Imaginarity has proven to be a valuable resource in various quantum information processing tasks. A natural question arises: can the imaginarity of quantum states be broadcast via real operations? In this work, we present explicit structures for nonreal states whose imaginarity can be broadcast and cloned. That is, for a nonreal state, its imaginarity can be cloned if and only if it is a direct sum of several maximally imaginary states under orthogonal transformation, and its imaginarity can be broadcast if and only if it is a direct sum of a real state and some nonreal qubit states which are mixtures of two orthogonal maximally imaginary states under orthogonal transformation. In particular, we show that for a nonreal pure state, its imaginarity cannot be broadcast unless it is a maximally imaginary state. Furthermore, we derive a trade-off relation on the imaginarity broadcasting of pure states in terms of the measure of irreversibility of quantum states concerning real operations and the geometric measure of imaginarity. In addition, we demonstrate that any faithful measure of imaginarity is not superadditive.

Photonic hyper-parallel quantum gates play a critical role in high-capacity quantum communication and fast quantum computing. Here, based on photon scattering in one-dimensional (1D) waveguides, we present some heralded schemes for constructing four-qubit hyper-controlled-not (hyper-CNOT) gates in two-photon systems. The qubits are encoded on both the polarization and spatial-mode degrees of freedoms (DOFs) of the photons, which can simplify the quantum circuit and reduce the quantum resource consumption. In our schemes, the faulty scattering events between photons and emitters caused by system imperfections can be filtered out and discarded. That is, our protocols for hyper-CNOT gates work in a heralded way. Our calculations show that, with great progress in the emitter-waveguide systems, our photonic hyper-CNOT gates may be experimentally feasible.

Variational quantum algorithms are promising methods with the greatest potential to achieve quantum advantage, widely employed in the era of noisy intermediate-scale quantum computing. This study presents an advanced variational hybrid algorithm (EVQLSE) that leverages both quantum and classical computing paradigms to address the solution of linear equation systems. Initially, an innovative loss function is proposed, drawing inspiration from the similarity measure between two quantum states. This function exhibits a substantial improvement in computational complexity when benchmarked against the variational quantum linear solver. Subsequently, a specialized parameterized quantum circuit structure is presented for small-scale linear systems, which exhibits powerful expressive capabilities. Through rigorous numerical analysis, the expressiveness of this circuit structure is quantitatively assessed using a variational quantum regression algorithm, and it obtained the best score compared to the others. Moreover, the expansion in system size is accompanied by an increase in the number of parameters, placing considerable strain on the training process for the algorithm. To address this challenge, an optimization strategy known as quantum parameter sharing is introduced, which proficiently minimizes parameter volume while adhering to exacting precision standards. Finally, EVQLSE is successfully implemented on a quantum computing platform provided by IBM for the resolution of large-scale problems characterized by a dimensionality of 2²⁰.

The eikonal approximation (EA) is widely used in various high-energy scattering problems. In this work we generalize this approximation from the scattering problems with time-independent Hamiltonian to the ones with periodical Hamiltonians, i.e., the Floquet scattering problems. We further illustrate the applicability of our generalized EA via the scattering problem with respect to a shaking spherical square-well potential, by comparing the results given by this approximation and the exact ones. The generalized EA we developed is helpful for the research of manipulation of high-energy scattering processes with external field, e.g. the manipulation of atom, molecule or nuclear collisions or reactions via strong laser fields.

In our study of super quantum discord between two excitonic qubits inside a coupled semiconductor quantum dots system, our primary focus is to uncover the impact of weak measurement on its quantum characteristics. To achieve this, we analyze how varying the measurement strength x, affects this super quantum correlation in the presence of thermal effects. Additionally, we assess the effect of this variation on the system's evolution against its associated quantum parameters; external electric fields, exciton–exciton dipole interaction energy and Förster interaction. Our findings indicate that adjusting x to smaller values effectively enhances the super quantum correlation, making weak measurements act as a catalyst. This adjustment ensures its robustness against thermal effects while preserving the non-classical attributes of the system. Furthermore, our study unveils that the effect of weak measurements on this latter surpasses the quantum effects associated with the system. Indeed, manipulating the parameter x allows the weak measurement to function as a versatile tool for modulating quantum characteristics and controlling exciton–exciton interactions within the coupled semiconductor quantum dots system.

