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We investigate the dynamics of fermion localization within the framework of $f(T, B)$ gravity featuring non-minimal couplings. Starting from the Dirac action for a spin-$1/2$ fermion in a five-dimensional spacetime governed by torsional $f(T, B)$ gravity, we derive the Dirac equation and we explore its solutions under various non-minimal coupling functions. We examine two realistic forms of the torsional non-minimal coupling and reveal distinct behaviors that impact the localization of both massless and massive fermionic modes on the brane. Additionally, we employ probabilistic measurements, including Shannon entropy theory, Fisher information theory, and relative probability, to analyze the localization of these fermionic modes. The observed effects offer potential insights into probing torsional modifications.

Using a random matrix approach, combined with the ergodicity hypothesis, we derive an analytical expression for the time-averaged quantum Fisher information (QFI) that applies to all quantum chaotic systems governed by Dyson's ensembles. Our approach integrates concepts of randomness, multipartite entanglement and quantum chaos. Furthermore, the QFI proves to be highly dependent on the dimension of the Krylov space confining the chaotic dynamics: it ranges from $N^2/3$ for $N$ qubits in the permutation-symmetric subspace (e.g. for chaotic kicked top models with long-range interactions), to $N$ when the dynamics extend over the full Hilbert space with or without bit reversal symmetry or parity symmetry (e.g. in chaotic models with short-range Ising-like interactions). In the former case, the QFI reveals multipartite entanglement among $N/3$ qubits. Interestingly this result can be related to isotropic substructures in the Wigner distribution of chaotic states and demonstrates the efficacy of quantum chaos for Heisenberg-scaling quantum metrology. Finally, our general expression for the QFI agrees with that obtained for random states and, differently from out-of-time-order-correlators, it can also distinguish chaotic from integrable unstable spin dynamics., Comment: 7+7 pages, 4+2 figures, comments are welcome

The Event Horizon Telescope (EHT) imaging of the supermassive black holes at the centers of Messier 87 galaxy and the Milky Way galaxy marks a significant step in observing the photon rings and central brightness depression that define the optical appearance of black holes with an accretion disk scenario. Inspired by this, we take into account a static and spherically symmetric magnetically charged regular black hole (MCRBH) metric characterized by its mass and an additional parameter q, which arises from the coupling of Einstein gravity and nonlinear electrodynamics (NLED) in the weak field approximation. This parameterized model offers a robust foundation for testing the coupling of Einstein gravity and NLED in the weak-field approximation, using the EHT observational results. In this study, we investigate the geodesic motion of particles around the solution, followed by a discussion of its fundamental geometrical characteristics such as scalar invariants. Using null geodesics, we examine how the model parameter influences the behavior of the photon sphere radius and the associated shadow silhouette. We seek constraints on q by applying the EHT results for supermassive black holes M87* and Sgr A*. Furthermore, it is observed that the geodesics of time-like particles are susceptible to variations in q, which can have an impact on the traits of the innermost stable circular orbit and the marginally bounded orbit. Our primary objective is to probe how the free parameter q affects various aspects of the accretion disk surrounding the MCRBH using the thin-disk approximation. Next, we discuss the physical characteristics of the thin accretion disk as well as the observed shadows and rings of the MCRBH, along with its luminosity, across various accretion models. Ultimately, variations in accretion models and the parameter q yield distinct shadow images and optical appearances of the MCRBH., Comment: 31 pages, 2 tables, 16 figures

This study delves deeply into braneworld scenarios within modified gravity models, investigating their impact on particle localization and the structure of branes. Through a comprehensive blend of numerical analyses and theoretical inquiries, we unravel a nuanced correlation between deviations from standard General Relativity (GR) and the emergence of split branes. By employing probabilistic measurements, we pinpoint stable configurations that align with brane division intervals, thus challenging prevailing assumptions regarding the gravitational framework of our universe. Furthermore, our investigation extends to the localization of fermions within the brane, exposing intricate dynamics shaped by scalar field characteristics and modifications to gravitational models. By harnessing quantum information measurements, notably Shannon entropy, we discern heightened probabilities of fermion localization within the brane as gravitational models diverge from standard paradigms. This underscores the limitations of General Relativity in comprehensively describing the complexities inherent in our universe. Lastly, our exploration of massive fermions unveils their potential to breach the confines of the brane, hinting at promising avenues for future experimental endeavors aimed at probing the nature of extra dimensions and gravitational interactions. This suggests exciting prospects for advancing our understanding of fundamental physics beyond conventional boundaries.

