complex optimization challenges in computational applications. The complexity arises not only from finely tuning parameters within routines but also potential interdependencies among them, rendering traditional optimization methods inefficient. Instead of scrutinizing interdependencies among parameters and routines, practitioners often face the dilemma of conducting independent tuning searches for each routine, thereby overlooking interdependence, or pursuing a more resource-intensive joint search for all routines. This decision is driven by the consideration that some interdependence analysis and high-dimensional decomposition techniques in literature may be prohibitively expensive in HPC tuning searches. Our methodology adapts and refines these methods to ensure computational feasibility while maximizing performance gains in real-world scenarios. Our methodology leverages a cost-effective interdependence analysis to decide whether to merge several tuning searches into a joint search or conduct orthogonal searches. Tested on synthetic functions with varying levels of parameter interdependence, our methodology efficiently explores the search space. In comparison to Bayesian-optimization-based full independent or fully joint searches, our methodology suggested an optimized breakdown of independent and merged searches that led to final configurations up to 8% more accurate, reducing the search time by up to 95%. When applied to GPU-offloaded Real-Time Time-Dependent Density Functional Theory (RT-TDDFT), an application in computational materials science that challenges modern HPC autotuners, our methodology achieved an effective tuning search. Its adaptability and efficiency extend beyond RT-TDDFT, making it valuable for related applications in HPC.

The logics $\mathsf{CS4}$ and $\mathsf{IS4}$ are the two leading intuitionistic variants of the modal logic $\mathsf{S4}$. Whether the finite model property holds for each of these logics have been long-standing open problems. It was recently shown that $\mathsf{IS4}$ has the finite frame property and thus the finite model property. In this paper, we prove that $\mathsf{CS4}$ also enjoys the finite frame property. Additionally, we investigate the following three logics closely related to $\mathsf{IS4}$. The logic $\mathsf{GS4}$ is obtained by adding the G\"odel--Dummett axiom to $\mathsf{IS4}$; it is both a superintuitionistic and a fuzzy logic and has previously been given a real-valued semantics. We provide an alternative birelational semantics and prove strong completeness with respect to this semantics. The extension $\mathsf{GS4^c}$ of $\mathsf{GS4}$ corresponds to requiring a crisp accessibility relation on the real-valued semantics. We give a birelational semantics corresponding to an extra confluence condition on the $\mathsf{GS4}$ birelational semantics and prove strong completeness. Neither of these two logics have the finite model property with respect to their real-valued semantics, but we prove that they have the finite frame property for their birelational semantics. Establishing the finite birelational frame property immediately establishes decidability, which was previously open for these two logics. Our proofs yield NEXPTIME upper bounds. The logic $\mathsf{S4I}$ is obtained from $\mathsf{IS4}$ by reversing the roles of the modal and intuitionistic relations in the birelational semantics. We also prove the finite frame property, and thereby decidability, for $\mathsf{S4I}$, Comment: arXiv admin note: substantial text overlap with arXiv:2104.15053

We present the PanAf20K dataset, the largest and most diverse open-access annotated video dataset of great apes in their natural environment. It comprises more than 7 million frames across ~20,000 camera trap videos of chimpanzees and gorillas collected at 14 field sites in tropical Africa as part of the Pan African Programme: The Cultured Chimpanzee. The footage is accompanied by a rich set of annotations and benchmarks making it suitable for training and testing a variety of challenging and ecologically important computer vision tasks including ape detection and behaviour recognition. Furthering AI analysis of camera trap information is critical given the International Union for Conservation of Nature now lists all species in the great ape family as either Endangered or Critically Endangered. We hope the dataset can form a solid basis for engagement of the AI community to improve performance, efficiency, and result interpretation in order to support assessments of great ape presence, abundance, distribution, and behaviour and thereby aid conservation efforts., Comment: Accepted at IJCV

In temporal extensions of Answer Set Programming (ASP) based on linear-time, the behavior of dynamic systems is captured by sequences of states. While this representation reflects their relative order, it abstracts away the specific times associated with each state. In many applications, however, timing constraints are important like, for instance, when planning and scheduling go hand in hand. We address this by developing a metric extension of linear-time Dynamic Equilibrium Logic, in which dynamic operators are constrained by intervals over integers. The resulting Metric Dynamic Equilibrium Logic provides the foundation of an ASP-based approach for specifying qualitative and quantitative dynamic constraints. As such, it constitutes the most general among a whole spectrum of temporal extensions of Equilibrium Logic. In detail, we show that it encompasses Temporal, Dynamic, Metric, and regular Equilibrium Logic, as well as its classic counterparts once the law of the excluded middle is added., Comment: arXiv admin note: text overlap with arXiv:2304.14778

The Gouy phase is essential for accurately describing various wave phenomena, ranging from classical electromagnetic waves to matter waves and quantum optics. In this work, we employ phase-space methods based on the cross-Wigner transformation to analyze spatial and temporal interference in the evolution of matter waves characterized initially by a correlated Gaussian wave packet. First, we consider the cross-Wigner of the initial function with its free evolution, and second for the evolution through a double-slit arrangement. Different from the wave function which acquires a global Gouy phase, we find that the cross-Wigner acquires a Gouy phase difference due to different evolution times. The results suggest that temporal like-Gouy phases are important for an accurate description of temporal interference. Furthermore, we propose a technique based on the Wigner function to reconstruct the cross-Wigner from the spatial intensity interference term in a double-slit experiment with matter waves.

