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Projected Entangled Pair States (PEPS) are recognized as a potent tool for exploring two-dimensional quantum many-body systems. However, a significant challenge emerges when applying conventional PEPS methodologies to systems with periodic boundary conditions (PBC), attributed to the prohibitive computational scaling with the bond dimension. This has notably restricted the study of systems with complex boundary conditions. To address this challenge, we have developed a strategy that involves the superposition of PEPS with open boundary conditions (OBC) to treat systems with PBC. This approach significantly reduces the computational complexity of such systems while maintaining their translational invariance and the PBC. We benchmark this method against the Heisenberg model and the $J_1$-$J_2$ model, demonstrating its capability to yield highly accurate results at low computational costs, even for large system sizes. The techniques are adaptable to other boundary conditions, including cylindrical and twisted boundary conditions, and therefore significantly expands the application scope of the PEPS approach, shining new light on numerous applications.

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. 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.

Frequency combs, specialized laser sources emitting multiple equidistant frequency lines, have revolutionized science and technology with unprecedented precision and versatility. Recently, integrated frequency combs are emerging as scalable solutions for on-chip photonics. Here, we demonstrate a fully integrated superconducting microcomb that is easy to manufacture, simple to operate, and consumes ultra-low power. Our turnkey apparatus comprises a basic nonlinear superconducting device, a Josephson junction, directly coupled to a superconducting microstrip resonator. We showcase coherent comb generation through self-started mode-locking. Therefore, comb emission is initiated solely by activating a DC bias source, with power consumption as low as tens of picowatts. The resulting comb spectrum resides in the microwave domain and spans multiple octaves. The linewidths of all comb lines can be narrowed down to 1 Hz through a unique coherent injection-locking technique. Our work represents a critical step towards fully integrated microwave photonics and offers the potential for integrated quantum processors.

Field-inhomogeneity-induced relaxation of atomic spins confined in vapor cells with depolarizing walls is studied. In contrast to nuclear spins, such as noble-gas spins, which experience minimal polarization loss at cell walls, atomic spins in uncoated cells undergo randomization at the boundaries. This distinct boundary condition results in a varied dependence of the relaxation rate on the field gradient. By solving the Bloch-Torrey equation under fully depolarizing boundary conditions, we illustrate that the relaxation rate induced by field inhomogeneity is more pronounced for spins with a smaller original relaxation rate (in the absence of the inhomogeneous field). We establish an upper limit for the relaxation rate through calculations in the perturbation regime. Moreover, we connect it to the spin-exchange-relaxation-free magnetometers, demonstrating that its linewidth is most sensitive to inhomogeneous fields along the magnetometer's sensitive axis. Our theoretical result agrees with the experimental data for cells subjected to small pump power. However, deviations in larger input-power scenarios underscore the importance of considering pump field attenuation, which leads to uniformly distributed light shift that behaves as an inhomogeneous magnetic field.

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.

Quantum computing offers potential solutions for finding ground states in condensed-matter physics and chemistry. However, achieving effective ground state preparation is also computationally hard for arbitrary Hamiltonians. It is necessary to propose certain assumptions to make this problem efficiently solvable, including preparing a trial state of a non-trivial overlap with the genuine ground state. Here, we propose a classical-assisted quantum ground state preparation method for quantum many-body systems, combining Tensor Network States (TNS) and Monte Carlo (MC) sampling as a heuristic method to prepare a trial state with a non-trivial overlap with the genuine ground state. We extract a sparse trial state by sampling from TNS, which can be efficiently prepared by a quantum algorithm on early fault-tolerant quantum computers. Our method demonstrates a polynomial improvement in scaling of overlap between the trial state and genuine ground state compared to random trial states, as evidenced by numerical tests on the spin-$1/2$ $J_1$-$J_2$ Heisenberg model. Furthermore, our method is a novel approach to hybridize a classical numerical method and a quantum algorithm and brings inspiration to ground state preparation in other fields.

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.

Quantum steering is commonly shared among multiple observers by utilizing unsharp measurements. However, their usage is limited to local measurements and is not suitable for nonlocal-measurement-based cases. Here, we present a novel approach in this study, suggesting a highly efficient technique to construct optimal nonlocal measurements by utilizing quantum ellipsoids to share quantum steering. This technique is suitable for any bipartite state and offers benefits even in scenarios with a high number of measurement settings. Using the Greenberger-Horne-Zeilinger state as an illustration, we show that employing unsharp nonlocal product measurements can activate the phenomenon of steering sharing in contrast to using local measurements. Moreover, our findings demonstrate that nonlocal measurements with unequal strength possess a greater activation capability compared to those with equal strength. Our activation method differs from previous ones as it eliminates the need to copy the shared states or diminish other quantum correlations, thus making it convenient for practical experimentation and conservation of resources.

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.

