Recently M. Horodecki, P. Horodecki, and R. Horodecki [Phys. Rev. Lett. 80, 5239 (1998)] have introduced a set of density matrices of two spin-1 particles from which it is not possible to distill any maximally entangled states, even though the density matrices are entangled. Thus these density matrices do not allow reliable teleportation. However, it might nevertheless be the case that these states can be used for teleportation, not reliably, but still with fidelity greater than that which may be achieved with a classical scheme. We show that, at least for some of these density matrices, teleportation cannot be achieved with better than classical fidelity.

In the quest to completely describe entanglement in the general case of a finite number of parties sharing a physical system of finite-dimensional Hilbert space an entanglement magnitude is introduced for its pure and mixed states: robustness. It corresponds to the minimal amount of mixing with locally prepared states which washes out all entanglement. It quantifies in a sense the endurance of entanglement against noise and jamming. Its properties are studied comprehensively. Analytical expressions for the robustness are given for pure states of two-party systems, and analytical bounds for mixed states of two-party systems. Specific results are obtained mainly for the qubit-qubit system (qubit denotes quantum bit). As by-products local pseudomixtures are generalized, a lower bound for the relative volume of separable states is deduced, and arguments for considering convexity a necessary condition of any entanglement measure are put forward.

A quantum telecloning process combining quantum teleportation and optimal quantum cloning from one input to M outputs is presented. The scheme relies on the establishment of particular multiparticle entangled states, which function as multiuser quantum information channels. The entanglement structure of these states is analyzed and shown to be crucial for this type of information processing.

We show how a quantum secret sharing protocol, similar to that of Hillery, Buzek, and Berthiaume (Los Alamos e-print archive quant-ph/9806063), can be implemented using two-particle quantum entanglement, as available experimentally today. We also discuss in some detail how both two- and three-particle protocols must be carefully designed in order to detect eavesdropping or a dishonest participant. We also discuss the extension of a multiparticle entanglement secret sharing and splitting scheme toward a protocol so that m of n persons with $m<~n$ can retrieve the secret.

We study the use of entanglement purification for quantum communication over long distances. For distances much longer than the coherence length of a corresponding noisy quantum channel, the fidelity of transmission is usually so low that standard purification methods are not applicable. It is possible, however, to divide the channel into shorter segments that are purified separately and then connected by the method of entanglement swapping. This method can be much more efficient than schemes based on quantum error correction, as it makes explicit use of two-way classical communication. An important question is how the noise, introduced by imperfect local operations (that constitute the protocols of purification and the entanglement swapping), accumulates in such a compound channel, and how it can be kept below a certain noise level. To treat this problem, we first study the applicability and the efficiency of entanglement purification protocols in the situation of imperfect local operations. We then present a scheme that allows entanglement purification over arbitrary long channels and tolerates errors on the percent level. It requires a polynomial overhead in time, and an overhead in local resources that grows only logarithmically with the length of the channel.

Large-order dimensional perturbation theory (DPT) has been used to study the ground and a number of excited states of two-electron atoms for the case $L=0.\mathrm{}$ Here we present an application of recent work generalizing DPT to any higher angular-momentum state. In this work we begin the investigation of $P^o$ states, presenting results for the energies of some of the lowest-lying states and discuss the analytic structure of these energies as functions of $1/D.$ We also obtain energies of corresponding $D^o$ states with almost no additional effort by making use of interdimensional degeneracies with the $P^o$ states.

Highly stripped xenon is produced by irradiating a gas-puff target with a laser pulse of 1-ns duration at an intensity of ${10}^{13}{\mathrm{W}/\mathrm{c}\mathrm{m}}^2.$ The spectrum in the 16.5–19.5-Å wavelength range is measured using a grazing incidence diffractive spectrograph. Spectral lines of Fe-, Co-, Ni-, and Cu-like xenon arising from $3d-4p$ radiative transitions are identified. A collisional-radiative model that includes dielectronic capture processes and radiation trapping is used to achieve the line identification and to describe the relative line intensities. The results of the model clearly show that the relatively strong intensities of the ${3d}^9{4l-3d}^{8}4p4l$ Ni-like quasicontinuum emission between 17.8 and 18.4 Å arise from dielectronic recombination processes, which probably take place during the cooling phase of the plasma. The resonant nature of the dielectronic recombination processes enables us to diagnose the average electron temperature of the plasma during the recombination phase, and it is found to be about 150 eV.

