Quantum Information in the Frame of Coherent States Representation

In this paper we have showed that the qubit can be expressed through the coherent states. Consequently, a message, i.e. a sequence of qubits, is expressed as a tensor product of coherent states. In the quantum information theory and practice, only the code and key message are expressed as a sequence of qubits, i.e. through a quantum channel, the properly information will be transmitted by using a classical channel. Even if the most used coherent states in the quantum information theory are the coherent states of the harmonic oscillator (particularly, expressing by them the Schrödinger “cat states” and the Bell states), several authors have been demonstrated that other kind of coherent states may be used in quantum information theory. For the ensembles of qubits, we must use the density operator, in order to describe the informational content of the ensemble. The diagonal representation of the density operator, in the coherent state representation, is also useful to examine the entanglement of the states.     

Higher-order Hong-Mandel's squeezing in superposed coherent states

We study 2nth order Hong and Mandel's squeezing of the Hermitian operator, X_θ ≡ X₁cosθ + X₂sinθ in the most general superposition state, |ψ〉 = Z₁|α〉 + Z₂|β〉 of two coherent states |α〉 and |β〉. Here operators X_1,2 are defined by X₁ + i X₂ = a, the annihilation operator, angle θ and complex numbers Z_1,2 , α, β are arbitrary and the only restriction on these is the normalization condition of |ψ〉. We find maximum 2nth-order Hong-Mandel squeezing of X_θ in the superposed coherent state |ψ〉 for an infinite combinations with , and with arbitrary values of (α + β) and θ. Here A_2n is a constant which depends on the order of squeezing. The maximum percentage of 2nth order Hong-Mandel squeezing and their respective constants A_2n have been reported for some values of n. We conclude that any large percentage of squeezing can be obtained by suitably choosing of the order 2n. For the order greater than 128 we obtained more than 99% higher-order squeezing at very low intensity of the optical field. Variations of higher-order squeezing with different parameters near its maxima have also been discussed.     

On nonlinear coherent states properties for electron-phonon dynamics

This work addresses a construction of a dual pair of nonlinear coherent states (NCS) in the context of changes of bases in the underlying Hilbert space for a model pertaining to an electron-phonon model in the condensed matter physics, obeying a f-deformed Heisenberg algebra. The existence and properties of reproducing kernel in the NCS Hilbert space are studied and discussed; the probability density and its dynamics in the basis of constructed coherent states are provided. A Glauber-Sudarshan P-representation of the density matrix and relevant issues related to the reproducing kernel properties are presented. Moreover, a NCS quantization of classical phase space observables is performed and illustrated in a concrete example of q-deformed coherent states. Finally, an exposition of quantum optical properties is given.     

Quantum interference between a single-photon Fock state and a coherent state

We derive analytical expressions for the single mode quantum field state at the individual output ports of a beam splitter when a single-photon Fock state and a coherent state are incident on the input ports. The output states turn out to be a statistical mixture between a displaced Fock state and a coherent state. Consequently we are able to find an analytical expression for the corresponding Wigner function. Because of the generality of our calculations the obtained results are valid for all passive and lossless optical four port devices. We show further how the results can be adapted to the case of the Mach-Zehnder interferometer. In addition we consider the case for which the single-photon Fock state is replaced with a general input state: a coherent input state displaces each general quantum state at the output port of a beam splitter with the displacement parameter being the amplitude of the coherent state.     

无限深量子阱量子比特及其声子效应

采用Peaker变分法,研究具有束缚势的无限深量子阱中量子比特及其声子效应。量子阱中这样的二能级体系可作为一个量子比特。当阱中电子处于基态和第一激发态的叠加态时,电子的概率密度在空间作周期性震荡,得出了振荡周期随耦合强度的增加而减小,随振动频率的增加而增大。     

Painlevé IV coherent states

A simple way to find solutions of the Painlevé IV equation is by identifying Hamiltonian systems with third-order differential ladder operators. Some of these systems can be obtained by applying supersymmetric quantum mechanics (SUSY QM) to the harmonic oscillator. In this work, we will construct families of coherent states for such subset of SUSY partner Hamiltonians which are connected with the Painlevé IV equation. First, these coherent states are built up as eigenstates of the annihilation operator, then as displaced versions of the extremal states, both involving the related third-order ladder operators, and finally as extremal states which are also displaced but now using the so called linearized ladder operators. To each SUSY partner Hamiltonian corresponds two families of coherent states: one inside the infinite subspace associated with the isospectral part of the spectrum and another one in the finite subspace generated by the states created through the SUSY technique.     