Common methods to achieve photon number resolution rely on fast on-off single-photon detectors in conjunction with temporal or spatial mode multiplexing. Yet, these methods suffer from an inherent trade-off between the efficiency of photon number discrimination and photon detection rate. Here, we introduce a method of photon number resolving detection that overcomes these limitations by replacing mode multiplexing with coherent absorption of a single optical mode in a distributed detector array. Distributed coherent absorption ensures complete and uniform absorption of light among the constituent detectors, enabling fast and efficient photon number resolution. As a proof-of-concept, we consider the case of a distributed array of superconducting nanowire single-photon detectors with realistic parameters and show that deterministic absorption and arbitrarily high photon number discrimination efficiency can be achieved by increasing the number of detectors in the array. Photon number resolution without optical mode multiplication provides a simple yet effective method to discriminate an arbitrary number of photons in large arrays of on-off detectors or in smaller arrays of mode multiplexed detectors.

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.

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.

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. \citeInt13. 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.

Polarization encoding quantum key distribution has been proven to be a reliable method to build a secure communication system. It has already been used in inter-city fiber channel and near-earth atmosphere channel, leaving underwater channel the last barrier to conquer. Here we demonstrate a decoy-state BB84 quantum key distribution system over a water channel with a compact system design for future experiments in the ocean. In the system, a multiple-intensity modulated laser module is designed to produce the light pulses of quantum states, including signal state, decoy state and vacuum state. The classical communication and synchronization are realized by wireless optical transmission. Multiple filtering techniques and wavelength division multiplexing are further used to avoid crosstalk of different light. We test the performance of the system and obtain a final key rate of 245.6 bps with an average QBER of 1.91% over a 2.4m water channel, in which the channel attenuation is 16.35dB. Numerical simulation shows that the system can tolerate up to 21.7dB total channel loss and can still generate secure keys in 277.9m Jelov type 1 ocean channel.

High-precision surface roughness estimation plays an important role in many applications. However, the classical estimating methods are limited by shot noise and only can achieve the precision of 0.1 nm with white light interferometer. Here, we propose two weak measurement schemes to estimate surface roughness through spectrum analysis and intensity analysis. The estimating precision with spectrum analysis is about $10 ^{-5}$ nm by using a currently available spectrometer with the resolution of $\Delta \lambda= 0.04$ pm and the corresponding sensitivity is better than 0.1 THz/nm. And the precision and sensitivity of the light intensity analysis scheme achieve as high as 0.07 nm and 1/nm, respectively. By introducing a modulated phase, we show that the sensitivity and precision achieved in our schemes can be effectively retained in a wider dynamic range. We further provide the experimental design of the surface profiler based on our schemes. It simultaneously meets the requirements of high precision, high sensitivity, and wide measurement range, making it to be a promising practical tool.

This paper has studied the three-dimensional Dunkl oscillator models in a generalization of superintegrable Euclidean Hamiltonian systems to curved ones. These models are defined based on curved Hamiltonians, which depend on a deformation parameter of underlying space and involve reflection operators. Their symmetries are obtained by the Jordan-Schwinger representations in the family of the Cayley-Klein orthogonal algebras using the creation and annihilation operators of the dynamical $sl_{-1}(2)$ algebra of the one-dimensional Dunkl oscillator. The resulting algebra is a deformation of $so_{\kappa_1\kappa_2}(4)$ with reflections, which is known as the Jordan-Schwinger-Dunkl algebra $jsd_{\kappa_1\kappa_2}(4)$. Hence, this model is shown to be maximally superintegrable. On the other hand, the superintegrability of the three-dimensional Dunkl oscillator model is studied from the factorization approach viewpoint. The spectrum of this system is derived through the separation of variables in geodesic polar coordinates, and the resulting eigenfunctions are algebraically given in terms of Jacobi polynomials.

Algorithms to simulate the ring-exchange models using the projected entangled pair states (PEPS) are developed. We generalize the imaginary time evolution (ITE) method to optimize PEPS wave functions for the models with ring-exchange interactions. We compare the effects of different approximations to the environment. To understand the numerical instability during the optimization, we introduce the ``singularity'' of a PEPS and develop a regulation procedure that can effectively reduce the singularity of a PEPS. We benchmark our method with the toric code model, and obtain extremely accurate ground state energies and topological entanglement entropy. We also benchmark our method with the two-dimensional cyclic ring exchange model, and find that the ground state has a strong vector chiral order. The algorithms can be a powerful tool to investigate the models with ring interactions. The methods developed in this work, e.g., the regularization process to reduce the singularity can also be applied to other models.

In this work we propose a quantum version of a generalized Monty Hall game, that is, one in which the parameters of the game are left free, and not fixed on its regular values. The developed quantum scheme is then used to study the expected payoff of the player, using both a separable and an entangled initial-state. In the two cases, the classical mixed-strategy payoff is recovered under certain conditions. Lastly, we extend our quantum scheme to include multiple independent players, and use this extension to sketch two possible application of the game mechanics to quantum networks, specifically, two validated, mult-party, key-distribution, quantum protocols.