This study investigates the efficacy of Stochastic Hill Climbing with Random Restarts (SHC-RR) compared to Local Search (LS) strategies within the Quantum Approximate Optimization Algorithm (QAOA) framework across various problem models. Employing uniform parameter settings, including the number of restarts and SHC steps, we analyze LS with two distinct perturbation operations: multiplication and summation. Our comparative analysis encompasses multiple versions of max-cut and random Ising model (RI) problems, utilizing QAOA models with depths ranging from $1L$ to $3L$. These models incorporate diverse mixing operator configurations, which integrate $RX$ and $RY$ gates, and explore the effects of an entanglement stage within the mixing operator. We also used Quantum Fisher Information (QFI) to compare the different QAOA models, demonstrating the importance of the placement of the entanglement stage in the overall performance of QAOA. Additionally, we observed that the QFI values of previous parameters are not affected as the depth of the quantum circuit increases. Our results consistently show that SHC-RR outperforms LS approaches, showcasing superior efficacy despite its ostensibly simpler optimization mechanism. Furthermore, we observe that the inclusion of entanglement stages within mixing operators significantly impacts model performance, either enhancing or diminishing results depending on the specific problem context., Comment: 51 pages, 19 tables, 22 figures

The pursuit of quantum-enhanced parameter estimations without the need for nonclassical initial states has long been driven by the goal of achieving experimentally accessible quantum metrology. In this paper, employing a coherent averaging mechanism, we prove that the prototypical cavity-quantum electrodynamics (QED) system, such as the Tavis-Cummings (TC) model, enables us to achieve not only the Heisenberg scaling (HS) precision in terms of the average photon number but also the double-HS sensitivity concerning both the average photon and atom numbers. Such a double sensibility can be experimentally realized by introducing either photon- or atom-number fluctuations through quantum squeezing. Furthermore, we discuss the methodology to achieve this double-HS precision in a realistic experimental circumstance where the squeezing is not perfect. Our results provide insights into understanding the coherent averaging mechanism for evaluating quantum-enhanced precision measurements and also present a usable metrological application of the cavity QED systems.

In this research, we delve into the localization patterns of fermionic fields within a braneworld setting, employing a modified gravity model denoted as $f(Q)$. Our investigation revolves around two specific models, $f_1(Q)=Q+kQ^n$ and $f_2(Q)=Q+k_1Q^2+k_2Q^3$, where we systematically vary the parameters $n$ and $k_{1,2}$. Through an in-depth analysis encompassing the effective potential, massless, and massive modes, we elucidate how deviations from the conventional symmetric teleparallel equivalent of general relativity (STEGR) gravity impact the localization of fermionic fields. To ensure greater precision, our methodology integrates probabilistic measures such as Shannon entropy and relative probability. Moreover, we gauge the stability of these models employing differential configurational entropy (DCE), revealing a compelling correlation between the most stable configurations and the emergence of novel structures within the background scalar field. This work significantly contributes to our understanding of the gravitational modifications' intricate influence on fermionic field localization within braneworld scenarios. By shedding light on these dynamics, it advances the broader comprehension of the interplay between gravity modifications and fermionic field behaviors in these theoretical frameworks.

The Tavis-Cummings (TC) model, which serves as a natural physical realization of a quantum battery, comprises $N_b$ atoms as battery cells that collectively interact with a shared photon field, functioning as the charger, initially containing $n_0$ photons. In this study, we introduce the invariant subspace method to effectively represent the quantum dynamics of the TC battery. Our findings indicate that in the limiting case of $n_0\!\gg\! N_b$ or $N_b\!\gg\! n_0$, a distinct SU(2) symmetry emerges in the dynamics, thereby ensuring the realization of optimal energy storage. We also establish a negative relationship between the battery-charger entanglement and the energy storage capacity. As a result, we demonstrate that the asymptotically optimal energy storage can be achieved in the scenario where $N_b\!=\!n_0\!\gg\! 1$. Our approach not only enhances our comprehension of the algebraic structure inherent in the TC model but also contributes to the broader theoretical framework of quantum batteries. Furthermore, it provides crucial insights into the relation between energy transfer and quantum correlations., Comment: 8 pages, 4 figures