双曲正弦、余弦算符与奇偶相干态

利用Fock空间的平移算符引入了双曲正弦和余弦算符,该算符作用在真空态上给出奇相干态和偶相干态的一种新表示形式,并讨论了奇、偶相干态的准概率分布函数和非经典特性．     

Comment on “Remarks on the structure of states of composite quantum systems and envariance” [Phys. Lett. A 355 (2006) 180]

Let ρ∈S(H₁⊗H₂) with dim(H₁⊗H₂)=∞. Suppose that L:S(H₁⊗H₂)→S(H₁) is a map. It is asserted in [1] that if L satisfies the condition Tr(PL(ρ))=Tr((P⊗I₂)ρ) for all rank-one orthogonal projectors P∈B(H₁), then L is given by L(ρ)=Tr₂(ρ). However the proof in Blanchard and Bruning (2006) [1] is not correct. The purpose of this short Letter is to give a proof of this result.     

Coherent states of general time-dependent harmonic oscillator

By introducing an invariant operator, we obtain exact wave functions for a general time-dependent quadratic harmonic oscillator. The coherent states, both inx- andp-spaces, are calculated. We confirm that the uncertainty product in coherent state is always larger thankh/2 and is equal to the minimum of the uncertainty product of the number states. The displaced wave packet for Caldirola-Kanai oscillator in coherent state oscillates back and forth with time about the center as for a classical oscillator. The amplitude of oscillation with no driving force decreases due to the dissipation in the system. However, the oscillation with resonant frequency oscillates with a large amplitude, even after a sufficient time elapse.     

Equiprobable unambiguous discrimination of quantum states by symmetric orthogonalisation

We show that the maximal probability of equiprobable unambiguous discrimination of a set of pure quantum states is given by the minimal eigenvalue of the Gram matrix of this set. We illustrate this result with several examples important for the protocols of quantum key distribution realized with weak coherent states of light.     

Quantum states with continuous spectrum for a general time-dependent oscillator

We investigated quantum states with continuous spectrum for a general time-dependent oscillator using invariant operator and unitary transformation methods together. The form of the transformed invariant operator by a unitary operator is the same as the Hamiltonian of the simple harmonic oscillator:I’ = p²/2 +ω ² q ²/2. The fact thatω ² of the transformed invariant operator is constant enabled us to investigate the system separately for three cases, whereω ² > 0,ω ² < 0, andω ² = 0. The eigenstates of the system are discrete forω ² > 0. On the other hand, forω ² <− 0, the eigenstates are continuous. The time-dependent oscillators whose spectra of the wave function are continuous are not oscillatory. The wave function forω ² < 0 is expressed in terms of the parabolic cylinder function. We applied our theory to the driven harmonic oscillator with strongly pulsating mass.     

Generation of macroscopic entangled coherent states with large Josephson junctions

We propose a simple and experimental architecture to generate macroscopic entanglement in a solid system which consists of two large Josephson junctions and a flux qubit. Through quantum measuring of flux qubit, entangled coherent states of two large Josephson junctions are obtained. The concurrence of entangled coherent states can be accommodated by adjusted systematic parameters. We also give a brief discussion on the experimental feasibility of this proposal.     

Generalized path-integral solution and coherent states of the harmonic oscillator in D-dimensions

We construct a general form of propagator in arbitrary dimensions and give an exact wavefunction of a time- dependent forced harmonic oscillator in D（D ≥ 1） dimensions. The coherent states, defined as the eigenstates of annihilation operator, of the D-dimensional harmonic oscillator are derived. These coherent states correspond to the minimum uncertainty states and the relation between them is investigated.     