This work illustrates a possible application of quantum game theory to the area of quantum information, in particular to quantum cryptography. The study proposed two quantum key-distribution (QKD) protocols based on the quantum version of the Monty Hall game devised by Flitney and Abbott. Unlike most QKD protocols, in which the bits from which the key is going to be extracted are encoded in a basis choice (as in BB84), these are encoded in an operation choice. The first proposed protocol uses qutrits to describe the state of the system and the same game operators proposed by Flitney and Abbott. The motivation behind the second proposal is to simplify a possible physical implementation by adapting the formalism of the qutrit protocol to use qubits and simple logical quantum gates. In both protocols, the security relies on the violation of a Bell-type inequality, for two qutrits and for six qubits in each case. Results show a higher ratio of violation than the E91 protocol.

In this work, we propose a new scheme to solve the angular Teukolsky equation for the particular case: $m=0, s=0$. We first transform this equation to a confluent Heun differential equation and then construct the Wronskian determinant to calculate the eigenvalues and normalized eigenfunctions. We find that the eigenvalues for larger $l$ are approximately given by $_{0}{A_{l0}} \approx [l(l + 1) - \tau_{R}^2/2] - i\;\tau_{I}^2/2$ with an arbitrary $\tau^2=\tau_R^2 + i\,\tau_{I}^2$. The angular probability distribution (APD) for the ground state moves towards the north and south poles for $\tau_R^2>0$, but aggregates to the equator for $\tau_R^2\leq0$. However, we also notice that the APD for large angular momentum $l$ always moves towards the north and south poles , regardless the choice of $\tau^2$.

We propose theoretical schemes to realize the cyon and anyon by atoms which possess non-vanishing electric dipole moments. To realize a cyon, besides the atom, we need a magnetic field produced by a long magnetic-charged filament. To realize an anyon, however, apart from these we need a harmonic potential and an additional magnetic field produced by a uniformly distributed magnetic charges. We find that the atom will be an anyon when cooled down to the negligibly small kinetic energy limit. The relationship between our results and the previous ones is investigated from the electromagnetic duality.

Using the single-mode approximation, we first calculate entanglement measures such as negativity ($1-3$ and $1-1$ tangles) and von Neumann entropy for a tetrapartite W-Class system in noninertial frame and then analyze the whole entanglement measures, the residual $\pi_{4}$ and geometric $\Pi_{4}$ average of tangles. Notice that the difference between $\pi_{4}$ and $\Pi_{4}$ is very small or disappears with the increasing accelerated observers. The entanglement properties are compared among the different cases from one accelerated observer to four accelerated observers. The results show that there still exists entanglement for the complete system even when acceleration $r$ tends to infinity. The degree of entanglement is disappeared for the $1-1$ tangle case when the acceleration $r > 0. 472473$. We reexamine the Unruh effect in noninertial frames. It is shown that the entanglement system in which only one qubit is accelerated is more robust than those entangled systems in which two or three or four qubits are accelerated. It is also found that the von Neumann entropy $S$ of the total system always increases with the increasing accelerated observers, but the $S_{\kappa\xi}$ and $S_{\kappa\zeta\delta}$ with two and three involved noninertial qubits first \it increases and then \it decreases with the acceleration parameter $r$, but they are equal to constants $1$ and $0. 811278$ respectively for zero involved noninertial qubit.

We present the entanglement measures of a tetrapartite W-Class entangled system in noninertial frame, where the transformation between Minkowski and Rindler coordinates is applied. Two cases are considered. First, when one qubit has uniform acceleration whilst the other three remain stationary. Second, when two qubits have nonuniform accelerations and the others stay inertial. The $1-1$ tangle, $1-3$ tangle and whole entanglement measurements ($\pi_4$ and $\Pi_4$), are studied and illustrated with graphics through their dependency on the acceleration parameter $r_d$ for the first case and $r_c$ and $r_d$ for the second case. It is found that the Negativities ($1-1$ tangle and $1-3$ tangle) and $\pi$-tangle decrease when the acceleration parameter $r_{d}$ or in the second case $r_c$ and $r_d$ increase, remaining a nonzero entanglement in the majority of the results. This means that the system will be always entangled except for special cases. It is shown that only the $1-1$ tangle for the first case, vanishes at infinite accelerations, but for the second case the $1-1$ tangle disappears completely when $r>0.472473$. It is found an analytical expression for von Neumann information entropy of the system and we notice that it increases with the acceleration parameter.

We show that it is possible to simulate an anyon by a trapped atom which possesses an induced electric dipole moment in the background of electromagnetic fields with a specific configuration. The electromagnetic fields we applied contain a magnetic and two electric fields. We find that when the atom is cooled down to the limit of the negligibly small kinetic energy, the atom behaves like an anyon because its angular momentum takes fractional values. The fractional part of the angular momentum is determined by both the magnetic and one of the electric fields. Roles two electromagnetic fields played are analyzed.

