It is shown that a quantum controlled-NOT gate simultaneously performs the logical functions of three distinct conditional local operations. Each of these local operations can be verified by measuring a corresponding truth table of four local inputs and four local outputs. The quantum parallelism of the gate can then be observed directly in a set of three simple experimental tests, each of which has a clear intuitive interpretation in terms of classical logical operations. Specifically, quantum parallelism is achieved if the average fidelity of the three classical operations exceeds $2∕3$. It is thus possible to evaluate the essential quantum parallelism of an experimental controlled-NOT gate by testing only three characteristic classical operations performed by the gate.

We consider the scenario where a company $C$ manufactures in bulk pure entangled pairs of particles, each pair intended for a distinct pair of distant customers. Unfortunately, its delivery service is inept—the probability that any given customer pair receives its intended particles is $S∊[0,1]$, and the customers cannot detect whether an error has occurred. Remarkably, no matter how small $S$ is, it is still possible for $C$ to distribute entanglement by starting with nonmaximally entangled pairs. We determine the maximum entanglement distributable for a given $S$, and also determine the ability of the parties to perform nonlocal tasks with the qubits they receive.

For first-principles density functional theory of a many fermion system, the determination of the kinetic energy functional is important. We consider $N$ independent fermions with spatially varying effective mass in two dimensions, we derive the corresponding kinetic energy density using the $\hslash$ semiclassical approach. Our result reduces, as expected, to the one obtained in the literature for a constant effective mass. We examine the analytical expressions of the position dependent effective mass terms in the kinetic energy density functional with respect to the dimensionality $d=1,2,3$ of the space.

The scattering of ortho-positronium $\left(o\text{−}\mathrm{Ps}\right)$ atoms has been investigated using the first Born approximation (FBA) and Born-Oppenheimer (B-O) model at medium energies. The angle integrated total elastic cross sections of $o\text{−}\mathrm{Ps}–o\text{−}\mathrm{Ps}$ scattering have been reported. Apart from this, the inelastic cross sections for discrete excitations (principal quantum number, $n⩽3$) of the single and both the Ps atoms as well as single and double Ps atom ionization have also been obtained. We have also predicted the total cross section of $o\text{−}\mathrm{Ps}–o\text{−}\mathrm{Ps}$ scattering by adding all these partial cross sections. The first Born and B-O scattering amplitudes have also been evaluated using partial wave technique. It has been noticed that odd values of the partial wave B-O amplitude vanishes for even parity transitions and vice versa. To the best of our knowledge, this feature has not been noticed for other systems.

The atomic masses of ${}^{32}\mathrm{S}$, ${}^{84,86}\mathrm{Kr}$, and ${}^{129,132}\mathrm{Xe}$ have been measured by comparing cyclotron frequencies of single ions in a Penning trap. The results (with one standard deviation uncertainties) are $M\left({}^{32}\mathrm{S}\right)=31.9720711735\left(16\right)$, $M\left({}^{84}\mathrm{Kr}\right)=83.9114977705\left(50\right)$, $M\left({}^{86}\mathrm{Kr}\right)=85.9106106722\left(84\right)$, $M\left({}^{129}\mathrm{Xe}\right)=128.904780960\left(10\right)$, and $M\left({}^{132}\mathrm{Xe}\right)=131.9041551907\left(92\right)$. Combining our mass of ${}^{32}\mathrm{S}$ with the high-precision mass difference between ${}^{33}\mathrm{S}^{+}$ and ${}^{32}\mathrm{S}{\mathrm{H}}^{+}$ obtained by Rainville et al. [submitted to Nature], we also obtain $M\left({}^{33}\mathrm{S}\right)=32.9714589087\left(16\right)$. These results are more precise than previous data by factors of 13 to 600.

We present calculated cross sections for dissociative recombination of the $\mathrm{He}_2{}^{+}$ molecular ion in the 1 to 15 eV energy region, where the cross section is dominated by a series of resonances, the repulsive Rydberg states converging to the first excited state of the ion. The resonance parameters for this system were obtained from electron scattering calculations using the complex Kohn variational method. The dissociation dynamics were studied using a time-dependent wave packet calculation. The calculated cross section is reported and compared to available experiment. The effects of rotation and vibration on the total cross section is examined, as well as the effect of electronic couplings on the final state distribution.