We report the spectroscopy of the ${8S}_{1/2}$ energy level in ${}^{210}\mathrm{Fr}$ by two-photon excitation of atoms confined and cooled in a magneto-optical trap. The resonant intermediate level is the upper state of either the ${7P}_{3/2}$ trapping transition or the ${7P}_{1/2}$ repumping transition. The center-of-gravity energy difference between the ${7S}_{1/2}$ ground level and the ${8S}_{1/2}$ level is $19732.523\pm 0.004\hspace{0.5em}{\mathrm{cm}}^{-1}.$ The hyperfine separation of the ${8S}_{1/2},F=11/2\mathrm{}$ and $F=13/2\mathrm{}$ states is $10256\pm 7\hspace{0.5em}\mathrm{MHz},$ giving a magnetic dipole hyperfine constant A of $1577.8\pm 1.1\hspace{0.5em}\mathrm{MHz}.$

Long-lived phosphorescence has been observed emanating from superfluid helium following excitation by ionizing radiation. This extreme ultraviolet light is predominantly from the radiative decay of metastable ${\mathrm{He}}_2\left(a{}^3{\Sigma }_u^{+}\right)$ molecules and is detected through frequency down-conversion and photon counting techniques. This allows measurement of the phosphorescence lifetime in a low-molecular-density regime that is not dominated by two-body reactions. A phosphorescence lifetime of $13\pm 2\hspace{0.5em}\mathrm{s}$ is observed.

The dipole polarizabilities of the ground states of the ions ${\mathrm{H}}_2^{+}$ and ${\mathrm{D}}_2^{+}$ have been calculated without making use of the Born-Oppenheimer approximation. Instead, the ions were treated as three-body systems whose ground states are spherically symmetric, and the polarizabilities were calculated using second-order perturbation theory with intermediate p pseudostates. The wave functions of both the ground and intermediate states are taken to be of generalized Hylleraas form, but it is necessary to use quite high powers of the internuclear coordinate to simulate the localized motion of the nuclei. We obtain good values of the ground-state energies, and report values of the polarizabilities, to be compared with recent measurements.

In the presence of a magnetic field, knowledge of both the density and the paramagnetic current density is required to derive a Hohenberg-Kohn theorem. The energy is written as a functional of these two variables in current-density functional theory (CDFT). The properties of the exact exchange-correlation functional are not well known in CDFT and the approximate current-density functional due to Vignale, Rasolt, and Geldart is the only functional valid for perturbing fields in routine use. Recent studies using this functional have shown that it is not a reliable predictor of molecular magnetic properties such as magnetizabilities and nuclear shielding constants. Zhao, Morrison, and Parr have shown that it is possible to construct exchange-correlation scalar potentials from densities for systems in the absence of any applied fields. By extending this technique, we have derived a quadratically convergent procedure to deliver numerical exchange-correlation scalar and vector potentials from densities and current densities at finite magnetic-field strengths. We demonstrate this technique by calculating exchange vector potentials for a number of small molecules from Hartree-Fock densities and current densities. We examine the relationship between the computed and true Kohn-Sham exchange-correlation potentials.

We have performed laser spectroscopy of metastable antiprotonic helium atoms $\left(\overline{p}{\mathrm{He}}^{+}\right)$ formed in helium media of 0.2–8.0 bars at 5.8–6.3 K and have observed a density dependence of the resonance vacuum wavelengths for the known transitions $\mathrm{}(n,l)=(39,35)\mathrm{}\to \mathrm{}(38,34)\mathrm{}$ and $\mathrm{}(37,34)\mathrm{}\to \mathrm{}(36,33).$ They showed linear redshifts of $0.61\pm 0.01$ GHz and $0.22\pm 0.02$ GHz per 1 g/l, respectively. With the shift parameters above, the transition vacuum wavelengths were extrapolated to zero-density limits, yielding ${\lambda }_0=597.2570\mathrm{}\pm 0.0003$ nm and ${\lambda }_0=470.7220\mathrm{}\pm 0.0006$ nm, respectively. These values, with a 0.5-ppm precision, were compared with the result of recent theoretical calculations on the energy of the Coulombic three-body system, including relativistic corrections and the Lamb shift. The agreement between our experimental values and the calculations has become as good as $2\times {10}^{-6}.$ This excellent agreement in turn provides a precise value of the antiproton Rydberg constant that surpasses the currently known precision and sets a severe constraint on the antiproton charge $\left(-Q_{\overline{p}}\right)$ and the mass ${(M}_{\overline{p}})$ that both $|Q_{\mathit{p}}-Q_{\overline{p}}|/e$ and $|M_{\mathit{p}}-M_{\overline{p}}|{/M}_p$ be less than $5\times {10}^{-7},$ when a more precisely known constraint on the charge-to-mass ratio is combined. Thus we have opened a possibility of determining fundamental constants of the antiproton.

Theories unifying gravity and other interactions suggest the possibility of spatial and temporal variation of physical “constants” in the Universe. Detection of high-redshift absorption systems intersecting the sight lines towards distant quasars provides a powerful tool for measuring these variations. We have previously demonstrated that high sensitivity to the variation of the fine-structure constant $\alpha$ can be obtained by comparing spectra of heavy and light atoms (or molecules). Here we describe new calculations for a range of atoms and ions, most of which are commonly detected in quasar spectra: Fe II, Mg II, Mg I, C II, C IV, N V, O I, Al III, Si II, Si IV, Ca I, Ca II, Cr II, Mn II, Zn II, Ge II (see the results in Table III). The combination of Fe II and Mg II, for which accurate laboratory frequencies exist, has already been used to constrain $\alpha$ variations. To use other atoms and ions, accurate laboratory values of frequencies of the strong $E1\mathrm{}$ transitions from the ground states are required. We wish to draw the attention of atomic experimentalists to this important problem. We also discuss a mechanism which can lead to a greatly enhanced sensitivity for placing constraints on variation on fundamental constants. Calculations have been performed for Hg II, Yb II, Ca I, and Sr II where there are optical transitions with the very small natural widths, and for hyperfine transition in Cs I and Hg II.