The study of strongly frustrated magnetic systems has drawn great attentions from both theoretical and experimental physics. Efficient simulations of these models are essential for understanding their exotic properties. Here we present PEPS++, a novel computational paradigm for simulating frustrated magnetic systems and other strongly correlated quantum many-body systems. PEPS++ can accurately solve these models at the extreme scale with low cost and high scalability on modern heterogeneous supercomputers. We implement PEPS++ on Sunway TaihuLight based on a carefully designed tensor computation library for manipulating high-rank tensors and optimize it by invoking various high-performance matrix and tensor operations. By solving a 2D strongly frustrated $J_1$-$J_2$ model with over ten million cores, PEPS++ demonstrates the capability of simulating strongly correlated quantum many-body problems at unprecedented scales with accuracy and time-to-solution far beyond the previous state of the art.

Inspired by the electromagnetic duality, we propose an approach to realize the fractional angular momentum by using a cold atom which possesses a permanent magnetic dipole momentum. This atom interacts with two electric fields and is trapped by a harmonic potential which enable the motion of the atom to be planar and rotationally symmetric. We show that eigenvalues of the canonical angular momentum of the cold atom can take fractional values when the atom is cooled down to its lowest kinetic energy level. The fractional part of canonical angular momentum is dual to that of the fractional angular momenta realized by using a charged particle. Another approach of getting the fractional angular momentum is also presented. The differences between these two approaches are investigated.

In this work we study the quantum system with the symmetric Razavy potential and show how to find its exact solutions. We find that the solutions are given by the confluent Heun functions. The eigenvalues have to be calculated numerically. The properties of the wave functions depending on $m$ are illustrated graphically for a given potential parameter $\xi$. We find that the even and odd wave functions with definite parity are changed to odd and even wave functions when the potential parameter $m$ increases. This arises from the fact that the parity, which is a defined symmetry for very small $m$, is completely violated for large $m$. We also notice that the energy levels $\epsilon_{i}$ decrease with the increasing potential parameter $m$.

The analytical solutions to a double ring-shaped Coulomb potential (RSCP) are presented. The visualizations of the space probability distribution (SPD) are illustrated for the two-(contour) and three-dimensional (isosurface) cases. The quantum numbers (n, l, m) are mainly relevant for those quasi quantum numbers (n' ,l' ,m' ) via the double RSCP parameter c. The SPDs are of circular ring shape in spherical coordinates. The properties for the relative probability values (RPVs) P are also discussed. For example, when we consider the special case (n, l, m)=(6, 5, 0), the SPD moves towards two poles of axis z when the P increases. Finally, we discuss the different cases for the potential parameter b which is taken as negative and positive values for c>0 . Compared with the particular case b=0 , the SPDs are shrunk for b=-0.5 while spread out for b=0.5.

The Schrödinger equation $\psi"(x)+\kappa^2 \psi(x)=0$ where $\kappa^2=k^2-V(x)$ is rewritten as a more popular form of a second order differential equation through taking a similarity transformation $\psi(z)=\phi(z)u(z)$ with $z=z(x)$. The Schrödinger invariant $I_{S}(x)$ can be calculated directly by the Schwarzian derivative $\{z, x\}$ and the invariant $I(z)$ of the differential equation $u_{zz}+f(z)u_{z}+g(z)u=0$. We find an important relation for moving particle as $\nabla^2=-I_{S}(x)$ and thus explain the reason why the Schrödinger invariant $I_{S}(x)$ keeps constant. As an illustration, we take the typical Heun differential equation as an object to construct a class of soluble potentials and generalize the previous results through choosing different $\rho=z'(x)$ as before. We get a more general solution $z(x)$ through integrating $(z')^2=\alpha_{1}z^2+\beta_{1}z+\gamma_{1}$ directly and it includes all possibilities for those parameters. Some particular cases are discussed in detail.

We first present the exact solutions of the single ring-shaped Coulomb potential and then realize the visualizations of the space probability distribution for a moving particle within the framework of this potential. We illustrate the two-(contour) and three-dimensional (isosurface) visualizations for those specifically given quantum numbers (n, l, m) essentially related to those so-called quasi quantum numbers (n',l',m') through changing the single ring-shaped Coulomb potential parameter b. We find that the space probability distributions (isosurface) of a moving particle for the special case and the usual case are spherical and circular ring-shaped, respectively by considering all variables in spherical coordinates. We also study the features of the relative probability values P of the space probability distributions. As an illustration, by studying the special case of the quantum numbers (n, l, m)=(6, 5, 1) we notice that the space probability distribution for a moving particle will move towards two poles of axis z as the relative probability value P increases. Moreover, we discuss the series expansion of the deformed spherical harmonics through the orthogonal and complete spherical harmonics and find that the principal component decreases gradually and other components will increase as the potential parameter b increases.