The excitation and charge transfer cross sections are calculated for the collision of ${\mathrm{H}}^{+}$ and ${\mathrm{He}}^{2+}$ with $\mathrm{H}_2{}^{+}$ molecular ions. This is the simplest example of collisions between ions and molecules or molecular ions since it involves only one electron. The results in this paper emphasize effects due to the alignment of the axis of the $\mathrm{H}_2{}^{+}$ molecular ion relative to the atomic ion velocity vector and due to the internuclear separation. The calculations show that the cross section versus the angle between the molecular ion axis and the ion velocity vector strongly depends on the ion velocity. Our results for ${\mathrm{He}}^{2+}$ collisions do not agree with the experiments and calculations of Reiser, Cocke, and Bräuning [Phys. Rev. A 67, 062718 (2003)] but are in qualitative agreement with the calculations of Cheng and Esry.

The C $K$ and O $K$ x-ray photoelectron spectra of the CO molecule, driven by a strong ir field, are studied theoretically. An enhancement of the recoil effect, which results in a strong dependence of the electron vibrational profile on the energy of x-ray photon, is found. The enhancement of the recoil effect happens due to an ir-induced increase of the wave-packet size. An extra enhancement occurs when the gradients of ground and ionized states approach each other. Under an increase of the photon energy, different sides of the x-ray photoelectron band experience blue- and redshifts, which are related to the difference of the gradients of the ground and core ionized states in the points of the vertical transitions near turning points of the wave packet. This makes the ir–x-ray pump-probe spectroscopy a very promising tool to study the shape of the potential energy surfaces.

We consider the quantum state of light produced via direct parametric decay of pump photons into photon triples in a medium with cubic nonlinearity. For this state generated in the near-collinear frequency-degenerate regime, the third- and second-order Glauber’s correlation functions are calculated and the intensity distribution over frequency and wave vector is found. It is shown that the number of photons generated into a single mode via the three-photon down-conversion is proportional to the width of the frequency-angular intensity distribution for the corresponding two-photon phase matching (spontaneous parametric down-conversion). The intensity of three-photon parametric down-conversion is shown to have an extremely broad frequency spectrum, even for a fixed angle of scattering.

We present a scheme to teleport an unknown atomic entangled state in driven cavity QED. In our scheme, the success probability can reach 1.0. In addition, the scheme is insensitive to the cavity decay and the thermal field.

We analyze a recent experiment on a Tonks-Girardeau gas of ${}^{87}\mathrm{Rb}$ atoms [T. Kinoshita, T. Wenger, and D.S. Weiss, Science 305, 1125 (2004)]. We find that the experimental data are compatible with the one-dimensional theory of Lieb, Seiringer, and Yngvason [Phys. Rev. Lett. 91, 150401 (2003)] but are better described by a theory that takes into account variations in the transverse width of the atomic cloud. By using this theory we investigate also the free axial expansion of the ${}^{87}\mathrm{Rb}$ gas in different regimes, Tonks-Girardeau gas, one-dimensional Bose-Einstein condensate and three-dimensional Bose-Einstein condensate.

Within a systematic approach based on dimensionally regularized nonrelativistic quantum electrodynamics, we derive a complete result for the two-loop correction to order ${(\alpha ∕\pi )}^2{\left(Z\alpha \right)}^4$ for the $g$ factor of an electron bound in an $nS$ state of a hydrogenlike ion. The results obtained significantly improve the accuracy of the theoretical predictions for the hydrogenlike carbon and oxygen ions and influence the value of the electron mass inferred from $g$-factor measurements.

A density-matrix formulation of classical bipartite correlations is constructed. This leads to an understanding of the appearance of classical statistical correlations intertwined with the quantum correlations as well as a physical underpinning of these correlations. As a by-product of this analysis, a physical basis of the classical statistical correlations leading to additive entropy in a bipartite system discussed recently by Tsallis emerges as inherent classical spin fluctuations. It is found that in this example, the quantum correlations shrink the region of additivity in phase space.