GPU-embedded systems have gained popularity across various domains due to their efficient power consumption. However, in order to meet the demands of real-time or time-consuming applications running on these systems, it is crucial for them to be tuned to exhibit high performance. This paper addresses the issue by developing and comparing two tuning methodologies on GPU-embedded systems, and also provides performance insights for developers and researchers seeking to optimize applications running on these architectures. We focus on parallel prefix operations, such as FFT, scan primitives, and tridiagonal system solvers, which are performance-critical components in many applications. The study introduces an analytical model-driven tuning methodology and a Machine Learning (ML)-based tuning methodology. We evaluate the performance of the two tuning methodologies for different parallel prefix implementations of the BPLG library in an NVIDIA Jetson system, and compare their performance to the ones achieved through an exhaustive search. The findings shed light on the best strategies for handling the open challenge of performance portability for major computational patterns among server and embedded devices, providing practical guidance for offline and online tuning. We also address the existing gap in performance studies for parallel computational patterns in GPU-embedded systems by comparing the BPLG performance against other state-of-the-art libraries, including CUSPARSE, CUB, and CUFFT.

Extensions of Answer Set Programming with language constructs from temporal logics, such as temporal equilibrium logic over finite traces (TELf), provide an expressive computational framework for modeling dynamic applications. In this paper, we study the so-called past-present syntactic subclass, which consists of a set of logic programming rules whose body references to the past and head to the present. Such restriction ensures that the past remains independent of the future, which is the case in most dynamic domains. We extend the definitions of completion and loop formulas to the case of past-present formulas, which allows capturing the temporal stable models of a set of past-present temporal programs by means of an LTLf expression.

We investigate a version of linear temporal logic whose propositional fragment is G\"odel-Dummett logic (which is well known both as a superintuitionistic logic and a t-norm fuzzy logic). We define the logic using two natural semantics: first a real-valued semantics, where statements have a degree of truth in the real unit interval and second a `bi-relational' semantics. We then show that these two semantics indeed define one and the same logic: the statements that are valid for the real-valued semantics are the same as those that are valid for the bi-relational semantics. This G\"odel temporal logic does not have any form of the finite model property for these two semantics: there are non-valid statements that can only be falsified on an infinite model. However, by using the technical notion of a quasimodel, we show that every falsifiable statement is falsifiable on a finite quasimodel, yielding an algorithm for deciding if a statement is valid or not. Later, we strengthen this decidability result by giving an algorithm that uses only a polynomial amount of memory, proving that G\"odel temporal logic is PSPACE-complete. We also provide a deductive calculus for G\"odel temporal logic, and show this calculus to be sound and complete for the above-mentioned semantics, so that all (and only) the valid statements can be proved with this calculus., Comment: arXiv admin note: substantial text overlap with arXiv:2205.00574, arXiv:2205.05182

Complementarity plays a pivotal role in understanding a diverse range of quantum phenomena. Here, we show how the tradeoff between quantities of a complete complementarity relation is modified in an arbitrary spacetime for a particle with an internal spin. This effect stems from local Wigner rotations in the spacetime, which couple the spin to the system's external degrees of freedom. To conduct our study, we utilize two generalized delayed-choice interferometers. Despite differences in complementarity tradeoffs inside the interferometers, the interferometric visibility of both setups coincides in any relativistic regime. Our results extend the finding that general relativity induces a universal decoherence effect on quantum superpositions, as local Wigner rotations, being purely kinematical, preclude any spin dynamics. To illustrate, we analyze the Newtonian limit of our results., Comment: Author's accepted manuscript

Correlation is the basic mechanism of every measurement model, as one never accesses the measured system directly. Instead, correlations are created, codifying information about the measurable property into the environment. Here, we address the problem of the emergence of physical reality from the quantum world by introducing a model that interpolates between weak and strong non-selective measurements for qudits. By utilizing Heisenberg-Weyl operators, our model suggests that independently of the interaction intensity between the system and the environment, full information about the observable of interest can always be obtained by making the system interact with many environmental qudits, following a Quantum Darwinism framework., Comment: 5 pages + Appendix, 1 figure