Quantum teleportation provides a `bodiless' way of transmitting the quantum state from one object to another, at a distant location, using a classical communication channel and a previously shared entangled state. In this paper, we present a tripartite scheme for probabilistic teleportation of an arbitrary single qubit state, without losing the information of the state being teleported, via a four-qubit cluster state of the form $\left.|{\phi}\right\rangle_{1234}=\left.\alpha|0000\right\rangle+\left.\beta|1010\right\rangle+\left.\gamma|0101\right\rangle-\eta\left.|1111\right\rangle$, as the quantum channel, where the nonzero real numbers $\alpha$, $\beta$, $\gamma$, and $\eta$ satisfy the relation $|\alpha|^2+|\beta|^2+|\gamma|^2+|\eta|^2=1$. With the introduction of an auxiliary qubit with state $\left|0\right\rangle$, using a suitable unitary transformation and a positive-operator valued measure (POVM), the receiver can recreate the state of the original qubit. An important advantage of the teleportation scheme demonstrated here is that, if the teleportation fails, it can be repeated without teleporting copies of the unknown quantum state, if the concerned parties share another pair of entangled qubit. We also present a protocol for quantum information splitting of an arbitrary two-particle system via the aforementioned cluster state and a Bell-state as the quantum channel. Problems related to security attacks were examined for both the cases and it was found that this protocol is secure. This protocol is highly efficient and easy to implement.

We find that the solution of the polar angular differential equation can be written as the universal associated Legendre polynomials. Its generating function is applied to obtain an analytical result for a class of interesting integrals involving complicated argument. The present method can in principle be generalizable to the integrals involving other special functions. As an illustration we also study a typical Bessel integral with a complicated argument.

The ladder operators for one dimensional quantum harmonic oscillator were constructed by Schrödinger in 1940s. We extend this method to a two dimensional uniform magnetic field and establish the ladder operators which depend on all spatial variables of quantum system. The Hamiltonian of quantum system can also be written by the velocity of the particle.

We scrutinize the behavior of eigenvalues of an electron of Helium atom as it interacts with electric field directed along $z$-axis and exposed to linearly polarized intense laser field radiation. In order to achieve this, we freeze one electron of the helium atom at its ionic ground state and the motion of the second electron in the ion core is treated via a more general case of screened Coulomb potential model. Using the Kramers-Henneberger (KH) unitary transformation, which is semiclassical counterpart of the Block-Nordsieck transformation in the quantized field formalism, the squared vector potential that appears in the equation of motion is eliminated and the resultant equation is expressed in KH frame. Within this frame, the resulting potential and the corresponding wave function have been expanded in Fourier series and using Ehlotzkys approximation, we obtain a laser-dressed potential to simulate intense laser field. By fitting the more general case of screened Coulomb potential model into the laser-dressed potential, and then expanding it in Taylor series up to $\mathcal{O}(r^4,\alpha_0^9)$, we obtain the solution (eigenvalues and wave function) of an electron of Helium atom under the influence of external electric field and high-intensity laser field, within the framework of perturbation theory formalism. We found that the variation in frequency of laser radiation has no effect on the eigenvalues of an electron of helium for a particular electric field intensity directed along $z$-axis. Also, for a very strong external electric field and an infinitesimal screening parameter, the system is strongly bound. This work has potential application in the areas of atomic and molecular processes in external fields including interactions with strong fields and short pulses.

This letter reports the influence of noisy channels on JRSP of two-qubit equatorial state. We present a scheme for JRSP of two-qubit equatorial state. We employ two tripartite Greenberger-Horne-Zeilinger (GHZ) entangled states as the quantum channel linking the parties. We find the success probability to be $1/4$. However, this probability can be ameliorated to $3/4$ if the state preparers assist by transmitting individual partial information through classical channel to the receiver non-contemporaneously. Afterward, we investigate the effects of five quantum noises: the bit-flip noise, bit-phase flip noise, amplitude-damping noise, phase-damping noise and depolarizing noise on the JRSP process. We obtain the analytical derivation of the fidelities corresponding to each quantum noisy channel, which is a measure of information loss as the qubits are being distributed in these quantum channels. We find that the system loses some of its properties as a consequence of unwanted interactions with environment. For instance, within the domain $0<\lambda<0.65$, the information lost via transmission of qubits in amplitude channel is most minimal, while for $0.65<\lambda\leq1$, the information lost in phase flip channel becomes the most minimal. Also, for any given $\lambda$, the information transmitted through depolarizing channel has the least chance of success.

By using a state of art tensor network state method, we study the ground-state phase diagram of an extended Bose-Hubbard model on the square lattice with frustrated next-nearest neighboring tunneling. In the hardcore limit, tunneling frustration stabilizes a peculiar half supersolid (HSS) phase with one sublattice being superfluid and the other sublattice being Mott Insulator away from half filling. In the softcore case, the model shows very rich phase diagrams above half filling, including three different types of supersolid phases depending on the interaction parameters. The considered model provides a promising route to experimentally search for novel stable supersolid state induced by frustrated tunneling in below half filling region with dipolar atoms or molecules.

