We provide a simple method to obtain an upper bound on the secret key rate that is particularly suited to analyze practical realizations of quantum key distribution protocols with imperfect devices. We consider the so-called trusted device scenario where Eve cannot modify the actual detection devices employed by Alice and Bob. The upper bound obtained is based on the available measurements results, but it includes the effect of the noise and losses present in the detectors of the legitimate users.

We analyze how entanglement between two components of a bipartite system behaves under the action of local channels of the form $\mathcal{E}\otimes \mathcal{I}$. We show that a set of maximally entangled states is by the action of $\mathcal{E}\otimes \mathcal{I}$ transformed into the set of states that exhibit the same degree of entanglement. Moreover, this degree represents an upper bound on entanglement that is available at the output of the channel irrespective of what the input state of the composite system is. We show that within this bound the entanglement-induced state ordering is “relative” and can be changed by the action of local channels. That is, two states ${\varrho }_1^{\left(\mathrm{in}\right)}$ and ${\varrho }_2^{\left(\mathrm{in}\right)}$ such that the entanglement $E\left[{\varrho }_1^{\left(\mathrm{in}\right)}\right]$ of the first state is larger than the entanglement $E\left[{\varrho }_2^{\left(\mathrm{in}\right)}\right]$ of the second state are transformed into states ${\varrho }_1^{\left(\mathrm{out}\right)}$ and ${\varrho }_2^{\left(\mathrm{out}\right)}$ such that $E\left[{\varrho }_2^{\left(\mathrm{out}\right)}\right]>E\left[{\varrho }_1^{\left(\mathrm{out}\right)}\right]$.

We present an analytical treatment of quantum walks on a cycle graph. The investigation is based on a realistic physical model of the graph in which decoherence is induced by continuous monitoring of each graph vertex with a nearby quantum point contact. We derive an analytical expression of the probability distribution along the cycle. An upper-bound estimate to the mixing time is shown.

A quantum secure communication protocol using correlations of continuous variable Einstein-Podolsky-Rosen (EPR) pairs is proposed. The proposed protocol may implement both quantum key distribution and quantum message encryption by using a nondegenerate optical parametric amplifier (NOPA). The general Gaussian-cloner attack strategy is investigated in detail by employing Shannon information theory. Results show that the proposed scheme is secure, which is guaranteed physically by the correlations of the continuous variable EPR entanglement pairs generated by the NOPA.

The Fuchs-Peres-Brandt (FPB) probe realizes the most powerful individual attack on Bennett-Brassard 1984 quantum key distribution (BB84 QKD) by means of a single controlled-NOT (CNOT) gate. This paper describes a complete physical simulation of the FPB-probe attack on polarization-based BB84 QKD using a deterministic CNOT constructed from single-photon two-qubit quantum logic. Adding polarization-preserving quantum nondemolition measurements of photon number to this configuration converts the physical simulation into a true deterministic realization of the FPB attack.

We demonstrate a simple, robust, and ultrabright parametric down-conversion source of polarization-entangled photons based on a polarization Sagnac interferometer. Bidirectional pumping in type-II phase-matched periodically poled $\mathrm{K}\mathrm{Ti}\mathrm{O}\mathrm{P}{\mathrm{O}}_4$ yields a measured flux of 5000 polarization-entangled pairs/s/mW of pump power in a $1\text{−}\mathrm{nm}$ bandwidth at 96.8% quantum-interference visibility. The common-path arrangement of the Sagnac interferometer eliminates the need for phase stabilization for the biphoton output state.

Formulas for the corrections to the energy levels and wave functions of a spin-zero particle bound in a strong field are derived. The general case of the sum of a Lorentz-scalar potential and zero component of a Lorentz-vector potential is considered. The forms of the corrections differ essentially from those for spin-$\frac{1}{2}$ particles. As an example of application of our results, we evaluated the electric polarizability of a ground state of a spin-zero particle bound in a strong Coulomb field.

x rays have been observed in low energy collisions of bare Kr, Ar, and Ne ions with a neutral gas target. Although largely neglected previously, we have found that multiple-electron transfer processes play a significant role in shaping the x-ray spectra. The observed ratios of normal-satellite to hyper-satellite line intensities are found to be roughly independent of the ion species and much larger than those estimated from previously reported electron transfer cross sections, suggesting that there may be a strong correlation between two electrons during the electron transfer or during the subsequent cascades. It is suggested that exact knowledge of the initial and final principal and angular momentum quantum numbers in electron transfer are the most essential missing ingredients for understanding the entire x-ray emission process in astrophysical, laboratory, and technological plasmas.