In temporal extensions of Answer Set Programming (ASP) based on linear-time, the behavior of dynamic systems is captured by sequences of states. While this representation reflects their relative order, it abstracts away the specific times associated with each state. However, timing constraints are important in many applications like, for instance, when planning and scheduling go hand in hand. We address this by developing a metric extension of linear-time temporal equilibrium logic, in which temporal operators are constrained by intervals over natural numbers. The resulting Metric Equilibrium Logic provides the foundation of an ASP-based approach for specifying qualitative and quantitative dynamic constraints. To this end, we define a translation of metric formulas into monadic first-order formulas and give a correspondence between their models in Metric Equilibrium Logic and Monadic Quantified Equilibrium Logic, respectively. Interestingly, our translation provides a blue print for implementation in terms of ASP modulo difference constraints., Comment: Under consideration in Theory and Practice of Logic Programming (TPLP)

The manual processing and analysis of videos from camera traps is time-consuming and includes several steps, ranging from the filtering of falsely triggered footage to identifying and re-identifying individuals. In this study, we developed a pipeline to automatically analyze videos from camera traps to identify individuals without requiring manual interaction. This pipeline applies to animal species with uniquely identifiable fur patterns and solitary behavior, such as leopards (Panthera pardus). We assumed that the same individual was seen throughout one triggered video sequence. With this assumption, multiple images could be assigned to an individual for the initial database filling without pre-labeling. The pipeline was based on well-established components from computer vision and deep learning, particularly convolutional neural networks (CNNs) and scale-invariant feature transform (SIFT) features. We augmented this basis by implementing additional components to substitute otherwise required human interactions. Based on the similarity between frames from the video material, clusters were formed that represented individuals bypassing the open set problem of the unknown total population. The pipeline was tested on a dataset of leopard videos collected by the Pan African Programme: The Cultured Chimpanzee (PanAf) and achieved a success rate of over 83% for correct matches between previously unknown individuals. The proposed pipeline can become a valuable tool for future conservation projects based on camera trap data, reducing the work of manual analysis for individual identification, when labeled data is unavailable.

Quantum thermodynamics seeks to extend non-equilibrium stochastic thermodynamics to small quantum systems where non-classical features are essential to its description. Such a research area has recently provided meaningful theoretical and experimental advances by exploring the wealth and the power of quantum features along with informational aspects of a system's thermodynamics. The relevance of such investigations is related to the fact that quantum technological devices are currently at the forefront of science and engineering applications. This short review article provides an overview of some concepts in quantum thermodynamics highlighting test-of-principles experiments using nuclear magnetic resonance techniques.

The Aharonov-Bohm effect is a fundamental topological phenomenon with a wide range of applications. It consists of a charge encircling a region with a magnetic flux in a superposition of wave packets having their relative phase affected by the flux. In this work, we analyze this effect using an entropic measure known as realism, originally introduced as a quantifier of a system's degree of reality and mathematically related to notions of global and local quantum coherence. More precisely, we look for observables that lead to gauge-invariant realism associated with the charge before it completes its loop. We find that the realism of these operators has a sudden change when the line connecting the center of both wave packets crosses the solenoid. Moreover, we consider the case of a quantized magnetic-field source, pointing out similarities and differences between the two cases. Finally, we discuss some consequences of these results., Comment: 13 pages (including appendixes and references), 4 figures. Author's published version

A quantum-controlled device may produce a scenario in which two general quantum operations can be performed in such a way that it is not possible to associate a definite order for the operations application. Such an indefinite causal order can be explored to produce nontrivial effects in quantum thermal devices. We investigate a measurement-powered thermal device that consists of generalized measurement channels with adjustable intensity parameters, where energy is exchanged with the apparatus in the form of work or heat. The measurement-based device can operate as a heat engine, a thermal accelerator, or a refrigerator, according to a measurement intensity setting. By employing a quantum switch of two measurement channels, we explore a thermal device fueled by an indefinite causal order. We also discuss how a coherent control over an indefinite causal order structure can change the operating regimes of the measurement-powered thermal device to produce an advantage when compared to a scenario with an incoherent control of the order switch., Comment: 14 pages, 9 figures, typos removed, closer to the published version

We consider G\"odel temporal logic ($\sf GTL$), a variant of linear temporal logic based on G\"odel--Dummett propositional logic. In recent work, we have shown this logic to enjoy natural semantics both as a fuzzy logic and as a superintuitionistic logic. Using semantical methods, the logic was shown to be {\sc pspace}-complete. In this paper we provide a deductive calculus for $\sf GTL$, and show this calculus to be sound and complete for the above-mentioned semantics., Comment: arXiv admin note: text overlap with arXiv:2205.00574

We investigate a non-classical version of linear temporal logic whose propositional fragment is G\"odel--Dummett logic (which is well known both as a superintuitionistic logic and a t-norm fuzzy logic). We define the logic using two natural semantics, a real-valued semantics and a bi-relational semantics, and show that these indeed define one and the same logic. Although this G\"odel temporal logic does not have any form of the finite model property for these two semantics, we show that every falsifiable formula is falsifiable on a finite quasimodel, which yields decidability of the logic. We then strengthen this result by showing that this G\"odel temporal logic is PSPACE-complete.