Effective propagation of information among multiple users is the purpose of realizing large-scale quantum communication networks. In this paper, multicast protocols for any single, two and three qubits with real amplitude and complex phase information are presented. They were realized using a composite of Greenberger–Horne–Zeilinger states as shared channels. Joint remote state preparation was the main method for completing quantum multicast. At the same time, quantum state tomography of the schemes was carried out on the IBM Quantum platform. The obtained states were compared with the target states by fidelity. The analysis of communication efficiency and noise effects shows that our protocol has advantages in the case of complex coefficients.

The Greenberger–Horne–Zeilinger (GHZ) paradox shows that it is possible to create a multipartite state involving three or more particles in which the measurement outcomes of the particles are correlated in a way that cannot be explained by classical physics. We extend it to witness quantum networks. We first extend the GHZ paradox to simultaneously verify the GHZ state and Einstein–Podolsky–Rosen states on triangle networks. We then extend the GHZ paradox to witness the entanglement of chain networks consisting of multiple GHZ states. All the present results are robust against the noise.

We discuss the possibility of constructing an effective gauge field theory of the nucleon interactions based on the ideas of isotopic invariance as well as hypercharge invariance as a local gauge symmetry and spontaneous breaking of this symmetry. The constructed effective field theory predicts the structure of interactions of protons and neutrons with ρ- and σ-mesons, and with pi-mesons and photons, as well as interactions of these particles with each other. The Lagrangian of the theory consists of several parts involving dimension 4 and 5 gauge invariant operators. Feynman rules for physical degrees of freedom that follow on from the Lagrangian define the structure of diagrams for one-boson exchanges between nucleons, predicting the internucleon one-boson-exchange potential as well as nucleon scattering amplitudes. The range of applicability of the effective theory is discussed and estimates are made of the resulting coupling constants. The theory predicts the mass of the neutral ρ⁰-meson to be about 1 MeV larger than the mass of the charged mesons ρ^±. The vector ω-meson, which is a sterile particle with respect to the considered gauge group SU_I(2) × U_Y(1), can be added to the scheme via a gauge-invariant operator of dimension 5, as shown in the appendix.

We solved the Dyson–Schwinger (DS) equations for a two-flavor system with symmetry to study its flavor mixing effects. Initially, we employed the point interaction model and bare vertex approximation to reveal the structure of the solutions. Using the point interaction model, the DS equations can be solved analytically, and we found that these solutions can be classified into three groups, each forming an ellipse. These solutions exhibit SO(2) symmetry, while the original SU(2) symmetry at the Lagrangian level is dynamically broken to SO(2), corresponding to the emergence of flavor mixing effects. However, this flavor mixing effect does not manifest in the final physical state. By utilizing the system's SO(2) symmetry, we can diagonalize the propagators of the DS equations, eliminating the flavor mixing effect but causing the originally degenerate masses at the Lagrangian level to split. These mass eigenstates have identical quantum numbers but different masses. If we can correspond these to quark particles of different generations, we can explain why the three generations of quarks have different masses and obtain the corresponding quark mass spectrum. Finally, we provide the corresponding numerical results using a more realistic interaction model.

Entanglement-breaking (EB) subspaces determine the additivity of entanglement of formation (EOF), which is a long-standing issue in quantum information. We explicitly construct the two-dimensional EB subspaces of any bipartite system, when system dimensions are equal, and we apply the subspaces to construct EB spaces of arbitrary dimensions. We also present partial construction when system dimensions are different. Then, we present the notion and properties of EB subspaces for some systems, and in particular the absolute EB subspaces. We construct some examples of absolute EB subspaces, as well as EB subspaces for some systems by using multiqubit Dicke states.

We present a lattice quantum chromodynamics (QCD) simulation with 2 + 1 + 1 flavor full QCD ensembles using near-physical quark masses and different spatial sizes L, at a ∼ 0.055 fm. The results show that the scalar and pesudoscalar 2-point correlator with a valence pion mass of approximately 230 MeV become degenerated at L ≤ 1.0 fm, and such an observation suggests that the spontaneous chiral symmetry breaking disappears effectively at this point. At the same time, the mass gap between the nucleon and pion masses remains larger than Λ_QCD in the entire L ∈ [0.2, 0.7] fm range.

