Probabilistic quantum cloning of real states

We construct the explicit formulation of the probabilistically perfect quantum cloning machine that perfectly duplicates the input states chosen from the special set consisting of the linearly independent and nonorthogonal quantum states with 〈φ_i ∣φ_j〉 = r ∈ (0, 1)(i ≠ j). The success probabilities of cloning the input states are equal and maximal. As two examples, we present the explicit transformations of the optimal 1 → 2 probabilistically perfect quantum cloning of the real states in 2 and 3 dimensions. The success probabilities of each of two cloning machines are equal and maximal.     

On the quantum polarization and entanglement of superpositions of two two-mode coherent states

This work discusses the entanglement and quantum polarization of superpositions of two-mode coherent states of the types |ψ₁〉 = N₁(|α, β〉 + |β, α〉) and |ψ₂〉 = N₂(|−α, −α〉 + |α, α〉). We use the concurrence to measure their entanglements and the quantum Stokes parameters and the Q function in order to analyze their polarization and degree of polarization.     

Non-classical properties of superposition of two coherent states having phase difference ?

Recently Ahmad et al. [Optik 2009;120;68; Optics Commun. 2007;271:162; Chin. Phys. Lett. 2006;23:2438] have studied non-classical properties of superposition of two-coherent states of the form, |ψ〉=K[|α〉+eiξ|αei?〉] for the special cases with values ? = π/2,  3π/2,  and π, and for arbitrarily fixed values of ξ. We point out that some of their results are special cases of our recently published work [Physica A 319, 305 (2003); Physica A 341, 201(2004)] on the most general superposition of two arbitrary coherent states of the form ∼(Z₁|α〉+Z₂|β〉), where X_1,2, α and β are arbitrary and only restriction on these is the normalization condition for the superposed state. To make our point we first obtain results for (i) squeezing of the most general Hermitian operator X_θ = X₁ cos θ + X₂ sin θ, with X₁ + iX₂ = a, is the annihilation operator, and (ii) sub-Poissonian photon statistics, for the superposed state |ψ〉 with a general ? and, then obtain results of Ahmad et al. for ? = π/2,  3π/2,  and π and for θ = 0 and π/2. It is interesting to note that the arbitrarily fixed values ξ = |α|² and −|α|² for ? = π/2 and 3π/2, respectively by Ahmad et al. are the values at which we get maximum squeezing working in a rigorous way.     

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.     

Calculation of baryon masses in quantum chromodynamics

The polarization operator of quark currents with baryon quantum numbers is considered in quantum chromodynamics. The non-zero mean vacuum values of the field operator products are taken into account. The sum rules are obtained assuming that in the virtuality region ～1 GeV, among the mean vacuum values violating the chiral invariance, the most important is $\text{〈0|}\text{ψ}\text{ψ|0〉}$. Saturating these sum rules by the lowest baryonic states one is able to calculate the masses of the isobar Δ and nucleon N, M_Δ = 1.4 GeV, M_N = 1 GeV, up to 15% through the known value $\text{〈0|}\text{ψ}\text{ψ|0〉}$. The mass splitting in the baryonic decuplet $\text{M}{}_{\mathrm{\Sigma 1}}\text{?M}{}_{\mathrm{\Delta }}\text{= 125}\text{MeV}$ is calculated in first order in the current strange quark mass m_s = 150 MeV. Certain results for other baryonic resonances have also been obtained.     

Peres-Wootters Measurement for Three Nonorthogonal States

We consider the Peres-Wootters measurement for three nonorthogonal states, |0〉, cosθ|0〉+sinθ|1〉, and cosθ|0〉?sinθ|1〉 (0<θ<π/2). We calculate probabilities to obtain the correct outcomes by the method and compare them to probabilities by the general orthogonal measurements. We show that θ=π/3 if and only if the Peres-Wootters measurement is optimal. We also present numerically that the optimal orthogonal measurement is better than the Peres-Wootters measurement for several cases when θ≠π/3.     

