Purifying noisy entanglement is a protocol that can increase the entanglement of a mixed state (as a source) at the expense of the entanglement of others (such as an ancilla) by collective measurement. A protocol with which one can get a pure entangled state from a mixed state is defined as purifying mixed states. We address a basic question: can one get a pure entangled state from a mixed state? We give a necessary and sufficient condition of purifying a mixed state by fit local operations and classical communication and show that for a class of source states and ancilla states in arbitrary bipartite systems purifying mixed states is impossible by finite rounds of purifying protocols. For $2\otimes 2$ systems, it is proved that arbitrary states cannot be purified by individual measurement. The possible application and meaning of the conclusion are discussed.

I show that a simple multiparty communication task can be performed more efficiently with quantum communication than with classical communication, even with low detection efficiency $\eta .$ The task is a communication complexity problem in which distant parties need to compute a function of the distributed inputs, while minimizing the amount of communication between them. A realistic quantum optical setup is suggested that can demonstrate a five-party quantum protocol with higher-than-classical performance, provided η>0.33.

We investigate a direct test of teleportation efficacy based on a Mach-Zehnder interferometer. The analysis is performed for continuous-variable teleportation of both discrete and continuous observables.

The configuration-interaction (CI) method is applied to the study of the positronium-hydride (PsH) and positronic-beryllium ${(e}^{+}\mathrm{Be})$ systems. The binding energy and other properties are slowly convergent with respect to the angular momentum of the orbitals used to construct the CI basis states. The largest calculations recover $94\%$ and $80\%$ of the binding energy against dissociation when compared with existing calculations of PsH and $e^{+}\mathrm{Be}.$ Extrapolating using CI convergence trends improves these results to $99\%$ and $98\%,$ respectively. Convergence is not so good for the electron-positron annihilation rates, but the extrapolated annihilation rates were within 10% of the best calculations. Two different schemes have been used to construct the CI basis, and it is found that it is possible to discard roughly half the CI basis with almost no degradation in the binding energy and the annihilation rate. These investigations demonstrate the feasibility of using single particle orbitals centred on the nucleus to represent positronic systems with two valence electrons.

The problem of focusing is considered for the one-dimensional time-dependent Schrödinger equation with a local potential. Focusing is also considered for the closely related plasma wave equation. It is supposed that an experimenter can send in an incident wave from one side of the potential. Then to what degree can the wave be focused? It will be shown that an incident wave can be found so that the real part of the wave collapses to a delta function $\delta \left(x-x_o\right)$ when $t=0.\mathrm{}$ The equation that governs this previously unsolved “single-sided” focusing problem is derived and shown to be Marchenko’s equation—the canonical equation of one-dimensional inverse-scattering theory.

We show that atomic spin motion can be controlled by circularly polarized light without light absorption in the strong pumping limit. In this limit, the pumping light, which drives the empty spin state, destroys the Zeeman coherence effectively and freezes the coherent transition via the quantum Zeno effect. It is verified experimentally that the amount of light absorption decreases asymptotically to zero as the incident light intensity is increased.

The transition temperature for a dilute, homogeneous, three-dimensional Bose gas has the expansion $T_{\mathrm{c}}{=T}_0\{{1+c}_1{\mathrm{an}}^{1/3}+\left[c_2^{\prime }\ln {(an}^{1/3}{)+c}_2^{″}\right]a^2{n}^{2/3}{+O(a}^{3}n)\},$ where a is the scattering length, n the number density, and $T_0$ the ideal gas result. The first-order coefficient $c_1$ depends on nonperturbative physics. In this paper, we show that the coefficient $c_2^{\prime }$ may be computed perturbatively. We also show that the remaining second-order coefficient $c_2^{″}$ depends on non-perturbative physics but may be related, by a perturbative calculation, to quantities that have previously been measured using lattice simulations of three-dimensional $O\left(2\right)\mathrm{}$ scalar field theory. Making use of those simulation results, we find $T_{\mathrm{c}}\simeq T_0\{1+(1.32\pm 0.02){\mathrm{an}}^{1/3}+\left[19.7518\ln {(an}^{1/3}\right)+(75.7\mathrm{}\pm 0.4)\left]a^2{n}^{2/3}{+O(a}^{3}n\right)\}.$

An atomic analog of Landau quantization based on the Aharonov-Casher interaction is developed. The effect provides a first step towards an atomic quantum Hall system using electric fields, which may be realized in a Bose-Einstein condensate.

We study a combination of two-level electromagnetically induced transparency and dark states, and show that desirable features of both phenomena can be obtained in a single system. In particular, large self-phase modulation can be produced without pump or probe absorption, and without spontaneous-emission noise. We point out possible application of our system as a source for squeezed light.

We propose a model for a single-trapped-ion vibronic Raman laser and study its dynamics by using quantum-trajectory methods. In our treatment, it is essential that both the cavity field of the high-finesse optical cavity and the center-of-mass vibrational motion of the trapped ion be quantized. A transition from a super-Poissonian light source to a Poissonian lasing regime is obtained by increasing the Raman coupling constant. Furthermore, we demonstrate that a nonclassical regime can be realized, where the photon statistics becomes sub-Poissonian and the photons leak out of the cavity in an antibunched manner. This is achieved by exploiting nonlinear Stark shifts inherent in the model, which depend on both the number of cavity photons and the number of vibrational quanta.

A calculation for the charge-sign dependence of the stopping power of solid targets for fast-charged particles is performed. The calculation rests on the Bohm-Pines concept for an interacting electron gas: the external bare charge interacts with independent, screened electrons. By using the kinetic theory for scattering description in such a homogeneous system, and the local plasma density approximation with the Jensen atomic model, an estimation for the Barkas effect in real targets is deduced. Comparisons with experimental data, obtained with protons and antiprotons on random stopping, and with the result based on an adiabatic, dressed-perturbation concept are made.