It is shown that a finite number of conditions are not sufficient to determine the locality of transformations between two probability distributions of pure states as well as the locality of transformations between two $d\times d$ mixed states with $d⩾4$. As an example, an infinite, but minimal, set of necessary and sufficient conditions for the existence of a local procedure that converts one probability distribution of two pure pair of qubits into another one is found.

Square-root measurement is a very useful suboptimal measurement in many applications. It was shown that the square-root measurement minimizes the squared error for pure states. In this paper, the least squared error problem is reformulated and a new proof is provided. It is found that the least squared error depends only on the average density operator of the input states. The properties of the least squared error are then discussed, and it is shown that if the input pure states are uniformly distributed, the average probability of error has an upper bound depending on the least squared error, the rank of the average density operator, and the number of the input states. The aforementioned properties help explain why the square-root measurement can be effective in decoding processes.

Optimal-control techniques and a fast-approach scheme are used to implement a collisional controlled-phase gate in a model of cold atoms in an optical lattice, significantly reducing the gate time as compared to adiabatic evolution while maintaining high fidelity. Objective functionals are given for which optimal paths are obtained for evolution that yields a controlled-phase gate up to single-atom Rabi shifts. Furthermore, the fast-approach procedure is used to design a path to significantly increase the fidelity of nonadiabatic transport in a recent experiment. In addition, the entanglement power of phase gates is quantified.

Bipartite and global entanglement are analyzed for the ground state of a system of $N$ spin-$1∕2$ particles interacting via a collective spin-spin coupling described by the Lipkin-Meshkov-Glick Hamiltonian. Under certain conditions, which include the special case of supersymmetry, the ground state can be constructed analytically. In the case of antiferromagnetic coupling and for an even number of particles, the system has a finite energy gap and the ground state undergoes a smooth transition, as a function of the continuous anisotropy parameter $\gamma$, from a separable $(\gamma =\infty )$ to a maximally entangled state $(\gamma =0)$. From the analytic expression for the ground state, the bipartite entanglement between two subsets of spins as well as the global entanglement are calculated. Despite the absence of a quantum phase transition a discontinuous change of the scaling of the bipartite entanglement with the number of spins in the subsystem is found at the isotropy point $\gamma =0$: While at $\gamma =0$ the entanglement grows logarithmically with the system size with no upper bound, it saturates for $\gamma \ne 0$ at a level only depending on $\gamma$.

The influence of decoherence on quantum memories for photons based on atomic ensembles is discussed. It is shown that despite the large entanglement of the collective storage states, corresponding to single photons or nonclassical states of light, the sensitivity to decoherence does not scale with the number of atoms. This is due to the existence of equivalence classes of storage states, which have the same projection onto the relevant quasiparticle mode (dark-state polariton). Several decoherence processes resulting from uncorrelated individual reservoir couplings are analyzed in detail: single-atom spin flips and dephasing, atom loss, and motion of atoms. Furthermore, it is shown that the sensitivity to collective decoherence processes that affect all polariton modes with comparable strength does also not increase with the number of atoms.

We generalize the adiabatic approximation to the case of open quantum systems, in the joint limit of slow change and weak open system disturbances. We show that the approximation is “physically reasonable” as under wide conditions it leads to a completely positive evolution, if the original master equation can be written on a time-dependent Lindblad form. We demonstrate the approximation for a non-Abelian holonomic implementation of the Hadamard gate, disturbed by a decoherence process. We compare the resulting approximate evolution with numerical simulations of the exact equation.

The Auger resonant Raman spectra of CO, arising from the transitions to the $X$ and $A$ final electronic states of $\mathrm{C}{\mathrm{O}}^{+}$, have been recorded at photon energies corresponding to the vibrational excitations $v^{\prime }=3,5$, and 8 in the O $1s\to 2\pi$ resonance. The spectra are simulated within the model that takes into account both the lifetime-vibrational interference (LVI) and interference with the nonresonant photoemission. The spectroscopic parameters, ${\omega }_e$, ${\omega }_e{x}_e$, $\Gamma$ and $r_e$, of the O $1s^{-1}2\pi$ core-excited state, necessary for the simulation, have been derived by fitting the Franck-Condon simulation to the total ion yield spectrum, assuming a Morse potential for the O $1s^{-1}2\pi$ state. Not only the LVI but also the interference with the nonresonant photoemission turn out to be significant.