In [Phys. Rev. A 107 012427 (2023)], Baldwin and Jones prove that Uhlmann–Jozsa’s fidelity between two quantum states ρ and σ, i.e., $F(\rho ,\sigma )\,:= \,{\left({\rm{Tr}}\sqrt{\sqrt{\rho }\sigma \sqrt{\rho }}\right)}^{2}$, can be written in a simplified form as $F(\rho ,\sigma )={\left({\rm{Tr}}\sqrt{\rho \sigma }\right)}^{2}$. In this article, we give an alternative proof of this result, using a function power series expansion and the properties of the trace function. Our approach not only reinforces the validity of the simplified expression but also facilitates the exploration of novel dissimilarity functions for quantum states and more complex trace functions of density operators.

We revisit the construction of the ${ \mathcal N }=1$ supersymmetric trinification models with gauge group U(3)_C × U(3)_L × U(3)_R in Type IIA string theory on ${{\mathbb{T}}}^{6}/({{\mathbb{Z}}}_{2}\times {{\mathbb{Z}}}_{2})$ orientifold with intersecting D6-branes. The non-trivial K-theory conditions and tadpole cancellation conditions severely restrict the number of allowed models even for the case of rectangular two-tori. Using a supervised search algorithm, we find a few four-family models where the highest wrapping number is 2. For these models, we present the complete particle spectra and the gauge coupling relations at the string-scale.

The axion-like particle (ALP) is one kind of the best-motivated new particles. We consider its production from the pseudoscalar mesonic decays $M\to M^{\prime} a$, with M being a pseudoscalar meson B or K. The upper limits on the flavor-conserving ALP–quark coupling parameter g_u are obtained by assuming the ALP to be an invisible particle. We find that the most severe constraint on g_u comes from the decay ${K}^{+}\to {\pi }^{+}\nu \bar{\nu }$ for 0.05 GeV ≤ M_a ≤ 0.35 GeV, while the decays ${B}^{+,0}\to {K}^{+,0}\nu \bar{\nu }$ and ${B}^{+,0}\to {\pi }^{+,0}\nu \bar{\nu }$ can also generate significant constraints.

Following the recent paper (Teittinen et al 2019 New J. Phys. 21 123041), one can see that in general there is no simple relation between non-Markovianity and quantum speed limit. Here, we investigate the connection between quantum speed limit time and non-Markovianity of an atom in structured environments (reservoirs) whose dynamics is governed by an exact pseudomode master equation (Garraway 1997 Phys. Rev. A 55 2290). In particular, we find an inverse relation between them, which means that the non-Markovian feature of the quantum process leads to speedup of evolution. Thus, there is a link between quantum speedup and memory effects for specific cases of dynamical evolution. Our results might shed light on the relationship between the speedup of quantum evolution and the backflow of information from the environment to the system.

We conducted a study on a simplified dark matter model that introduces a vector-like intermediate particle, facilitating exclusive interactions between dark matter and the top quark in the Standard Model. The analysis focused on the relic density of Dirac-type fermion dark matter and highlighted the complementary role of direct detection in constraining the dark matter model. Notably, in instances when dark matter mass is small, the tree-level two-body annihilation process experiences suppression. In such scenarios, the contributions of the three-body process ($\chi \bar{\chi }\to t\bar{b}{W}^{-}$) and the one-loop process ($\chi \bar{\chi }\to {gg}$) dominate the relic abundance. With regard to direct detection, calculations were performed for the two-loop contribution to the dark-matter–gluon interaction, yielding the corresponding spin-independent scattering cross section.

Collective quantum states, such as subradiant and superradiant states, are useful for controlling optical responses in many-body quantum systems. In this work, we study novel collective quantum phenomena in waveguide-coupled Bragg atom arrays with inhomogeneous frequencies. For atoms without free-space dissipation, collectively induced transparency is produced by destructive quantum interference between subradiant and superradiant states. In a large Bragg atom array, multi-frequency photon transparency can be obtained by considering atoms with different frequencies. Interestingly, we find collectively induced absorption (CIA) by studying the influence of free-space dissipation on photon transport. Tunable atomic frequencies nontrivially modify decay rates of subradiant states. When the decay rate of a subradiant state equals to the free-space dissipation, photon absorption can reach a limit at a certain frequency. In other words, photon absorption is enhanced with low free-space dissipation, distinct from previous photon detection schemes. We also show multi-frequency CIA by properly adjusting atomic frequencies. Our work presents a way to manipulate collective quantum states and exotic optical properties in waveguide quantum electrodynamics (QED) systems.