一种新型的两态叠加多模叠加态光场的广义非线性等阶N次方Y压缩

本文根据量子力学中的线性叠加原理,构造了由多模(即q模)相干态的相反态|{-Z_j}〉_q及多模虚相干态的相反态|{-iZ_j}〉_q这两者的线性叠加所组成的一种新型的两态叠加多模叠加态光场|ψ_msc⁽²⁾〉_q.利用新近建立的多模辐射场的广义非线性等阶高阶压缩理论,研究了态|ψ_msc⁽²⁾〉_q的广义非线性等阶N次方Y压缩特性.结果发现,1)当压缩阶数N=2P且P=2m(m=1,2,3,…,…)时,态|ψ_msc⁽²⁾〉_q恒处于N-Y最小测不准态;2)当N=2P且P=2m’+1(m’=0,1,2,…,…)时,如果各模的初始相位φ_j、态间的初始相位差与各单模相干态光场的平均光子数之和∑_j=1^qR_j²即[(θ_pq^(R)-θ_nq^(I))-∑_j=1^qR_j²]满足一定的量子化条件,态|ψ_msc⁽²⁾〉_q可呈现周期性变化的、任意阶的等阶N次方Y压缩效应;3)当N为奇数时,态|ψ_msc⁽²⁾〉_q在一定条件下恒处于N-Y测不准态;4)态|ψ_msc⁽²⁾〉_q与文献21中的态|ψ⁽²⁾〉_q出现部分压缩简并现象,从而更进一步表明压缩简并现象的存在是有某种客观内在联系的.     

一种新型的两态叠加MSCS光场的广义非线性等阶N次方H压缩

本文利用新近建立的多模压缩态理论,详细研究了一种新型的两态叠加多模薛定谔猫态(即MSCS)光场|ψ⁽²⁾〉_q的广义非线性等阶N次方H压缩效应.结果发现:1态|ψ⁽²⁾〉_q是一种典型的非经典光场;当压缩阶数N与腔模总数q这两者之积为偶数,即qN=2p,并且p为奇数亦即p=2m’+1(m’=0,1,2,3,…,…)时,如果各模的初始相位和∑_j=1^qψ_j态间的初始相位差(θ_pq^(I)-θ_nq^(R))、各多模相干态光场的总的平均光子数∑_j=1^qR_j²等满足一定的量子化条件(或者当∑_j=1^qR_j²在总的平均光子数∑_j=1^qR_j²的一系列压缩区内连续取值时),态|ψ(2)〉q总可呈现出周期性变化的、任意阶的广义非线性等阶N次方H压缩效应.2态|ψ⁽²⁾〉_q的第一及第二两个正交分量,其压缩结果(亦即压缩程度和压缩深度)完全相同,但压缩条件不同;两者的等阶N次方H压缩效应呈现出周期性的互补关系.3与文献16相比,本文所研究的态|ψ⁽²⁾〉_q的等阶N次方H压缩效应是比其等阶N次方Y压缩效应更高阶的广义非线性等阶高阶压缩效应.     

Enhancing entanglement of entangled coherent states by single-mode coherent superposition of photon subtraction and addition

We introduce a new entangled quantum state generated by applying single-mode coherent superposition of photon subtraction and addition (a^† cos θ + a sin θ)^m to the entangled coherent state |Ψ_±(α,0)〉$|{\Psi }_{\pm }\left(\alpha ,0\right)〉$, and then investigate the entanglement properties affected by coherent superposition operation. It is shown that this operation can be applied to enhance the entanglement of the state |Ψ₊(α,0)〉$|{\Psi }_{+}\left(\alpha ,0\right)〉$. In addition, the effects of the coherent operation is better to improve the entanglement than that of the creation operation (a^†m) for |Ψ₊(α,0)〉$|{\Psi }_{+}\left(\alpha ,0\right)〉$ in a small-amplitude regime and for |Ψ₋(α,0)〉$|{\Psi }_{-}\left(\alpha ,0\right)〉$ in any regime.     

Complex Wavelet Transform of the Two-mode Quantum States

By employing the bipartite entangled state representation and the technique of integration within an ordered product of operators, the classical complex wavelet transform of a complex signal function can be recast to a matrix element of the squeezing-displacing operator U ₂(μ, σ) between the mother wavelet vector 〈ψ| and the two-mode quantum state vector |f〉 to be transformed. 〈ψ|U ₂(μ, σ)|f〉 can be considered as the spectrum for analyzing the two-mode quantum state |f〉. In this way, for some typical two-mode quantum states, such as two-mode coherent state and two-mode Fock state, we derive the complex wavelet transform spectrum and carry out the numerical calculation. This kind of wavelet-transform spectrum can be used to recognize quantum states.     