In a previous paper [A. K. Bhatia, Phys. Rev. A 69, 032714 (2004)], electron-hydrogen $P$-wave scattering phase shifts were calculated using the optical potential approach based on the Feshbach projection operator formalism. This method is now extended to the singlet and triplet electron-${\mathrm{He}}^{+}$ $P$-wave scattering in the elastic region. Phase shifts are calculated using Hylleraas-type correlation functions with up to 220 terms. Results are rigorous lower bounds to the exact phase shifts, and they are compared to phase shifts obtained from the method of polarized orbitals and close-coupling calculations. The continuum functions calculated here are used to calculate photoabsorption cross sections. Photoionization cross sections of He and photodetachment cross sections of ${\mathrm{H}}^{-}$ are calculated in the elastic region—i.e., leaving ${\mathrm{He}}^{+}$ and H in their respective ground states—and compared with previous calculations. Radiative attachment rates are also calculated.

We report a new measurement of the photoionization cross section for the $\left(2p\right){}^5\left(3p\right)$ ${}^{3}D_3$ state of neon at the wavelengths of 351 and $364\mathrm{nm}$. These data were obtained by monitoring the decay of the fluorescence of atoms trapped in a magneto-optical atom trap under the presence of a photoionizing laser, a technique developed by Dinneen et al. [Opt. Lett. 17, 1706 (1992)]. We obtain absolute photoionization cross sections of $2.05\pm 0.25\times {10}^{-18}{\mathrm{cm}}^2$ at $\lambda =351\mathrm{nm}$ and $2.15\pm 0.25\times {10}^{-18}{\mathrm{cm}}^2$ at $\lambda =364\mathrm{nm}$, an improvement in accuracy of a factor of 4 over previously published values. These new values are not consistent with published theoretical data.

We investigate the problem of two atoms interacting via a short range $s$-wave potential in the presence of a deep optical lattice of arbitrary dimension $D$. Using a tight-binding approach, we derive analytical results for the properties of the bound state and the scattering amplitude. We show that the tunneling through the barriers induces a dimensional crossover from a confined regime at high energy to an anisotropic three-dimensional regime at low energy. The critical value of the scattering length needed to form a two-body bound state shows a logaritmic dependence on the tunneling rate for $D=1$ and a power law for $D>1$. For the special case $D=1$, we also compare our analytical predictions with exact numerics, finding remarkably good agreement.

We investigate the dynamic response of a highly degenerate ultracold Fermi gas to varying magnetic fields near the Feshbach resonance. Following the experimental practice, we calculate the dynamics of the excitation gap in response to the oscillating and linearly ramped magnetic fields, respectively. For oscillating magnetic fields, depending on the frequencies and the amplitudes of the oscillations, the response of the system shows either linear or rich nonlinear behavior. In addition, both the spectral studies through the linear-response theory and the time-domain simulations suggest the existence of a resonant frequency corresponding to the dissociation threshold of the fermion atom pairs. For linearly ramped magnetic fields, the response of the excitation gap shows damped oscillations, with the final value dependent on the rate of the field sweep. This work may find its applications in exploring the dynamics of the ultracold atom superfluidity near the BCS–Bose-Einstein-condensation crossover region.

Quantum cluster states and entangled-state analyzers are essential to measurement-based quantum computing. We propose to generate a quantum cluster state and to make a multipartite entanglement analyzer by using noninteracting free electrons or conduction electrons in quantum dots, based on polarizing beam splitters, charge detectors, and single-spin rotations. Our schemes are deterministic without the need of qubit-qubit interaction.

A single photon which is initially uncorrelated with an atom will evolve to be entangled with the atom on their continuous kinetic variables in the process of resonant scattering. We find the relations between the entanglement and their physical control parameters, which indicates that high entanglement can be reached by broadening the scale of the atomic wave or squeezing the linewidth of the incident single-photon pulse.