Quantum measurements are key to quantum metrology. Constrained by experimental capabilities, collective measurements on a large number of copies of metrological probes can pose significant challenges. Therefore, the locality in quantum measurements must be considered. In this work, we propose a method dubbed as the "iterative matrix partition" approach to elucidate the underlying structures of optimal local measurements, with and without classical communications, that saturate the quantum Cram\'er-Rao Bound (qCRB). Furthermore, we find that while exact saturation is possible for all two-qubit pure states, it is generically restrictive for multi-qubit pure states. However, we demonstrate that the qCRB can be universally saturated in an approximate manner through adaptive coherent controls, as long as the initial state is separable and the Hamiltonian allows for interaction. Our results bridge the gap between theoretical proposals and experiments in many-body metrology and can find immediate applications in noisy intermediate-scale quantum devices., Comment: 6+13 pages, 3 figures. Comments are welcome!

Quantum many-body interactions can induce quantum entanglement among particles, rendering them valuable resources for quantum-enhanced sensing. In this work, we derive a universal and fundamental bound for the growth of the quantum Fisher information. We apply our bound to the metrological protocol requiring only separable initial states, which can be readily prepared in experiments. By establishing a link between our bound and the Lieb-Robinson bound, which characterizes the operator growth in locally interacting quantum many-body systems, we prove that the precision cannot surpass the shot noise limit at all times in locally interacting quantum systems. This conclusion also holds for an initial state that is the non-degenerate ground state of a local and gapped Hamiltonian. These findings strongly hint that when one can only prepare separable initial states, nonlocal and long-range interactions are essential resources for surpassing the shot noise limit. This observation is confirmed through numerical analysis on the long-range Ising model. Our results bridge the field of many-body quantum sensing and operator growth in many-body quantum systems and open the possibility to investigate the interplay between quantum sensing and control, many-body physics and information scrambling, Comment: Close to the published version

Quantum metrology is recognized for its capability to offer high-precision estimation by utilizing quantum resources, such as quantum entanglement. Here, we propose a generalized Tavis-Cummings model by introducing the $XY$ spin interaction to explore the impact of the many-body effect on estimation precision, quantified by the quantum Fisher information (QFI). By deriving the effective description of our model, we establish a closed relationship between the QFI and the spin fluctuation induced by the $XY$ spin interaction. Based on this exact relation, we emphasize the indispensable role of the spin anisotropy in achieving the Heisenberg-scaling precision for estimating a weak magnetic field. Furthermore, we observe that the estimation precision can be enhanced by increasing the strength of the spin anisotropy. We also reveal a clear scaling transition of the QFI in the Tavis-Cummings model with the reduced Ising interaction. Our results contribute to the enrichment of metrology theory by considering many-body effects, and they also present an alternative approach to improving the estimation precision by harnessing the power provided by many-body quantum phases.

Structured light beams, in particular those carrying orbital angular momentum (OAM), have gained a lot of attention due to their potential for enlarging the transmission capabilities of communication systems. However, the use of OAM-carrying light in communications faces two major problems, namely distortions introduced during propagation in disordered media, such as the atmosphere or optical fibers, and the large divergence that high-order OAM modes experience. While the use of non-orthogonal modes may offer a way to circumvent the divergence of high-order OAM fields, artificial intelligence (AI) algorithms have shown promise for solving the mode-distortion issue. Unfortunately, current AI-based algorithms make use of large-amount data-handling protocols that generally lead to large processing time and high power consumption. Here we show that a low-power, low-cost image sensor can itself act as an artificial neural network that simultaneously detects and reconstructs distorted OAM-carrying beams. We demonstrate the capabilities of our device by reconstructing (with a 95$\%$ efficiency) individual Vortex, Laguerre-Gaussian (LG) and Bessel modes, as well as hybrid (non-orthogonal) coherent superpositions of such modes. Our work provides a potentially useful basis for the development of low-power-consumption, light-based communication devices.