In this study, we focus into the non-relativistic wave equation described by the Schrödinger equation, specifically considering angular-dependent potentials within the context of a topological defect background generated by a cosmic string. Our primary goal is to explore quasi-exactly solvable problems by introducing an extended ring-shaped potential. We utilize the Bethe ansatz method to determine the angular solutions, while the radial solutions are obtained using special functions. Our findings demonstrate that the eigenvalue solutions of quantum particles are intricately influenced by the presence of the topological defect of the cosmic string, resulting in significant modifications compared to those in a flat space background. The existence of the topological defect induces alterations in the energy spectra, disrupting degeneracy. Afterwards, we extend our analysis to study the same problem in the presence of a ring-shaped potential against the background of another topological defect geometry known as a point-like global monopole. Following a similar procedure, we obtain the eigenvalue solutions and analyze the results. Remarkably, we observe that the presence of a global monopole leads to a decrease in the energy levels compared to the flat space results. In both cases, we conduct a thorough numerical analysis to validate our findings.

Higher dimensional entangled states demonstrate significant advantages in quantum information processing tasks. The Schmidt number is a quantity of the entanglement dimension of a bipartite state. Here we build families of k-positive maps from the symmetric information complete positive operator-valued measurements and mutually unbiased bases, and we also present the Schmidt number witnesses, correspondingly. At last, based on the witnesses obtained from mutually unbiased bases, we show the distance between a bipartite state and the set of states with a Schmidt number less than k.

Ultracold atoms endowed with tunable spin-orbital-angular-momentum coupling (SOAMC) represent a promising avenue for delving into exotic quantum phenomena. Building on recent experimental advancements, we propose the generation of synthetic gauge fields, and by including exotic vortex phases within spinor Bose–Einstein condensates, employing a combination of a running wave and Laguerre–Gaussian laser fields. We investigate the ground-state characteristics of the SOAMC condensate, revealing the emergence of exotic vortex states with controllable orbital angular momenta. It is shown that the interplay of the SOAMC and conventional spin-linear-momentum coupling induced by the running wave beam leads to the formation of a vortex state exhibiting a phase stripe hosting single multiply quantized singularity. The phase of the ground state will undergo the phase transition corresponding to the breaking of rotational symmetry while preserving the mirror symmetry. Importantly, the observed density distribution of the ground-state wavefunction, exhibiting broken rotational symmetry, can be well characterized by the synthetic magnetic field generated through light interaction with the dressed spin state. Our findings pave the way for further exploration into the rotational properties of stable exotic vortices with higher orbital angular momenta against splitting in the presence of synthetic gauge fields in ultracold quantum gases.

Effects of a Bohmian type quantum-relativistic theory are explored. The model is obtained by introducing a new and independent time parameter whose relative motions are not directly observable and cause quantum uncertainties of the physical observables. Unlike the usual de Broglie–Bohm theories, the Quantum Potential does not directly affect the observable motion, but determines the one that is relative to the new time variable. It turns out that the Zitterbewegung of a free particle, of which a more general law is obtained, is the key example of these hidden motions and, through it, it seems possible to give physical reality to the Feynman's paths. A relativistic revision of the uncertainty principle is also derived from the theory.

We consider generating maximally entangled states (Bell states) between two qubits coupled to a common bosonic mode, based on f-STIRAP. Utilizing the systematic approach developed by Wang et al (2017 New J. Phys. 19 093016), we quantify the effects of non-adiabatic leakage and system dissipation on the entanglement generation, and optimize the entanglement by balancing non-adiabatic leakage and system dissipation. We find the analytical expressions of the optimal coupling profile, the operation time, and the maximal entanglement. Our findings have broad applications in quantum state engineering, especially in solid-state devices where dissipative effects cannot be neglected.

