Convolution Theorem of Fractional Fourier Transformation Derived by Representation Transformation in Quantum Mechancis

Based on our previous paper （Commun. Theor. Phys. 39 （2003） 417） we derive the convolution theorem of fractional Fourier transformation in the context of quantum mechanics, which seems a convenient and neat way. Generalization of this method to the complex fractional Fourier transformation case is also possible.     

Solutions of the Schrodinger Equation with Quantum Mechanical Gravitational Potential Plus Harmonic Oscillator Potential

The solutions of the Schrodinger equation with quantum mechanical gravitational potential plus harmonic oscillator potential have been presented using the parametric Nikiforov-Uvarov method. The bound state energy eigen values and the corresponding un-normalized eigen functions are obtained in terms of Laguerre polynomials. Also a special case of the potential has been considered and its energy eigen values are obtained.     

Effective Mass of Strong-Coupling Bound Polaron in a Triangular Quantum Well Induced by Rashba Effect

In this paper, on the basis of Huybrechts＇ strong-coupling polaron model, the Tokuda modified linearcombination operator method and the unitary transformation method are used to study the properties of the strongcoupling bound polaron considering the influence of Rashba effect, which is brought by the spin-orbit （SO） interaction, in the semiconductor triangular quantum well （TQW）. Numerical calculation on the RbCI TQW, as the example, is performed. The expressions for the effective mass of the polaron as a function of the vibration frequency, the velocity, the Coulomb bound potential and the electron areal density are derived. Numerical results show that the total effective mass of the polaron is composed of three parts. The interactions between the orbit and the spin with different directions have different effects on the effective mass of the bound polaron.     

Spin-Dependent Electron Properties of a Triple-Terminal Quantum Dot Structure

Electron transport properties of a triple-terminal Aharonov-Bohm interferometer are theoretically studied. By applying a Rashba spin-orbit coupling to a quantum dot locally, we find that remarkable spin polarization comes about in the electron transport process with tuning the structure parameters, i.e., the magnetic flux or quantum dot levels. When the quantum dot levels are aligned with the Fermi level, there only appear spin polarization in this structure by the presence of an appropriate magnetic flux. However, in absence of magnetic flux spin polarization and spin separation can be simultaneously realized with the adjustment of quantum dot levels, namely, an incident electron from one terminal can select a specific terminal to depart from the quantum dots according to its spin state.     

New 3-mode bosonic operator realization of SU（2） Lie algebra： From the point of view of squeezing

We consider the quantum mechanical SU(2) transformation e2λ JzJ± e-2λJz= e±2λJ± as if the meaning of squeezing with e±2λbeing squeezing parameter. By studying SU(2) operators(J±,Jz) from the point of view of squeezing we find that(J±,Jz) can also be realized in terms of 3-mode bosonic operators. Employing this realization, we find the natural representation(the eigenvectors of J+ or J-) of the 3-mode squeezing operator e2λ Jz. The idea of considering quantum SU(2) transformation as if squeezing is liable for us to obtain the new bosonic operator realization of SU(2) and new squeezing operators.     

An Efficient Scheme for Multiparty Multi-particle State Sharing

We present an efficient scheme for sharing an arbitrary m-qubit state with n agents. In our scheme, the sender Alice first shares m Bell states with the agent Bob, who is designated to recover the original m-qubit state. Furthermore, Alice introduces n- 1 auxiliary particles in the initial state ｜0）, applies Hadamard （H） gate and Controlled-Not （CNOT） gate operations on the particles, which make them entangled with one of m particle pairs in Bell states, and then sends them to the controllers （i.e., other n - 1 agents）, where each controller only holds one particle in hand. After Alice performing m Bell-basis measurements and each controller a single-particle measurement, the recover Bob can obtain the original unknown quantum state by applying the corresponding local unitary operations on his particles. Its intrinsic efficiency for qubits approaches 100%, and the total efficiency really approaches the maximal value.     

Metric of States

Metric of quantum states plays an important role in quantum information theory. In this letter, we find the deep connection between quantum logic theory and quantum information theory. Using the method of quantum logic, we can get a famous inequality in quantum information theory, and we answer a question raised by S. Gudder.     