We scrutinize the behaviour of hydrogen atom's eigenvalues in a quantum plasma as it interacts with electric field directed along $\theta=\pi$ and exposed to linearly polarized intense laser field radiation. Using the Kramers-Henneberger (KH) unitary transformation, which is semiclassical counterpart of the Block-Nordsieck transformation in the quantized field formalism, the squared vector potential that appears in the equation of motion is eliminated and the resultant equation is expressed in KH frame. Within this frame, the resulting potential and the corresponding wavefunction have been expanded in Fourier series and using Ehlotzky's approximation, we obtain a laser-dressed potential to simulate intense laser field. By fitting the exponential-cosine-screened Coulomb potential into the laser-dressed potential, and then expanding it in Taylor series up to $\mathcal{O}(r^4,\alpha_0^9)$, we obtain the eigensolution (eigenvalues and wavefunction) of hydrogen atom in laser-plasma encircled by electric field, within the framework of perturbation theory formalism. Our numerical results show that for a weak external electric field and gargantuan length of Debye screening parameter, the system is strongly repulsive in contrast for strong external electric field and small length of Debye screening parameter, the system is very attractive. This work has potential application in the areas of atomic and molecular processes in external fields including interactions with strong fields and short pulses.

We present a scheme for joint remote state preparation (JRSP) of three-particle state via three tripartite Greenberger-Horne-Zeilinger (GHZ) entangled states as the quantum channel linking the parties. We use eight-qubit mutually orthogonal basis vector as measurement point of departure. The likelihood of success for this scheme has been found to be $1/8$. However, by putting some special cases into consideration, the chances can be ameliorated to $1/4$ and $1$. The effects of amplitude-damping noise, phase-damping noise and depolarizing noise on this scheme have been scrutinized and the analytical derivations of fidelities for the quantum noisy channels have been presented. We found that for $0.55\leq\eta\leq1$, the states conveyed through depolarizing channel lose more information than phase-damping channel while the information loss through amplitude damping channel is most minimal.

Single-photon stimulated four wave mixing (StFWM) processes have great potential for photonic quantum information processing, compatible with optical communication technologies and integrated optoelectronics. In this paper, we demonstrate single-photon StFWM process in a piece of optical fiber, with seeded photons generated by spontaneous four wave mixing process (SpFWM). The effect of the single-photon StFWM is confirmed by time-resolved four-photon coincidence measurement and variation of four-photon coincidence counts under different seed-pump delays. According to the experiment results, the potential performance of quantum cloning machine based on the process is analyzed.

This study presents the confinement influences of Aharonov-Bohm-flux (AB-flux), electric and magnetic fields directed along $z$-axis and encircled by quantum plasmas, on the hydrogen atom. The all-inclusive effects result to a strongly attractive system while the localizations of quantum levels change and the eigenvalues decrease. We find that, the combined effect of the fields is stronger than solitary effect and consequently, there is a substantial shift in the bound state energy of the system. We also find that to perpetuate a low-energy medium for hydrogen atom in quantum plasmas, strong electric field and weak magnetic field are required, where AB-flux field can be used as a regulator. The application of perturbation technique utilized in this paper is not restricted to plasma physics, it can also be applied in molecular physics.

Inspired by the scenario by Bennett et al., a teleportation protocol of qubits formed in a two-dimensional electron gas formed at the interface of a GaAs heterostructure is presented. The teleportation is carried out using three GaAs quantum dots (say $\mathcal{P}\mathcal{P}'$, $\mathcal{Q}\mathcal{Q}'$, $\mathcal{R}\mathcal{R}'$) and three electrons. The electron spin on GaAs quantum dots $\mathcal{P}\mathcal{P}'$ is used to encode the unknown qubit. The GaAs quantum dot $\mathcal{Q}\mathcal{Q}'$ and $\mathcal{R}\mathcal{R}'$ combine to form an entangled state. Alice (the sender) performs a Bell measurement on pairs ($\mathcal{P},\mathcal{Q}$) and ($\mathcal{P}',\mathcal{Q}'$). Depending on the outcome of the measurement, a suitable Hamiltonian for the quantum gate can be used by Bob (receiver) to transform the information based on a spin to charge-based information. This work offers relevant corrections to misconception in \it Chem. Phys. Lett. \bf421 (2006) 338.

We derive the relativistic energy spectrum for the modified Dirac equation by adding a harmonic oscillator potential where the coordinates and momenta are assumed to obey the commutation relation $\left[\hat{x},\hat{p}\right]=i\hbar\left(1+\eta p^2\right)$. In the nonrelativistic limit, our results are in agreement with the ones obtained previously. Furthermore, the extension to the construction of creation and annihilation operators for the harmonic oscillators with minimal length uncertainty relation is presented. Finally, we show that the commutation relation of the $su(1, 1)\sim so(2,1)$ algebra is satisfied by the operators $\hat{\mathcal{L}_{\pm}}$ and $\hat{\mathcal{L}_{z}}$.