Quark masses

In quark gluon theory with very small bare masses, -$\text{ψ}$$\text{M}$ψ, spontaneous breakdown of chiral symmetry generates sizable masses M_u, M_d, M_s, … We find ($\text{M}{}_{\mathrm{<mtext>u</mtext>}}\text{+ M}{}_{\mathrm{<mtext>d</mtext>}}\text{) /2 ≈ m}\text{p}\text{/ √6 ≈ 312}\text{MeV}\text{,}\text{and}\text{M}{}_{\mathrm{<mtext>s</mtext>}}\text{≈ 432}\text{MeV}$. Scalar densities have well determined non-zero vaccum expectations $\text{〈0|u}{}^{\mathrm{a}}\text{|0〉 ≡ 〈0|ψ(x) (λ}{}^{\mathrm{a}}\text{/2)ψ(x)/0〉 ≈ ?}{}_{\mathrm{\pi }}{}^2\text{M}{}^{\mathrm{a}}\text{,}\text{i.e}\text{〈0? u}{}^{\mathrm{o}}\text{/vb0〉 ≈ 8 × 10}{}^{\mathrm{?3}}\text{(}\text{GeV}\text{)}{}^3$ at an SU(3) breaking of the vacuum c′ ≡ 〈0|u⁸|〉/〈0|u^o|0〉 ≈ ? 16%     

多模叠加态光场|ψ5(3)〉q中广义磁场4m次方Y压缩

构造了由多模复共轭相干态|{Z_j^*}〉_q、多模复共轭相干态的相反态|{-Z_j^*}〉_q以及多模虚相干态|{iZ_j^*}〉_q的线性叠加所组成的第Ⅴ类三态叠加多模叠加态光场|ψ₅⁽³⁾〉_q.利用多模压缩态理论研究了态|ψ₅⁽³⁾〉_q中广义磁场分量的等幂次N次方Y压缩特性.结果发现:当压缩次数N=2p且p=2m(m=1,2,3,…,…)时,只要各模的初始相位φ_j(j=1,2,…,…,q)、态间的初始相位差(θ₁-θ₂)、(θ₁-θ₃)和(θ₂-θ₃)以及受各模的初始相位φ_j调制的各单模相干态光场的平均光子数之和 等分别满足一定的取值条件,则态|ψ₅⁽³⁾〉_q的广义磁场分量就可呈现出周期性变化的广义非线性等幂次4m次方Y压缩效应.     

Chiral symmetry,the 1/N expansion and the SU(N) thirring model

In the two-dimensional SU(N) Thirring model, the 1/N expansion seems to predict spontaneous breaking of the continuous chiral symmetry. This is impossible in two-dimensions. Reasoning along the lines of Berezinski, Kosterlitz and Thouless for the two-dimensional XY model, we argue that, in fact, rather than showing long-range order, $\text{〈}\text{ψ}\text{ψ(x)}\text{ψ}\text{ψ(0)〉}$ vanishes in this model as |x|^?1/N at large |x|. The 1/N expansion is, in fact, a rather good guide to the properties of this model.     

Local transformations of superpositions of entangled states

Suppose that we have two entangled states |?₁〉, |ψ₁〉 that cannot be converted to any of other two states |?₂〉, |ψ₂〉 by local operations and classical communication. We analyze the possibility of locally transforming a superposition of |?₁〉 and |ψ₁〉 into a superposition of |?₂〉 and |ψ₂〉. By using the Nielsen's theorem we find the necessary and sufficient conditions for this conversion to be performed.     

Rovibrational spectrum and potential energy surface of the N2-N2O van der Waals complex

The rovibrational spectrum of the N₂-N₂O van der Waals complex has been recorded in the N₂O ν₁ region (∼1285 cm⁻¹) using a tunable diode laser spectrometer to probe a pulsed supersonic slit jet. The observed transitions together with the data observed previously in the N₂O ν₃ region are analyzed using a Watson S-reduced asymmetric rotor Hamiltonian. The rotational and centrifugal distortion constants for the ground and excited vibrational states are accurately determined. The band-origin of the spectrum is determined to be 1285.73964(14) cm⁻¹. A restricted two-dimensional intermolecular potential energy surface for a planar structure of N₂-N₂O has been calculated at the CCSD(T) level of theory with the aug-cc-pVDZ basis sets and a set of mid-bond functions. With the intermolecular distance fixed at the ground state value R = 3.6926 Å, the potential has a global minimum with a well depth of 326.64 cm⁻¹ at θ_N2 = 11.0° and θ_N2O = 84.3° and has a saddle point with a barrier height of 204.61 cm⁻¹ at θ_N2 = 97.4° and θ_N2O = 92.2°, where θ_N2(θ_N2O) is the enclosed angle between the N-N axis (N-N-O axis) and the intermolecular axis.     