Multiformity of Optical Quantum Coherence Systems with Y and Inverted Y-type Schemes

Y and inverted Y-type four-level schemes for optical quantum coherence systems, which may be intuitively considered to be very simple, have not been studied intensively till now. In this paper, we present the multiformity of these two types of schemes by considering that they can be classified into nine possible level styles as the second-order sub-schemes using laser fields. Further we point out the complexity of their more than one hundred realistic configurations as the third-order four-level sub-schemes that may appear in the optical quantum coherence experiments. Throughout this paper we review which configurations have been studied in some research aspects and which ones not, according to our knowledge, in order to be propitious to next steps of theoretical and experimental investigations, especially for applications in the fields of quantum optics, quantum information science, laser spectroscopy, and so on.     

Entropy of Quantum Dynamical Systems and Sufficient Families in Orthomodular Lattices with Bayessian State

The purpose of the present paper is to study the entropy hs（Ф） of a quantum dynamical systems Ф = （ L, s, Ф）, where s is a bayessian state on an orthomodular lattice L. Having introduced the notion of entropy hs（ Ф, A） of partition A of a Boolean algebra B with respect to a state s and a state preserving homomorphism Ф, we prove a few results on that, define the entropy of a dynamical system hs（Ф）, and show its invariance. The concept of sufficient families is also given and we establish that hs （Ф） comes out to be equal to the supremum of hs （Ф,A）, where A varies over any sufficient family. The present theory has then been extended to the quantum dynamical system （ L, s, Ф）, which as an effect of the theory of commutators and Bell inequalities can equivalently be replaced by the dynamical system （B, s0, Ф）, where B is a Boolean algebra and so is a state on B.     

Quantum correlation of a three-particle W-class state under quantum decoherence

We investigate the quantum characteristics of a three-particle W-class state and reveal the relationship between quan- tum discord and quantum entanglement under decoherence. We can also identify the state for which discord takes a maximal value for a given decoherence factor, and present a strong bound on quantum entanglement-quantum discord. In contrast, a striking result will be obtained that the quantum discord is not always stronger than the entanglement of formation in the case of decoherence. Furthermore, we also theoretically study the variation trend of the monogamy of quantum correlations for the three-particle W-class state under the phase flip channel, and find that the three-particle W-class state could transform from polygamous into monogamous, owing to the decoherence.     

Hawking Radiation of Charged Particles in Reissner-NordstrSm Black Hole

We extend the method that Banerjee and Majhi have used to discuss Hawking radiation. Under the condition that the total energy and electrical charge of spacetime are conserved, we investigate Hawking radiation of the charged black hole by a new Tortoise coordinate transformation. Taking the reaction of the radiation of the particle to the spacetime into consideration, we not only derive the radiation spectrum that satisfies the unitary principle in quantum mechanics but also show that the contribution of ingoing particles is equal to the one of outgoing particles on the similar chemical potential term in radiation spectrum caused by charged particles.     

Energy levels of ls2n d （n ≤ 9） states for lithium-like ions

The full-core plus correlation method with multi-configuration interaction wave functions is extended to the calcu- lation of the non-relativistic energies of ls2nd （n ≤9） states for the lithium isoelectronic sequence from Z = 11 to 20. Relativistic and mass-polarization effects on the energy are calculated as the first-order perturbation correction. The quantum-electrodynamics correction is also included. The fine structure splittings are determined from the expectation values of spin-orbit and spin-other-orbit interaction operators in the Pauli-Breit approximation. Combining the term energies of lowly excited states obtained with the quantum defects calculated by the single channel quantum defect theory, each of which is a smooth function of energy and approximated by a weakly varying function of energy, the ion potentials of highly excited states （n ≥ 6） are obtained with the semi-empirical iteration method. The results are compared with experimental data in the literature and found to be closely consistent with the regularity.     

Enhanced electron positron pair creation by the frequency chirped laser pulse

Based on the quantum Vlasov equation, the effect of frequency chirp on electron-positron pair production is investigated. The cycle parameter, which characterizes the laser field cycle degree within the pulse, is also considered. In both supercycle and subcycle laser pulses the frequency chirp can greatly enhance the momentum distribution function of created pairs and the pair number density. The pair number density created by a supercycle laser pulse is larger than that by a subcycle pulse under the same laser frequency and chirping. There exists an optimal cycle parameter corresponding to the maximum value of the created pair number density for different chirp rates. It is found that the pair number density is sensitive/insensitive to chirping rate when the cycle parameter lies below/above the optimal one.     