It is well known that nonlocal coherence reflects nonclassical correlations better than quantum entanglement. Here, we analyze nonlocal coherence harvesting from the quantum vacuum to particle detectors adiabatically interacting with a quantum scalar field in Minkowski spacetime. We find that the harvesting-achievable separation range of nonlocal coherence is larger than that of quantum entanglement. As the energy gap grows sufficiently large, the detectors harvest less quantum coherence, while the detectors could extract more quantum entanglement from the vacuum state. Compared with the linear configuration and the scalene configuration, we should choose the model of equilateral triangle configuration to harvest tripartite coherence from the vacuum. Finally, we find a monogamous relationship, which means that tripartite l₁-norm of coherence is essentially bipartite types.

Quantifying entanglement measures for quantum states with unknown density matrices is a challenging task. Machine learning offers a new perspective to address this problem. By training machine learning models using experimentally measurable data, we can predict the target entanglement measures. In this study, we compare various machine learning models and find that the linear regression and stack models perform better than others. We investigate the model's impact on quantum states across different dimensions and find that higher-dimensional quantum states yield better results. Additionally, we investigate which measurable data has better predictive power for target entanglement measures. Using correlation analysis and principal component analysis, we demonstrate that quantum moments exhibit a stronger correlation with coherent information among these data features.

Classical machine learning algorithms seem to be totally incapable of processing tremendous data, while quantum machine learning algorithms could deal with big data unhurriedly and provide exponential acceleration over classical counterparts. In this paper, we propose two quantum support vector machine algorithms for multi classification. One is the quantum version of the directed acyclic graph support vector machine. The other one is to use the Grover search algorithm before measurement, which amplifies the amplitude of the phase storing of the classification result. For k classification, the former provides quadratic reduction in computational complexity when classifying. The latter accelerates the training speed significantly and more importantly, the classification result can be read out with a probability of at least 50% using only one measurement. We conduct numerical simulations on two algorithms, and their classification success rates are 96% and 88.7%, respectively.

We investigate the non-Gaussian feature of radiation in a circuit quantum electrodynamics (QED) system where two qubits are strongly coupled to a single-mode cavity. In the regime of ultrastrong coupling (USC), the rotating-wave approximation is not valid, and the Rabi Hamiltonian contains counter-rotating wave terms, leading to level crossing and avoided crossings in the energy spectrum. We further analyze the intensity-amplitude correlation of the output field in these two novel scenarios. In the USC regime, the creation and annihilation operators in the correlation function are replaced, allowing for the identification of non-Gaussian features in the output field. Our findings reveal that despite the absence of squeezing effects in the output light, significant non-Gaussian characteristics are present. Additionally, we demonstrate that as the driving or coupling strength increases, the non-Gaussian features of the output field become more pronounced. This suggests that USC systems hold broad potential applications in the realms of nonlinear optics and the generation of non-Gaussian states.

The bootstrap method which has been studied under many quantum mechanical models turns out to be feasible in microcanonical ensembles as well. While the approach of Nakayama (2022 Mod. Phys. Lett. A 37 2250054) produces a sector when energy is negative, in this paper we report a method that has stronger constraints and results in a smaller region. We also study other models to demonstrate the effectiveness of our method.

A quantum network concerns several independent entangled resources and can create strong quantum correlations by performing joint measurements on some observers. In this paper, we discuss an n-partite chain network with each of two neighboring observers sharing an arbitrary Bell state and all intermediate observers performing some positive-operator-valued measurements with parameter λ. The expressions of all post-measurement states between any two observers are obtained, and their quantifications of Bell nonlocality, Einstein–Podolsky–Rosen steering and entanglement with different ranges of λ are respectively detected and analyzed.

The SARG04 quantum key distribution protocol can offer greater robustness against photon number splitting attacks than the BB84 protocol that is implemented with weak pulses. In this paper, we propose a tight key analysis for the SARG04 protocol, by considering the one-decoy method and investigating its performance under the influence of a detector afterpulse. Our results demonstrate that an increase in block size leads to a slight increase in both the secure key rate and the maximum transmission distance. Importantly, the detector afterpulse plays a crucial role in practical applications and has a more pronounced effect on the SARG04 protocol compared to the BB84 protocol.