In this paper, we employ PCA and t-SNE analysis to gain deeper insights into the behavior of entangled and non-entangled mixing operators within the Quantum Approximate Optimization Algorithm (QAOA) at varying depths. Our study utilizes a dataset of parameters generated for max-cut problems using the Stochastic Hill Climbing with Random Restarts optimization method in QAOA. Specifically, we examine the $RZ$, $RX$, and $RY$ parameters within QAOA models at depths of $1L$, $2L$, and $3L$, both with and without an entanglement stage inside the mixing operator. The results reveal distinct behaviors when we process the final parameters of each set of experiments with PCA and t-SNE, where in particular, entangled QAOA models with $2L$ and $3L$ present an increase in the amount of information that can be preserved in the mapping. Furthermore, certain entangled QAOA graphs exhibit clustering effects in both PCA and t-SNE. Overall, the mapping results clearly demonstrate a discernible difference between entangled and non-entangled models, quantified numerically through explained variance in PCA and Kullback-Leibler divergence (after optimization) in t-SNE, where some of these differences are also visually evident in the mapping data produced by both methods., Comment: 38 pages, 36 figures, 24 tables

Magnons, as fundamental quasiparticles emerged in elementary spin excitations, hold a big promise for innovating quantum technologies in information coding and processing. Here we discover subtle roles of entanglement in a metrological scheme based on an experimentally feasible cavity magnomechanical system, where the magnons are responsible for sensing a weak magnetic field whereas the cavity field carries out a precision measurement of the weak field. By establishing exact relations between the Fisher information and entanglement, we show that for the weak coupling case the measurement precision can reach the Heisenberg limit, whereas quantum criticality enables us to enhance measurement precision for the strong coupling case. In particular, we also find that the entanglement between magnons and photons is of crucial importance during the dynamical encoding process, but the presence of such an entanglement in the measurement process dramatically reduces the final measurement precision., Comment: 7pages+ Supplemental material 7 pages

AST3-2 is the second of the three Antarctic Survey Telescopes, aimed at wide-field time-domain optical astronomy. It is located at Dome A, Antarctica, which is by many measures the best optical astronomy site on the Earth's surface. Here we present the data from the AST3-2 automatic survey in 2016 and the photometry results. The median 5$\sigma$ limiting magnitude in $i$-band is 17.8 mag and the light curve precision is 4 mmag for bright stars. The data release includes photometry for over 7~million stars, from which over 3,500 variable stars were detected, with 70 of them newly discovered. We classify these new variables into different types by combining their light curve features with stellar properties from surveys such as StarHorse., Comment: 16 pages, 20 figures, accepted for publication in MNRAS

We introduce the Dunkl-Darboux III oscillator Hamiltonian in N dimensions, defined as a $\lambda-$deformation of the N-dimensional Dunkl oscillator. This deformation can be interpreted either as the introduction of a non-constant curvature related to $\lambda$ on the underlying space or, equivalently, as a Dunkl oscillator with a position-dependent mass function. This new quantum model is shown to be exactly solvable in arbitrary dimension N, and its eigenvalues and eigenfunctions are explicitly presented. Moreover, it is shown that in the two-dimensional case both the Darboux III and the Dunkl oscillators can be separately coupled with a constant magnetic field, thus giving rise to two new exactly solvable quantum systems in which the effect of a position-dependent mass and the Dunkl derivatives on the structure of the Landau levels can be explicitly studied. Finally, the whole 2D Dunkl-Darboux III oscillator is coupled with the magnetic field and shown to define an exactly solvable Hamiltonian, where the interplay between the $\lambda$-deformation and the magnetic field is explicitly illustrated.