Quantum mechanics has been formulated in phase space, with the Wigner function as the representative of the quantum density operator, and classical mechanics has been formulated in Hilbert space, with the Groenewold operator as the representative of the classical Liouville density function. Semiclassical approximations to the quantum evolution of the Wigner function have been defined, enabling the quantum evolution to be approached from a classical starting point. Now analogous semiquantum approximations to the classical evolution of the Groenewold operator are defined, enabling the classical evolution to be approached from a quantum starting point. Simple nonlinear systems with one degree of freedom are considered, whose Hamiltonians are polynomials in the Hamiltonian of the simple harmonic oscillator. The behavior of expectation values of simple observables and of eigenvalues of the Groenewold operator are calculated numerically and compared for the various semiclassical and semiquantum approximations.

We present analytical treatment of quantum walks on multidimensional hypercycle graphs. We derive the analytical expression of the probability distribution for strong and weak decoherence regimes. Upper bound to mixing time is obtained.

We demonstrate that the entropy of entanglement and the distillable entanglement of regions with respect to the rest of a general harmonic-lattice system in the ground or a thermal state scale at most as the boundary area of the region. This area law is rigorously proven to hold true in noncritical harmonic-lattice systems of arbitrary spatial dimension, for general finite-ranged harmonic interactions, regions of arbitrary shape, and states of nonzero temperature. For nearest-neighbor interactions—corresponding to the Klein-Gordon case—upper and lower bounds to the degree of entanglement can be stated explicitly for arbitrarily shaped regions, generalizing the findings of Phys. Rev. Lett. 94, 060503 (2005). These higher-dimensional analogs of the analysis of block entropies in the one-dimensional case show that under general conditions, one can expect an area law for the entanglement in noncritical harmonic many-body systems. The proofs make use of methods from entanglement theory, as well as of results on matrix functions of block-banded matrices. Disordered systems are also considered. We moreover construct a class of examples for which the two-point correlation length diverges, yet still an area law can be proven to hold. We finally consider the scaling of classical correlations in a classical harmonic system and relate it to a quantum lattice system with a modified interaction. We briefly comment on a general relationship between criticality and area laws for the entropy of entanglement.

The one-loop self-energy is evaluated for $d_{3∕2}$ and $d_{5∕2}$ states in hydrogenic ions, and good agreement found with previous calculations. Results are compared to what is known of the $Z\alpha$ expansion and higher-order binding corrections inferred for these states as well as for their fine structures. Screened Kohn-Sham potentials are then used to evaluate the one-loop self-energy corrections to $n=2$ states of lithiumlike ions for $Z=10–100$, $n=3$ states of sodiumlike ions for $Z=20–100$, and $n=4$ states of copperlike ions for $Z=40–100$. The importance of these screened calculations for the interpretation of recent high accuracy experiments is emphasized.

We present an accurate ab initio method of calculating isotope shifts and relativistic shifts in atomic spectra. We test the method on neutral carbon and three carbon ions. The relativistic shift of carbon lines may allow them to be included in analyses of quasar absorption spectra that seek to measure possible variations in the fine structure constant $\alpha$ over the lifetime of the Universe. Carbon isotope shifts can be used to measure isotope abundances in gas clouds: isotope abundances are potentially an important source of systematic error in the $\alpha$-variation studies. These abundances are also needed to study nuclear reactions in stars and supernovae, and test models of chemical evolution of the Universe.

In view of modelization of experiments involving cold atoms and molecules, we develop a method that allows us to calculate weakly bound levels of triatomic molecules. The method combines (1) the hyperspherical coordinates to describe interparticle motion in the three-body system, (2) the solution of the Schrödinger equation in two steps: determination of adiabatic states for a fixed hyper-radius and then solution of a set of coupled hyper-radial equations using the slow variable representation of Tolstikhin et al. [J. Phys. B: At. Mol. Opt. Phys. 29, L389 (1996)], (3) and a mapping procedure that reduces considerably the number of basis functions needed to represent wave functions of weakly bound levels. We apply the method to the three different systems: the helium trimer ${}^4\mathrm{He}_3$, isotopomers of the $\mathrm{H}_3{}^{+}$ ion, and finally a model three-body problem involving three nucleons. For all these systems, we show that the suggested method provides accurate results.