We investigate the classical dynamical stability of a hydrogen molecular ion beyond the Born-Oppenheimer approximation. We study both the coplanar and collinear arrangements. Results show that invariant structures exist in phase space, including a quasiperiodic zone surrounding the antisymmetric stretching periodic orbit. Outside this zone, bound chaotic orbits exist which correspond to a hybrid motion between two types of motion, quite different from the normal quasiperiodic or chaotic motion. We extend the dynamical stability study to several other three-body Coulomb systems, similar to the hydrogen molecular ion, and present results of primitive semiclassical quantization of the quasiperiodic zone of the collinear hydrogen molecular ion. These semiclassical results suggest that the ground electronic state of the hydrogen molecular ion is stable.

A measurement of the shape of the spectral distribution of two-photon decay of the $1s2s{}^1{S}_0$ level in heliumlike nickel is described. Uncertainties in detector efficiencies which had limited the precision of earlier measurements were eliminated by comparing the continuum emission from two-photon decays of H-like and He-like nickel. Our results are in agreement with the nonrelativistic calculation of Drake and the fully relativistic calculation of Derevianko and Johnson and suggest a method for testing relativistic atomic many-body theory in strong fields.

The quadrupole moment and dipole polarizibilities of the ${\mathrm{Ne}}^{+}$ ground state are obtained from previous experimental data using nondegenerate perturbation theory and the method of Dalgarno and Lewis. A modified finite-difference approach to numerically solve the resulting differential equations is discussed in detail. The value of the quadrupole moment of the ${}^2{P}_{3/2}$ ground state of ${\mathrm{Ne}}^{+}$ is thereby found to be $-0.204{015\left(26\right)\mathrm{ea}}_0^2,$ in disagreement with the value from atomic structure calculations. Comparison of the results with those obtained by other approaches used to extract the same parameters from the experiment suggests that the results of the present method are more reliable. Furthermore, the present method is faster, requires no initial theoretical input for the core parameters, and provides sufficient precision to form a restrictive test for theoretical predictions of the quadrupole moment and other ${\mathrm{Ne}}^{+}$ parameters.

Solving the relativistic many-body problem using either many-body perturbation theory or configuration-interaction techniques is shown to lead to energies that depend slightly on the starting potential if the effects of virtual electron-positron pairs are excluded. If they are included without a correct implementation of quantum electrodynamics (QED), while this dependence is eliminated in a mathematical sense, the procedure is shown to give unphysical answers. When instead the effects of virtual electron-positron pairs are included using the S-matrix theory implementation of QED, the potential dependence is shown to be eliminated in a physical way through the inclusion of a particular class of Feynman diagrams.

The lifetimes of the metastable $1s2s2p{\hspace{0.5em}}^4{P}_{5/2}$ level of ${\mathrm{He}}^{-},$ as well as the lifetime of the average of the ${}^4{P}_{3/2}$ and ${}^4{P}_{1/2}$ levels, have been measured using a new type of ion trap that stores keV ion beams using electrostatic fields only. The use of a pure electrostatic field avoids the complication of magnetic-field-induced mixing effects, which can interfere with the measurement of the spontaneous decay. The measured lifetime for the ${}^4{P}_{5/2}$ state, after correction for decay induced by blackbody radiation, is $343\pm 10\hspace{0.5em}\mu \mathrm{s}.$ This value is consistent with previous experiments, and in excellent agreement with the most recent theoretical calculations. The average lifetime of the ${}^4{P}_{3/2}$ and ${}^4{P}_{1/2}$ is $8.9\pm 0.2\hspace{0.5em}\mu \mathrm{s},$ which is about 20% lower than the weighted theoretical value.

We have experimentally investigated the resonant optical response of a partially excited high-density atomic potassium vapor under conditions where local-field effects strongly influence the response. We have measured the excitation dependence of the Lorentz local-field shift, and found it to be in excellent agreement with theoretical predictions.

A theoretical model is suggested for the calculation of ionization cross sections in heavy particle collisions in the impact parameter formalism, considering the influence of coupling with the important bound states in direct as well as in rearrangement channels in a two-centered atomic state expansion. We solve the relevant time-dependent Schrödinger equation by a variational method in the two-state approximation. In the present paper, we calculate total ionization cross sections of a hydrogen atom by 5–300-keV proton impact. The results thus obtained are compared with the measured data and existing theoretical findings.