The electron affinity of thulium has been measured using laser photodetachment electron spectroscopy. The electron affinity of $\mathrm{Tm}{(}^2{F}_{7/2})$ was determined to be $1.029\pm 0.022\mathrm{eV}.$ The data also show that ${\mathrm{Tm}}^{\mathrm{-}}$ has at least one bound excited state with a binding energy of $0.979\pm 0.017\mathrm{eV}$ relative to the ground state of the thulium atom. The present experimental measurements are compared to a recent calculation of the electronic structure of ${\mathrm{Tm}}^{\mathrm{-}}$ and a recent experimental investigation of ${\mathrm{Tm}}^{\mathrm{-}}.$

Experimental magnetic substate cross section ratios ${\sigma }_0/{\sigma }_1$ and scattering angle-integrated cross sections following ionization-excitation of helium to ${\mathrm{He}}^{+}\mathrm{}\left(2p\right)\mathrm{}{}^2{P}^o$ in ${\mathrm{H}}^{+}+\mathrm{H}\mathrm{e}$ collisions have been determined, using polarization measurements of emitted radiation in the extreme ultraviolet region in combination with total cross sections, over a wide range of proton velocities (2–6 a.u.). These results are compared with second Born calculations fully including off-energy terms for the ${\mathrm{He}}^{+}\mathrm{}\left(2p\right)\mathrm{}{}^2{P}^o$ sublevels. We have found good agreement between theory and our ${\mathrm{He}}^{+}$ Lyman-α measurements.

Slow light in moving media reaches a counterintuitive regime when the flow speed of the medium approaches the group velocity of light. Pulses can penetrate a region where a counterpropagating flow exceeds the group velocity. When the counterflow slows down, pulses are reflected.

We continue to study the relation between the redistribution of levels in quantum energy spectra and monodromy of the corresponding classical system [see Phys. Lett. A 256, 235 (1999)]. A system with two coupled angular momenta and $\mathrm{SO}\mathrm{}\left(2\right)\mathrm{}$ symmetry is compared to a system with three momenta and $\mathrm{SO}\mathrm{}\left(3\right)\mathrm{}$ symmetry.

Corrections from the Breit interaction to basic properties of atomic ${}^{133}\mathrm{Cs}$ are determined in the framework of third-order relativistic many-body perturbation theory. The corrections to energies, hyperfine-structure constants, off-diagonal hyperfine $6S-7S$ amplitude, and electric-dipole matrix elements are tabulated. It is demonstrated that the Breit corrections to correlations are comparable to the Breit corrections at the Hartree-Fock level. Modification of the parity-nonconserving (PNC) $6S-7S$ amplitude due to Breit interaction is also evaluated; the resulting weak charge of ${}^{133}\mathrm{Cs}$ shows no significant deviation from the prediction of the standard model of elementary particles. The neutron skin correction to the PNC amplitude is also estimated to be -0.2% with an error bound of 30% based on the analysis of recent experiments with antiprotonic atoms. The present work supplements publication [A. Derevianko, Phys. Rev. Lett. 85, 1618 (2000)] with a discussion of the formalism and provides additional numerical results and updated discussion of parity violation.

We point out a loophole problem in some recent experimental claims to produce three-particle entanglement. The problem consists in the question whether mixtures of two-particle entangled states might suffice to explain the experimental data. In an attempt to close this loophole, we review two sufficient conditions that distinguish between N-particle states in which all N particles are entangled to each other and states in which only M particles are entangled (with $M<N).\mathrm{}$ It is shown that three recent experiments to obtain three-particle entangled states [Bouwmeester et al., Phys. Rev. Lett. 82, 1345 (1999); Pan et al., Nature 403, 515 (2000); and Rauschenbeutel et al., Science 288, 2024, (2000)] do not meet these conditions. We conclude that the question whether these experiments provide confirmation of three-particle entanglement remains unresolved. We also propose modifications of the experiments that would make such confirmation feasible.

Quantum secret-sharing protocols involving N partners are key distribution protocols in which Alice encodes her key into $N-1$ qubits, in such a way that all the other partners must cooperate in order to retrieve the key. On these protocols, several eavesdropping scenarios are possible: some partners may want to reconstruct the key without the help of the other ones, and consequently collaborate with an Eve that eavesdrops on the other partners’ channels. For each of these scenarios, we give the optimal individual attack that Eve can perform. A link with Bell’s inequality is demonstrated analytically for half of the scenarios, and is conjectured on the basis of numerical estimates for the other scenarios: the authorized partners have a higher information on the key than the unauthorized ones if and only if they can violate a Bell’s inequality.

We present a different attack on quantum key distribution based on the idea of adaptive absorption [J. Calsamiglia et al., Phys. Rev. A (64, 043814 (2001)]. The conditional beam-splitting attack is shown to be much more efficient than the conventional beam splitting attack, achieving a performance similar to the, powerful but currently unfeasible, photon number splitting attack. The implementation of the conditional beam-splitting attack, based solely on linear optical elements, is well within the reach of current technology.

The properties of continuous-variable teleportation of single-photon states are investigated. The output state is different from the input state due to the nonmaximal entanglement in the Einstein-Podolsky-Rosen beams. The photon statistics of the teleportation output are determined and the correlation between the field information β obtained in the teleportation process and the change in photon number is discussed. The results of the output photon statistics are applied to the transmission of a qubit encoded in the polarization of a single photon.