Nonrelativistic scale anomaly, and composite operators with complex scaling dimensions

It is demonstrated that a nonrelativistic quantum scale anomaly manifests itself in the appearance of composite operators with complex scaling dimensions. In particular, we study nonrelativistic quantum mechanics with an inverse square potential and consider a composite s-wave operator O=ψψ. We analytically compute the scaling dimension of this operator and determine the propagator 〈0|TOO^†|0〉. The operator O represents an infinite tower of bound states with a geometric energy spectrum. Operators with higher angular momenta are briefly discussed.     

Teleportation of A Single Qubit State via Unique W State

We propose a scheme for teleporting a single qubit state employing a unique three-particle W state as quantum channel. By adopting QED cavity technologies, our scheme does not involve the Bell-state measurements(BMs). An unknown state a|0〉 + b|1〉 can be probabilistically teleported by communicators' single particle measurements, unitary operations and classical communications. We can perfectly teleport quantum state ½1√2(|0〉 +|1〉) with 100% probability.     

The experimental study of Ba 6pjnk |M| = 0, 1 autoionizing series

The spectra of the Ba 6pnk autoionizing Stark states with |M| = 0, 1, converging to the 6p_1/2⁺ and 6p_3/2⁺ ionization thresholds, are measured as a function of the electric field strength F. Several 6p_jnk Stark manifolds with n = 13–15 have been systematically studied in order to explore their characteristics of configuration interaction. Experimental results are analyzed by fitting them to the Lorentzian profile, from which the positions and widths are determined. Different spectroscopic properties between the Ba 6p_1/2nk and 6p_3/2nk autoionizing Stark states are investigated. Comparison between the Ba 6p_jnk autoionizing Stark states with |M| = 0 and those with |M| = 1 are made.     

Nonclassical and non-Gaussian properties of states generated by the superposed photon added-and-subtracted operation on squeezed vacuum

A new kind of non-Gaussian quantum state is constructed by operating the superposed operator (SO) (cos θaa^† + sin θa^†a) on a squeezed vacuum state (SVS) S(r)|0〉. It is found that the SOSVS is just a superposition state between S(r)|0〉 and S(r)|2〉 with only even numbers of photons. The nonclassicality is investigated by exploring the negativity of Wigner function (WF) and the sub-Poissonian distribution of Mandel's Q-parameter. The non-Guassianity is exhibited via the fidelity between the SOSVS and the SVS and the marginal distribution of its Wigner function. It is found that such SO on the SVS can enhance the nonclassicality and change the non-Gaussianity of the SOSVS. This provides the possibility of generating quantum states with specific nonclassical and non-Gaussian properties.     

Computable upper bounds for the adiabatic approximation errors

For a given Hermitian Hamiltonian H(s)(s∈[0,1])with eigenvalues Ek(s)and the corresponding eigenstates|Ek(s)(1 k N),adiabatic evolution described by the dilated Hamiltonian HT(t):=H(t/T)(t∈[0,T])starting from any fixed eigenstate|En(0)is discussed in this paper.Under the gap-condition that|Ek(s)-En(s)|λ0 for all s∈[0,1]and all k n,computable upper bounds for the adiabatic approximation errors between the exact solution|ψT(t)and the adiabatic approximation solution|ψadi T(t)to the Schr¨odinger equation i|˙ψT(t)=HT(t)|ψT(t)with the initial condition|ψT(0)=|En(0)are given in terms of fidelity and distance,respectively.As an application,it is proved that when the total evolving time T goes to infinity,|ψT(t)-|ψadi T(t)converges uniformly to zero,which implies that|ψT(t)≈|ψadi T(t)for all t∈[0,T]provided that T is large enough.