This study presents the Fisher information for the position-dependent mass Schrödinger equation with hyperbolical potential $V(x)=-V_0{\rm csch}^2(ax)$. The analysis of the quantum-mechanical probability for the ground and exited states $(n=0, 1, 2)$ has been obtained via the Fisher's information. This controls both chemical and physical properties of some molecular systems. The Fisher information is considered only for $x>0$ due to the singular point at $x=0$. We found that Fisher-information-based uncertainty relation and the Cramer-Rao inequality holds. Some relevant numerical results are presented. The results presented shows that the Cramer-Rao and the Heisenberg products in both spaces provide a natural measure for anharmonicity of $-V_0{\rm csch}^2(ax)$

Since the first quantum ghost imaging (QGI) experiment in 1995, many QGI schemes have been put forward. However, the position-position or momentum-momentum correlation required in these QGI schemes cannot be distributed over optical fibers, which limits their large geographical applications. In this paper, we propose and demonstrate a scheme for long distance QGI utilizing frequency correlated photon pairs. In this scheme, the frequency correlation is transformed to the correlation between the illuminating position of one photon and the arrival time of the other photon, by which QGI can be realized in the time domain. Since frequency correlation can be preserved when the photon pairs are distributed over optical fibers, this scheme provides a way to realize long-distance QGI over large geographical scale. In the experiment, long distance QGI over 50 km optical fibers has been demonstrated.

The non-Markovianity is a prominent concept of the dynamics of the open quantum systems, which is of fundamental importance in quantum mechanics and quantum information. Despite of lots of efforts, the experimentally measuring of non-Markovianity of an open system is still limited to very small systems. Presently, it is still impossible to experimentally quantify the non-Markovianity of high dimension systems with the widely used Breuer-Laine-Piilo (BLP) trace distance measure. In this paper, we propose a method, combining experimental measurements and numerical calculations, that allow quantifying the non-Markovianity of a $N$ dimension system only scaled as $N^2$, successfully avoid the exponential scaling with the dimension of the open system in the current method. After the benchmark with a two-dimension open system, we demonstrate the method in quantifying the non-Markovanity of a high dimension open quantum random walk system.

We demonstrate controlled entanglement routing between bunching and antibunching path-entangled two-photon states in an unbalanced Mach-Zehnder interferometer (UMZI), in which the routing process is controlled by the relative phase difference in the UMZI. Regarding bunching and antibunching path-entangled two-photon states as two virtual ports, we can consider the UMZI as a controlled entanglement router, which bases on the coherent manipulation of entanglement. Half of the entanglement within the input two-photon state is coherently routed between the two virtual ports, while the other is lost due to the time distinguishability introduced by the UMZI. Pure bunching or antibunching path entangled two-photon states are obtained based on this controlled entanglement router. The results show that we can employ the UMZI as general entanglement router for practical quantum information application.

In this paper, the generation of polarization entangled photon pairs at 1.5 \mum is experimentally demonstrated utilizing a polarization maintaining all-fiber loop, consisting of a piece of commercial polarization maintaining fiber and a polarization beam splitter/combiner with polarization maintaining fiber pigtails. A quantum state tomography measurement is performed to analyze the entanglement characteristic of the generated quantum state. In the experiment, a polarization entangled Bell state is generated with a entanglement fidelity of 0.97+/-0.03 and a purity of 0.94+/-0.03 demonstrating that the proposed scheme can realize polarization entangled photon pair generation with polarization maintaining property which is desired in applications of quantum communication and quantum information.

We pinpoint that the work about "a new exactly solvable quantum model in $N$ dimensions" by Ballesteros et al. [Phys. Lett. A \bf 375 (2011) 1431, arXiv:1007.1335] is not a new exactly solvable quantum model since the flaw of the position-dependent mass Hamiltonian proposed by them makes it less valuable in physics.

Mandel Q-parameter, which is determined from single event photon statistics, provides an alternative to differentiate single-molecule with fluorescence detection. In this work, by using the Q-parameter of the sample fluorescence compared to that of an ideal double-molecule system with the same average photon number, we present a novel and fast approach for identifying single molecules based on single event photon statistics analyses, compared with commonly used two-time correlation measurements. The error estimates for critical values of photon statistics are also presented for single-molecule determination.

