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Shi-Hai Dong

Publications and source records attributed to Shi-Hai Dong.

At least 37 records · Page 2Linked to original sources
arXiv2022

Superpotential for novel symmetry beyond shape invariance

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.

quant-ph↗
arXiv2022

Witnessing Entangled Two-Photon Absorption via Quantum Interferometry

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.

quant-ph↗
arXiv2022

Quantum version of the k-NN classifier based on a quantum sorting algorithm

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.

quant-ph↗
arXiv2021

Superintegrability on the Dunkl oscillator model in three-Dimensional spaces of constant curvature

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 $so_{κ_1κ_2}(4)$ with reflections, which is known as the Jordan-Schwinger-Dunkl algebra $jsd_{κ_1κ_2}(4)$. 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.

nlin.SI↗
arXiv2020

Quantum version of a generalized Monty Hall game and its possible applications to quantum secure communications

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.

quant-ph↗
arXiv2020

Quantum Key-Distribution Protocols Based on a Quantum Version of the Monty Hall Game

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.

quant-ph↗
arXiv2020

Exact solutions of the angular Teukolsky equation in particular cases

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 $_{0}{A_{l0}} \approx [l(l + 1) - τ_{R}^2/2] - i\;τ_{I}^2/2$ with an arbitrary $τ^2=τ_R^2 + i\,τ_{I}^2$. The angular probability distribution (APD) for the ground state moves towards the north and south poles for $τ_R^2>0$, but aggregates to the equator for $τ_R^2\leq0$. However, we also notice that the APD for large angular momentum $l$ always moves towards the north and south poles , regardless the choice of $τ^2$.

gr-qc↗
arXiv2020

Simulate anyons by cold atoms with induced electric dipole momentum

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.

quant-ph↗
arXiv2019

Realization of cyons and anyons by atoms

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.

quant-ph↗
arXiv2019

Tetrapartite entanglement features of W-Class state in uniform acceleration

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 $π_{4}$ and geometric $Π_{4}$ average of tangles. Notice that the difference between $π_{4}$ and $Π_{4}$ 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 $S_{κξ}$ and $S_{κζδ}$ 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.

quant-ph↗
arXiv2018

Application of Flexible Presentation of Quantum Images in Multipartite Correlations

We apply quantum model inspired on the classical Bayesian method also called mutual information to study the multipartite correlation in quantum images by using the flexible representation of quantum images (FRQI). This can be reflected by considering von Neumann entropy. The results are compared between two images of size $2\times 2$ and $8\times 8$ from different classical and quantum methods. We find that the classical joint entropy is invariant under transformation of change of color but the quantum entropy is sensitive to this change. It is shown that the total correlation $I_T$ could arrive to the double amount of the classical joint entropy.

quant-ph↗
arXiv2018

The fractional angular momentum realized by a cold neutral atom

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.

quant-ph↗
arXiv2018

Tetrapartite entanglement measures of W-Class in noninertial frames

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 ($π_4$ and $Π_4$), 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 $π$-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.

quant-ph↗
arXiv2018

Semi-exact solutions of the Razavy potential

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 $ξ$. 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 $ε_{i}$ decrease with the increasing potential parameter $m$.

quant-ph↗
arXiv2018

The visualization of the space probability distribution for a particle moving in a double ring-shaped Coulomb potential

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.

quant-ph↗
arXiv2017

Constructions of the soluble potentials for the non-relativistic quantum system by means of the Heun functions

The Schrödinger equation $ψ"(x)+κ^2 ψ(x)=0$ where $κ^2=k^2-V(x)$ is rewritten as a more popular form of a second order differential equation through taking a similarity transformation $ψ(z)=ϕ(z)u(z)$ 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 $ρ=z'(x)$ as before. We get a more general solution $z(x)$ through integrating $(z')^2=α_{1}z^2+β_{1}z+γ_{1}$ directly and it includes all possibilities for those parameters. Some particular cases are discussed in detail.

quant-ph↗
arXiv2017

The visualization of the space probability distribution for a moving particle I: in a single ring-shaped Coulomb potential

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.

quant-ph↗