Probabilistically perfect quantum cloning and unambiguous state discrimination

We consider the N → M probabilistically perfect quantum cloning machine that perfectly produces M faithful copies from N identical input states, where the input states are selected, with prior probabilities η₁and η₂ = 1 − η₁, from a given set of the two linearly independent states |ψ₁〉^⊗ N = (cosθ|0〉 + sinθ|1〉)^⊗ N and |ψ₂〉^⊗ N = (sinθ|0〉 + cosθ|1〉)^⊗ N (θ∈(0,π/2)). We derive the optimal distribution of the success probabilities. When M approaches infinite, the probabilistically perfect quantum cloning can be regarded as a kind of the unambiguous state discrimination, and theoretically provides the upper bound of the unambiguous state discrimination. By using the optimal distribution of the success probabilities of the optimal asymmetric 1 → M probabilistically perfect quantum cloning, we can derive the maximum average success probability of the unambiguous discrimination of two nonorthogonal quantum states |ψ₁〉and|ψ₂〉. As an example, we give the explicit transformation of the optimal symmetric 1 → M probabilistically perfect quantum cloning to copy the two input states |ψ₁〉 and |ψ₂〉.     

On the generation of a generalized superposition of displaced squeezed states

A feasible scheme is presented to generate a generalized superposition of displaced squeezed states, cosθ|α,z〉±sinθ|-α,z〉, in a single mode of the electromagnetic field inside a microwave cavity. The scheme employs a two-level (Rydberg) atom driven by an external classical field. The success probability and the interaction time of such generation are also considered.     

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.     

More radiative corrections for β-decay

A calculation is performed of a hitherto ignored “radiative” correction to neutron β-decay. Conventional electromagnetism does not allow η → 3π decay; the mechanism responsible for this decay will lead to a correction to β-decay not taken into account by the standard O(α/π) coreection of one-photon exchange. While an order of magnitude estimate indicates this correction could in principle compete with the one-photon-exchange correction, explicit calculation puts it at three orders of magnitude down. Thus the agreement between the Cabibbo cosθ and the sinθ obtained from ΔS = 1 decays remains unspoilt.     

The generalized Fresnel–Hadamard complementary transformation for asymmetric beamsplitter

Based on the newly developed parameterized coherent-entangled state representation we propose so-called the generalized Fresnel–Hadamard complementary transformation for asymmetric beamsplitter, which is unitary. The new unitary operator plays the role of both Fresnel transformation for a₁ sin θ ? a₂ cos θ and Hadamard transformation for a₁ cos θ + a₂ sin θ, respectively. Physically, a₁ sin θ ? a₂ cos θ and a₁ cos θ + a₂ sin θ could be a asymmetric beamsplitter’s two output fields. We show that the two transformations are concisely expressed in the parameterized coherent-entangled state representation as a projective operator in integration form.     

Angular variation of ESR linewidth in organic ionic radical salt: 3,3′-diethyl-2,2′-selenacyanine-[TCNQ]2

Angular dependence of ESR linewidth of 3,3′-diethyl-2,2′-selenacyanine-[TCNQ]₂ single crystal reveals the two-dimensional magnetic nature of the system. The dependence is represented well by ΔH(θ)=α(3 cos²θ?1)²+β sin⁴θ where α and β are temperature-dependent parameters.     

Differential cross-sections for pp → π−π+, K−K+ between 0.8 and 2.4 GeV/c

We present measurements from a spark chamber experiment of the differential cross-sections for $\text{p}$p → π^?π⁺, K^?K⁺ at 20 momenta in the range 0.8–2.4 GeV/c (c.m. energy 2.02 to 2.57 GeV). The c.m. angular range was $\text{?0.95 <}\text{cos}\text{θ}{}^1\text{< 0.95}$. There are about 2000π^?π⁺ events and about 300 K^?K⁺ events at each momentum.     

A measurement of e+e− → pp for (1975 ⩽ s ⩽ 2250) MeV

The $\text{e}{}^{\mathrm{+}}\text{e}{}^{\mathrm{?}}\text{→}\text{p}\text{p}$ cross section has been measured in the energy interval (1975 ? 2E ? 2250) MeV for |cosθ| < 0.7. The measurement is based on ～ 100 events, thus improving by a factor 3 on the previous existing statistics in this energy interval. The form factor |G|² is given as a function of energy under the assumption |G_E| = |G_M|. We also give the first measurement of the differential cross section, averaged over the energy interval, and estimate the ratio G_M|/|G_E| from it.     