The properties of the modified Pöschl-Teller (MPT) potential are outlined. The ladder operators are constructed directly from the wave functions without introducing any auxiliary variable. It is shown that these operators are associated to the $su(2)$ algebra. Analytical expressions for the functions $\sinh(\alpha x)$ and $\frac{\cosh(\alpha x)}{\alpha} \frac{d}{dx}$ are evaluated from these ladder operators. The expansions of the coordinate $x$ and momentum $\hat p$ in terms of the $su(2)$ generators are presented. This analysis allows to establish an exact quantum-mechanical connection between the $su(2)$ vibron model and the traditional descriptions of molecular vibron.

In this Letter the bound states of (2+1) Dirac equation with the cylindrically symmetric $\delta (r-r_{0})$-potential are discussed. It is surprisingly found that the relation between the radial functions at two sides of $r_{0}$ can be established by an SO(2) transformation. We obtain a transcendental equation for calculating the energy of the bound state from the matching condition in the configuration space. The condition for existence of bound states is determined by the Sturm-Liouville theorem.

By applying an ansatz to the eigenfunction, an exact closed form solution of the Schrödinger equation in 2D is obtained with the potentials, $V(r)=ar^2+br^4+cr^6$, $V(r)=ar+br^2+cr^{-1}$ and $V(r)=ar^2+br^{-2}+cr^{-4}+dr^{-6}$, respectively. The restrictions on the parameters of the given potential and the angular momentum $m$ are obtained.

Levinson's theorem for the one-dimensional Schrödinger equation with a symmetric potential, which decays at infinity faster than $x^{-2}$, is established by the Sturm-Liouville theorem. The critical case, where the Schrödinger equation has a finite zero-energy solution, is also analyzed. It is demonstrated that the number of bound states with even (odd) parity $n_{+}$ ($n_{-}$) is related to the phase shift $\eta_{+}(0)[\eta_{-}(0)]$ of the scattering states with the same parity at zero momentum as $\eta_{+}(0)+\pi/2=n_{+}\pi, \eta_{-}(0)=n_{-}\pi$, for the non-critical case, $\eta_{+}(0)=n_{+}\pi, \eta_{-}(0)-\pi/2=n_{-}\pi$, for the critical case.

The Schrodinger equation for stationary states is studied in a central potential V(r) proportional to the inverse power of r of degree beta in an arbitrary number of spatial dimensions. The presence of a single term in the potential makes it impossible to use previous algorithms, which only work for quasi-exactly-solvable problems. Nevertheless, the analysis of the stationary Schrodinger equation in the neighbourhood of the origin and of the point at infinity is found to provide relevant information about the desired solutions for all values of the radial coordinate. The original eigenvalue equation is mapped into a differential equation with milder singularities, and the role played by the particular case beta=4 is elucidated. In general, whenever the parameter beta is even and larger than 4, a recursive algorithm for the evaluation of eigenfunctions is obtained. Eventually, in the particular case of two spatial dimensions, the exact form of the ground-state wave function is obtained for a potential containing a finite number of inverse powers of r, with the associated energy eigenvalue.

Utilizing an ${\it ansatz}$ for the eigenfunctions, we arrive at an exact closed form solution to the Schrödinger equation with the inverse-power potential, $V(r)=ar^{-4}+br^{-3}+cr^{-2}+dr^{-1}$ in two dimensions, where the parameters of the potential $a, b, c, d$ satisfy a constraint.

The Schrödinger equation with the central potential is first studied in the arbitrary dimensional spaces and obtained an analogy of the two-dimensional Schrödinger equation for the radial wave function through a simple transformation. As an example, applying an ${\it ansatz}$ to the eigenfunctions, we then arrive at an exact closed form solution to the modified two-dimensional Schrödinger equation with the octic potential, $V(r)=ar^2-br^4+cr^6-dr^4+er^{10}$.

Making use of an ${\it ansatz}$ for the eigenfunctions, we obtain an exact closed form solution to the non-relativistic Schrödinger equation with the anharmonic potential, $V(r)=a r^2+b r^{-4}+c r^{-6}$ in two dimensions, where the parameters of the potential $a, b, c$ satisfy some constraints.

By making use of an ${\it ansatz}$ for the eigenfunction, we obtain the exact solutions to the Schrödinger equation with the anharmonic potential, $V(r)=a r^2+b r^{-4}+c r^{-6}$, both in three dimensions and in two dimensions, where the parameters $a$, $b$, and $c$ in the potential satisfy some constraints.

The two-dimensional Levinson theorem for the Klein-Gordon equation with a cylindrically symmetric potential $V(r)$ is established. It is shown that $N_{m}\pi=\pi (n_{m}^{+}-n_{m}^{-})= [\delta_{m}(M)+\beta_{1}]-[\delta_{m}(-M)+\beta_{2}]$, where $N_{m}$ denotes the difference between the number of bound states of the particle $n_{m}^{+}$ and the ones of antiparticle $n_{m}^{-}$ with a fixed angular momentum $m$, and the $\delta_{m}$ is named phase shifts. The constants $\beta_{1}$ and $\beta_{2}$ are introduced to symbol the critical cases where the half bound states occur at $E=\pm M$.