W类态三纠缠原子与相干态光场相互作用过程中光场的量子特性

研究了处于W类态的三纠缠原子与相干态光场相互作用过程中光场的量子特性;运用数值方法,讨论了三纠缠原子初始状态和相干态光场的强弱对系统光场压缩和二阶相干特性的影响。     

Curvature-induced bound states and coherent electron transport on the surface of a truncated cone

We study the curvature-induced bound states and the coherent transport properties for a particle constrained to move on a truncated cone-like surface. With longitudinal hard wall boundary condition, the probability densities and spectra energy shifts are calculated, and are found to be obviously affected by the surface curvature. The bound-state energy levels and energy differences decrease as increasing the vertex angle or the ratio of axial length to bottom radius of the truncated cone. In a two-dimensional (2D) GaAs substrate with this geometric structure, an estimation of the ground-state energy shift of ballistic transport electrons induced by the geometric potential (GP) is addressed, which shows that the fraction of the ground-state energy shift resulting from the surface curvature is unnegligible under some region of geometric parameters. Furthermore, we model a truncated cone-like junction joining two cylinders with different radii, and investigate the effect of the GP on the transmission properties by numerically solving the open-boundary 2D Schrödinger equation with GP on the junction surface. It is shown that the oscillatory behavior of the transmission coefficient as a function of the injection energy is more pronounced when steeper GP wells appear at the two ends of the junction. Moreover, at specific injection energy, the transmission coefficient is oscillating with the ratio of the cylinder radii at incoming and outgoing sides.     

On “multiparty quantum secret sharing with Bell states and Bell measurements”

Recently, Shi et al. proposed a multiparty quantum secret sharing (QSS) using Bell states and Bell measurements. This study shows that their scheme has a pitfall that could be mounted to a collusion attack if precaution has not been taken in implementation. That is, two dishonest agents can collude to reveal the secret without the help of the others. A possible solution is also presented to avoid the attack.     

Construction of coherent states for Morse potential: A su(2)-like approach

We propose a generalized su(2) algebra that perfectly describes the discrete energy part of the Morse potential. Then, we examine particular examples and the approach can be applied to any Morse oscillator and to practically any physical system whose spectrum is finite. Further, we construct the Klauder coherent state for Morse potential satisfying the resolution of identity with a positive measure, obtained through the solution of truncated Stieltjes moment problem. The time evolution of the uncertainty relation of the constructed coherent states is analyzed. The uncertainty relation is more localized for small values of radius of convergence.     

Holomorphic representation of coherent states of a singular oscillator and their Darboux representation

We consider the coherent states of a singular oscillator; these states are defined to be the characteristic states of an operator that reduces the number of basis functions for a discrete spectrum to one. We use the Darboux transform to study the coherent states of a transformed Hamiltonian. We obtain an expression for measures that can be used to decompose unity. We construct a holomorphic representation for the state vectors in the space of functions holomorphic everywhere in the complex plane, including vectors for discrete spectra and coherent states. We obtain a holomorphic representation of the Darboux transformation operators. Tomsk State University. Institute of High-Energy Electronics. Siberian Division of the Russian Academy of Sciences. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 46–53, February, 1998.     

Atomic coherent states studied by virtue of the EPR entangled state and their Wigner functions

Based on the newly constructed Einstein, Podolsky and Rosen (EPR) entangled state representation we introduce macroscopic classical functions associated with atomic coherent state τ with angular momentum value j. These functions are proportional to the ordinary one-variable Hermite polynomials of order 2j. The corresponding Wigner quasiprobability function for τ in phase space is also derived which turns out to be a two-variable Hermite polynomial H _{2j, 2j}. In so doing, a new classical-quantum correspondence scheme for angular momentum system is established. Received 7 August 2002 / Received in final form 14 December 2002 Published online 24 April 2003 RID="a" ID="a"Work supported by the National Natural Science Foundation of China under grant 10175057. RID="b" ID="b"e-mail: fhym@sjtu.edu.en     

两纠缠原子与相干态光场相互作用过程中光场的量子特性

采用时间演化算符和数值计算方法,研究了两全同二能级纠缠原子与相干态光场相互作用过程中光场的量子特性,结果表明:两原子初始纠缠度和相干态光场强度对系统光场的二阶相干性质和压缩效应有很大的影响.