Angular distribution for the np → dπ0 reaction

The relative differential cross section for the reaction np → dπ⁰ has been measured at incident neutron energies of 459, 648 and 802 MeV. The c.m. angular distributions are fitted by the functional form A + cos²θ + B cos⁴θ. The values obtained for the parameters A and B are in agreement with those obtained from pp → dπ⁺ analyses, consistent with isospin invariance in these reactions.     

Role of dipole-dipole interactions in half-field quantum transitions in magnetic nanoparticles

In order to better understand the origin of “forbidden” quantum transitions observed in superparamagnetic nanoparticles at low magnetic fields, electron magnetic resonance (EMR) studies have been performed at room temperature on iron oxide nanoparticles assembled inside parallel nanosized channels penetrating the anodic alumina membrane. The positions of both the main resonance and “forbidden” (2Q) transitions observed at the half-field demonstrate the characteristic angular dependence with the line shifts proportional to 3cos²θ−1, where θ is the angle between the channel axis and external magnetic field B. This result can be attributed to the inter-particle dipole-dipole interactions within elongated aggregates inside the channels. The angular dependence of the 2Q intensity is found to be proportional to sin²θcos²θ, that is consistent with the predictions of quantum-mechanical calculations with the account for the mixing of states by non-secular inter-particle dipole-dipole interactions. Good agreement is obtained between different kinds of measurements (magnetization curves, line shifts and 2Q intensity), pointing to possibility of the quantum approach to the magnetization dynamics of superparamagnetic objects.     

Angular dependence of tunneling magnetoresistance in La0.7Sr0.3MnO3 step-edge junctions

La_0.7Sr_0.3MnO₃ (LSMO) tunneling magnetoresistance (TMR) junctions have been fabricated on step-edge (0 0 1) SrTiO₃ substrates with a high step-edge angle. In the measurement of magnetoresistance (MR) ratio versus external magnetic field H, butterfly-like MR curves are clearly observed. The MR(H  ) curves vary with θ$\theta$, the angle between the applied magnetic field and the current direction in the substrate plane, showing anisotropic MR properties. A much broader MR(H) response is observed for the configuration of H perpendicular to the substrate plane. Additionally, the maxima-MR field H_p almost coincides with the coercive field H_c for θ<60°$\theta <60°$ but obeys a different form from _Hc(θ)$H_{\mathrm{c}}(\theta )$. The high-field junction resistance shows an intrinsic sin²θ${\sin }^2\theta$ angular dependence, while the low-field resistance shows an extrinsic cos(4θ)$\cos (4\theta )$ angular dependence. The distinctive features are mainly due to the induced magnetization anisotropy in the artificial steps of grain boundaries.     

Lattice Green's function for the simple cubic and tetragonal lattices at arbitrary points

The lattice Green's function for the simple cubic lattice (γ = 1) and tetragonal lattice at an arbitrary point (l, m, n)

$\text{I(a;l,m,n;γ) =}\text{1}\text{π}{}^3\text{∫∫}\text{∫}\text{o}\text{π}\text{cos}\text{lx}\text{cos}\text{my}\text{cos}\text{nx}\text{a?i??γ}\text{cos}\text{x?}\text{cos}\text{y?}\text{cos}\text{x}\text{dxdydz}$

is evaluated, assuming a ? 0, γ ? 0 without loss of generality. The integral I(a; l, m, n; γ) which has singularities at a = ± γ ± 1 ± 1, is expressed in all regions of (a, γ), i.e., for (i) a > 2 + γ, (ii) 2 ? γ > a > γ(γ < 2), (iii) a <γ ? 2 (γ > 2), (iv) a < 2 ? γ (1 < γ < 2) and γ > a (0 < γ < 1), (v) |a ? γ| < 2 and a + γ > 2, in terms of Kampé de Fériet function by the method of the analytic continuation using the Mellin-Barnes type integral. The numerical values are shown in figures. The high temperature susceptibilities of the Heisenberg model of the ferro- and antiferromagnets are calculated using the results of I(a; l, m, n; γ), showing a shift from three to two dimensions and that from three to one dimensions. The correlation function of the isotropic ferromagnet is calculated and the critical index ν is observed to be 1.     