Switching and Fano resonance via exciton–plasmon interaction

We fnrther study theoretically the properties of switching and Fano resonance in a hybrid nanosystem consisting of two quantum dots （QDs） and a metal nanowire via exciton-plasmon interaction. The transmission of the single plasmon can be switched on or off in a wide-frequency region by adjusting the transition frequencies of the QDs and the phase of the propagating plasmon. Specifically, the dynamical mechanism of Fano-type transmission is further revealed and analyzed in detail.     

Quantum correlation switches for dipole arrays

We investigate the characteristics of three kinds of quantum correlations, measured by pairwise quantum discord （QD）, geometric measure of quantum discord （GMQD）, and measurement-induced disturbance （MID）, in the systems of three- and four-dipole arrays. The influence of the temperature on the three quantum correlations and entanglement of the systems is also analyzed numerically. It is found that novel quantum correlation switches called QD, GMQD, and MID respectively can be constructed with the qubits consisting of electric dipoles coupled by the dipole-dipole interaction and oriented along or against the external electric field. Moreover, with the increase of temperature, QD, GMQD, and MID are more robust than entanglement against the thermal environment. It is also found that for each dipole pair of the three- and four-dipole arrangements, the MID is always the largest and the GMQD the smallest.     

Quantum Secure Direct Communication and Quantum Sealed-Bid Auction with EPR Pairs

I present a new protocol for three-party quantum secure direct communication （QSDC） with a set of ordered M Einstein-Podolsky-Rosen （EPR） pairs. In the scheme, by performing two unitary operations and Bell state measurements, it is shown that the three legitimate parties can exchange their respective secret message simultaneously. Then I modify it for an experimentally feasible and secure quantum sealed-bid auction （QSBD） protocol. Furthermore, I also analyze th~ecurity of the protocol, and the scheme is proven to be secure against the intercept-and-resend attack, the disturbancb attack and the entangled-and-measure attack.     

Realization of quantum Fourier transform over ZN

Since the difficulty in preparing the equal superposition state of amplitude is 1/√N, we construct a quantile transform of quantum Fourier transform （QFT） over ZN based on the elementary transforms, such as Hadamard transform and Pauli transform. The QFT over Z_N can then be realized by the quantile transform, and used to further design its quantum circuit and analyze the requirements for the quantum register and quantum gates. However, the transform needs considerable quantum computational resources and it is difficult to construct a high-dimensional quantum register. Hence, we investigate the design of t-bit quantile transform, and introduce the definition of t-bit semiclassical QFT over Z_N. According to probability amplitude, we prove that the transform can be used to realize QFT over ZN and further design its quantum circuit. For this transform, the requirements for the quantum register, the one-qubit gate, and two-qubit gate reduce obviously when compared with those for the QFT over Z_N.     

Nonequilibrium work equalities in isolated quantum systems

We briefly introduce the quantum Jarzynski and Bochkov–Kuzovlev equalities in isolated quantum Hamiltonian systems, including their origin, their derivations using a quantum Feynman–Kac formula, the quantum Crooks equality, the evolution equations governing the characteristic functions of the probability density functions for the quantum work, and recent experimental verifications. Some results are given here for the first time. We particularly emphasize the formally structural consistence between these quantum equalities and their classical counterparts, which are useful for understanding the existing equalities and pursuing new fluctuation relations in other complex quantum systems.     

Implementation of Quantum Fourier Transform and Its Applications via Quantum-Dot Spins and Microcavity

A scheme for implementing discrete quantum Fourier transform is proposed via quantum dots embedded in a microcavity, and then some of its applications are investigated, i.e., Deutsch 3ozsa. algorithm and Shor＇s quantum factoring. In particular, the detailed process of implementing one~qubit Deutsch Jozsa algorithm and the factorization of N = 15 are given. The microcavity mode is only virtually excited in the whole interaction, so the effective decoherent has slight effect on the current scheme. These schemes would be an important step to fabricate a solid quantum computer.     

Enhancing the precision of phase estimation by weak measurement and quantum measurement reversal

The enhancement of the precision of phase estimation in quantum metrology is investigated by employing weak measurement （WM） and quantum measurement reversal （QMR）. We derive the exact expressions of the optimal quantum Fisher information （QFI） and success probability of phase estimation for an exactly solving model consisting of a qubit interacting with a structured reservoir. We show that the QFI can be obviously enhanced by means of the WM and QMR in different regimes. In addition, we also show that the magnitude of the decoherence involved in the WM and QMR can be a general complex number, which extends the applicable scope of the WM and QMR approach.