We propose a theoretical scheme to realize a two-dimensional (2D) diffraction grating in a four-level inverted-Y-type atomic system coupled by a standing-wave (SW) field and a Laguerre–Gaussian (LG) vortex field. Owing to asymmetric spatial modulation of the LG vortex field, the incident probe field can be lopsidedly diffracted into four domains and an asymmetric 2D electromagnetically induced grating is created. By adjusting the detunings of the probe field and the LG vortex field, the intensities of the LG vortex field and the coherent SW field, as well as the interaction length, the diffraction properties and efficiency, can be effectively manipulated. In addition, the effect of the azimuthal parameter on the Fraunhofer diffraction of the probe field is also discussed. This asymmetric 2D diffraction grating scheme may provide a versatile platform for designing quantum devices that require asymmetric light transmission.

By casting evolution to the Bloch sphere, the dynamics of 2 × 2 matrix non-Hermitian systems are investigated in detail. This investigation reveals that there are four kinds of dynamical modes for such systems. The different modes are classified by different kinds of fixed points, namely, the elliptic point, spiral point, critical node, and degenerate point. The Hermitian systems and the unbroken ${ \mathcal P }{ \mathcal T }$ non-Hermitian cases belong to the category with elliptic points. The degenerate point just corresponds to the systems with exceptional point (EP). The topological properties of the fixed point are also discussed. It is interesting that the topological charge for the degenerate point is two, while the others are one.

Neural networks possess formidable representational power, rendering them invaluable in solving complex quantum many-body systems. While they excel at analyzing static solutions, nonequilibrium processes, including critical dynamics during a quantum phase transition, pose a greater challenge for neural networks. To address this, we utilize neural networks and machine learning algorithms to investigate time evolutions, universal statistics, and correlations of topological defects in a one-dimensional transverse-field quantum Ising model. Specifically, our analysis involves computing the energy of the system during a quantum phase transition following a linear quench of the transverse magnetic field strength. The excitation energies satisfy a power-law relation to the quench rate, indicating a proportional relationship between the excitation energy and the kink numbers. Moreover, we establish a universal power-law relationship between the first three cumulants of the kink numbers and the quench rate, indicating a binomial distribution of the kinks. Finally, the normalized kink-kink correlations are also investigated and it is found that the numerical values are consistent with the analytic formula.

We investigate nonclassical correlations via negativity, local quantum uncertainty (LQU) and local quantum Fisher information (LQFI) for two-dimensional graphene lattices. The explicitly analytical expressions for negativity, LQU and LQFI are given. The close forms of LQU and LQFI confirm the inequality between the quantum Fisher information and skew information, where the LQFI is always greater than or equal to the LQU, and both show very similar behavior with different amplitudes. Moreover, the effects of the different system parameters on the quantified quantum correlation are analyzed. The LQFI reveals more nonclassical correlations than LQU in a two-dimensional graphene lattice system.

We construct a doped holographic superconductor in the Gubser–Rocha model, and realize a superconducting dome in the middle of the temperature-doping phase diagram. It is worth noting that unlike in previous research, the profile of our dome shrinks inward near to zero temperature. From the numerical observation for the coupling dependence of the phase diagram, we find that the coupling between the two gauge fields plays a crucial role in the formation of the dome. We also analytically calculate the DC conductivity of the normal phase of the system in the momentum dissipation and obtain resistivity which is proportional to the temperature. The AC conductivity is calculated numerically.

Fundamental matrix operations and solving linear systems of equations are ubiquitous in scientific investigations. Using the 'sender-receiver' model, we propose quantum algorithms for matrix operations such as matrix-vector product, matrix-matrix product, the sum of two matrices, and the calculation of determinant and inverse matrix. We encode the matrix entries into the probability amplitudes of the pure initial states of senders. After applying proper unitary transformation to the complete quantum system, the desired result can be found in certain blocks of the receiver's density matrix. These quantum protocols can be used as subroutines in other quantum schemes. Furthermore, we present an alternative quantum algorithm for solving linear systems of equations.