Winkelverteilung der Kernphotoreaktion3He (γ,p)2H

The angular distribution of the photonuclear reaction³He(γ,p)²H was measured with an exitation energyE _x=16 to 27 MeV using a 32.5 MeV betatron. In agreement with a theoretical calculation of Böschet al. we found for the coefficients of the distributionf(θ)=b (a/b+sin²θ(1+β·cosθ+γ·cos²θ)) the values:a/b≦0.14; β=0.77 (+0.14; ?0.07); γ≦0.30. This was the first attempt to use spark chambers as a detection device for photonuclear reactions in the low energy range. We found it to be a promising new facility.     

The research on beat length of polarization maintaining optical fiber with external pressure

Based on the coupled mode equations and elastic optic effect theory, the relationship between polarization maintaining fiber (PMF) beat length and external pressure was analyzed. Moreover, the beat length variation with different external pressure values F as well as angles θ between the pressure direction and PMF's x-axis was calculated numerically. The results demonstrated that the beat length variation was determined both by F and θ simultaneously. When F was a constant, the beat length was changed periodically in π cycle sinusoidal form with θ variation. Then, the minimum and maximum values of beat length would be obtained when θ were even and odd multiples of π/2, respectively. Meanwhile, the beat length variation was linear with F as θ was fixed. In this situation and with F increasing, if θ ∈ (kπ + π/4, kπ + 3π/4) (k ∈ Z), the beat length would increase linearly; otherwise, the beat length variation would be in the opposite direction while θ ∈ (kπ − π/4, kπ + π/4) (k ∈ Z); however, it remained almost unchanged in the case of θ = kπ ± π/4 (k ∈ Z). Finally, the beat length was measured with different pressure values F and angles θ based on a Sagnac interferometer system, and the results shown a great agreement with the theoretical analysis and simulation.     

Measurement of Large-angle πp elastic scattering at 5 GeV/c

The differential cross-section for 5 GeV/cπ⁺p and π⁻p elastic scattering have been measured in the c.m. angular region 27° < θ_cm < 130° corresponding to 0.5 < |t| < 7.8 (GeV/c)². Dips are observed in both reactions at −t = 2.8 and 4.8 (GeV/c)² where the cross-sections are approximately 0.1 μb/(GeV/c)².     

Field-free molecular orientation with chirped laser pulse

We demonstrate theoretically that an efficient field-free molecular orientation driven by the positively chirped laser pulse whose frequency is in the terahertz regime can be achieved, taking the LiH molecule for example. Exact numerical calculations are performed by solving the time-dependent Schrödinger equation including the vibrational and rotational degrees of freedom. The maximal orientation degree of the LiH molecule  |  ? cosθ ?  |  _max  = 0.85 under the action of chirped laser pulse with the peak intensity of 4.78 × 10⁸ W/cm² at T = 0 K, which is larger than  |  ? cosθ ?  |  _max =0.75 driven by the half-cycle laser pulse with the same intensity. The molecular orientation degree decreases with the increase of temperature.     

Angular distribution of the reaction np → dπ0

Differential cross sections of the reaction np → dπ⁰ have been measured for incident neutron energies between 470 MeV and 590 MeV. The angular distributions are fitted by a power series. A significant cos⁴θ contribution is found.     

Quantum key distribution with several intercepts and resend attacks with partially non-orthogonal basis states

The effect of partially non-orthogonal basis states for several intercept and resend attacks of the Bennett–Brassard cryptographic protocol has been studied. The quantum error and the mutual information are computed for arbitrary angles η of the non-orthogonal basis states. It is found that the secure information depend strongly on the angle η, the probability of intercepts and resend attack and the number of eavesdropper. Besides, it is found that for any eavesdroppers number N ≥ 2, the protocol is more secured for (π/2) < η < (3π/2), while for N = 1, the protocol is more secured for η = π/2 or 3π/2 which correspond to the totally orthogonal basis states.     

An SO(10) model with 54 + 126 + 10 higgs

We find an absolute minimum of an SO(10) symmetric potential with SU(3) × U(1) invariance. By fixing the higher scales M_R(〈126〉) ? M_x(〈54〉), the model is consistent with the experimental knowledge about matter stability and the value of sin²θ_w. We determine the spectrum of scalar particles and show that their tree-diagram contributions to nucleon decay amplitudes are proportional to 1/M_x².