To advance the full potential of quantum networks one should be able to distribute quantum resources over long distances at appreciable rates. As a consequence, all components in the networks need to have large multimode capacity to manipulate photonic quantum states. Towards this end, a multimode photonic quantum memory, especially one operating at telecom wavelength, remains a key challenge. Here we demonstrate a spectro-temporally multiplexed quantum memory at 1532 nm. Multimode quantum storage of telecom-band heralded single photons is realized by employing the atomic frequency comb protocol in a 10-m-long cryogenically cooled erbium doped silica fibre. The multiplexing encompasses five spectral channels - each 10 GHz wide - and in each of these up to 330 temporal modes, resulting in the simultaneous storage of 1650 modes of single photons. Our demonstrations open doors for high-rate quantum networks, which are essential for future quantum internet.

Recent investigations suggest that the use of non-classical states of light, such as entangled photon pairs, may open new and exciting avenues in experimental two-photon absorption spectroscopy. Despite several experimental studies of entangled two-photon absorption (eTPA), there is still a heated debate on whether eTPA has truly been observed. This interesting debate has arisen, mainly because it has been recently argued that single-photon-loss mechanisms, such as scattering or hot-band absorption may mimic the expected entangled-photon linear absorption behavior. In this work, we focus on transmission measurements of eTPA, and explore three different two-photon quantum interferometers in the context of assessing eTPA. We demonstrate that the so-called N00N-state configuration is the only one amongst those considered insensitive to linear (single-photon) losses. Remarkably, our results show that N00N states may become a potentially powerful tool for quantum spectroscopy, and place them as a strong candidate for the certification of eTPA in an arbitrary sample., Comment: 10 pages, 4 figures. Updated References

We propose a new "superpotential" and find that neither the supersymmetric energy conditions nor the associated shape invariance condition remain valid. On the other hand a new energy condition $E_{n}^{+}-E_{n}^{(-)}=2$ between the two partner Hamiltonian $H^{(\pm)}$ emerges. Mathematical proof supported the present findings with examples are presented. It is observed that, when the superpotential is associated with discontinuity or distortion, SUSY energy conditions and the shape invariance condition will no longer hold good., Comment: There are a few mistakes occurred in this work

We investigate the connection between quantum resources and extractable work in quantum batteries. We demonstrate that quantum coherence in the battery or the battery-charger entanglement is a necessary resource for generating nonzero extractable work during the charging process. At the end of the charging process, we also establish a tight link of coherence and entanglement with the final extractable work: coherence naturally promotes the coherent work while coherence and entanglement inhibit the incoherent work. We also show that obtaining maximally coherent work is faster than obtaining maximally incoherent work. Examples ranging from the central-spin battery and the Tavis-Cummings battery to the spin-chain battery are given to illustrate these results., Comment: 6+1 pages, 2 figures

We consider a central-spin battery where $N_b$ central spins serve as battery cells and $N_c$ bath spins serve as charging units. It is shown that the energy stored in the battery that can be extractable is quantified by the ergotropy, and that battery-charger entanglement is quantified via the Von Neumann entropy. By using an exact approach to a one-cell and two-cell battery, our analytical results suggest that, during the charging process, the extractable work slowly increases before the battery-charger entanglement reaches its maximum and then it will rapidly increase when the entanglement begins to decrease. In particular, we rigorously show that there is an inverse relationship between the extractable work and the entanglement at the end of the charging process. Moreover, we investigate different approaches to realize optimal work extraction without wasted energy. Among them a central-spin battery with an unpolarized Dicke state as the charger possesses a universal charging time $\propto 1/N_c$, large extractable work, and $\sqrt{N_c}$-improvement of charging power compared with the battery in the Tavis-Cummings limit. The above-mentioned results have also been numerically verified in multi-cell batteries. Our results pave the way to improve extractable work storage in the central-spin battery and highlight a competitive relation between the extractable work and the battery-charger entanglement., Comment: 8 pages, 4 figures

In this work we introduce a quantum sorting algorithm with adaptable requirements of memory and circuit depth, and then use it to develop a new quantum version of the classical machine learning algorithm known as k-nearest neighbors (k-NN). Both the efficiency and performance of this new quantum version of the k-NN algorithm are compared to those of the classical k-NN and another quantum version proposed by Schuld et al. \cite{Int13}. Results show that the efficiency of both quantum algorithms is similar to each other and superior to that of the classical algorithm. On the other hand, the performance of our proposed quantum k-NN algorithm is superior to the one proposed by Schuld et al. and similar to that of the classical k-NN.