We establish tighter uncertainty relations for arbitrary finite observables via (α, β, γ) weighted Wigner–Yanase–Dyson ((α, β, γ) WWYD) skew information. The results are also applicable to the (α, γ) weighted Wigner–Yanase–Dyson ((α, γ) WWYD) skew information and the weighted Wigner–Yanase–Dyson (WWYD) skew information. We also present tighter lower bounds for quantum channels and unitary channels via (α, β, γ) modified weighted Wigner–Yanase–Dyson ((α, β, γ) MWWYD) skew information. Detailed examples are provided to illustrate the tightness of our uncertainty relations.

A protocol of quantum dense coding with gravitational cat states is proposed. We explore the effects of temperature and system parameters on dense coding capacity and provide an efficient strategy to preserve the quantum advantage of dense coding for these states. Our results may open new opportunities for secure communication and insights into the fundamental nature of gravity in the context of quantum information processing.

In this paper, the proton structure function ${F}_{2}^{p}(x,{Q}^{2})$ at small-x is investigated using an analytical solution to the Balitsky-Kovchegov (BK) equation. In the context of the color dipole description of deep inelastic scattering (DIS), the structure function ${F}_{2}^{p}(x,{Q}^{2})$ is computed by applying the analytical expression for the scattering amplitude N(k, Y) derived from the BK solution. At transverse momentum k and total rapidity Y, the scattering amplitude N(k, Y) represents the propagation of the quark-antiquark dipole in the color dipole description of DIS. Using the BK solution we extracted the integrated gluon density xg(x, Q²) and then compared our theoretical estimation with the LHAPDF global data fits, NNPDF3.1sx and CT18. Finally, we have investigated the behavior of ${F}_{2}^{p}(x,{Q}^{2})$ in the kinematic region of 10⁻⁵ ≤ x ≤ 10⁻² and 2.5 GeV² ≤ Q² ≤ 60 GeV². Our predicted results for ${F}_{2}^{p}(x,{Q}^{2})$ within the specified kinematic region are in good agreement with the recent high-precision data for ${F}_{2}^{p}(x,{Q}^{2})$ from HERA (H1 Collaboration) and the LHAPDF global parametrization group NNPDF3.1sx.

We present the first numerical solution that corresponds to a pair of Cho-Maison monopoles and antimonopoles (MAPs) in the SU(2) × U(1) Weinberg-Salam (WS) theory. The monopoles are finitely separated, while each pole carries a magnetic charge ±4π/e. The positive pole is situated in the upper hemisphere, whereas the negative pole is in the lower hemisphere. The Cho-Maison MAP is investigated for a range of Weinberg angles, $0.4675\leqslant \tan {\theta }_{{\rm{W}}}\leqslant 10$, and Higgs self-coupling, 0 ≤ β ≤ 1.7704. The magnetic dipole moment (μ_m) and pole separation (d_z) of the numerical solutions are calculated and analyzed. The total energy of the system, however, is infinite due to point singularities at the locations of monopoles.

Quantum resources such as entanglement and coherence are the holy grail for modern quantum technologies. Although the unwanted environmental effects tackle quantum information processing tasks, suprisingly these key quantum resources may be protected and even enhanced by the implementation of some special hybrid open quantum systems. Here, we aim to show how a dissipative atom-cavity-system can be accomplished to generate enhanced quantum resources. To do so, we consider a couple of dissipative cavities, where each one contains two effective two-level atoms interacting with a single-mode cavity field. In practical applications, a classical laser field may be applied to drive each atomic subsystem. After driving the system, a Bell-state measurement is performed on the output of the system to quantify the entanglement and coherence. The obtained results reveal that the remote entanglement and coherence between the atoms existing inside the two distant cavities are not only enhanced, but can be stabilized, even under the action of dissipation. In contrast, the local entanglement between two atoms inside each dissipative cavity attenuates due to the presence of unwanted environmental effects. Nevertheless, the local coherence may show the same behavior as the remote coherence. Besides, the system provides the steady state entanglement in various interaction regimes, particularly in the strong atom-cavity coupling and with relatively large detuning. More interestingly, our numerical analyses demonstrate that the system may show a memory effect due to the fact that the death and revival of the entanglement take place during the interaction. Our proposed model may find potential applications for the implementation of long distance quantum networks. In particular, it facilitates the distribution of quantum resources between the nodes of large-scale quantum networks for secure communication.