We describe and examine entanglement between different degrees of freedom in multiphoton states based on the permutation properties. From the state description, the entanglement comes from the permutation asymmetry. According to the different permutation properties, the multiphoton states can be divided into several parts. It will help to deal with the multiphoton interference, which can be used as the measurement of the entanglement.

The properties of a special class of correlated many-body wave functions, named rotating vortex clusters (RVCs), that preserve the total angular momentum of a small cloud of trapped rotating bosons are investigated. They have lower energy and provide a superior description for the formation of vortices compared to the mean-field Gross-Pitaevskii (GP) states that break the rotational symmetry. The GP vortex states are shown to be wave packets composed of such RVC states. Our results suggest that, for a small number of bosons, the physics is different from that of ideal Bose-Einstein condensates which characterize larger assemblies.

We obtain, analytically, the global negativity, partial $K$-way negativities $(K=2,3)$, Wootter’s tangle, and three-tangle for the generic three-qubit canonical state. It is found that the product of global negativity and partial three-way negativity is equal to the three-tangle, while the partial two-way negativity is related to the tangle of qubit pairs. We also calculate similar quantities for the state canonical to a single-parameter $(0<q<1)$ pure state which is a linear combination of a Greenberger-Horne-Zeilinger state and a $W$ state. In this case, for $q=0.62685$, the state has zero three-tangle and zero three-way negativity, having only $W$-like entanglement. The difference between the product of global and partial three-way negativities and the three-tangle for a given state is a quantitative measure of two-qubit coherences transformed by unitary transformations on the canonical state into three-qubit coherences. The global negativity and partial $K$-way negativities, obtained by selective partial transpositions on multiqubit state operators, satisfy inequalities which for three qubits are equivalent to the Coffman-Kundu-Wootter inequality.

In this paper, we investigate what kinds of quantum states are feasible to perform perfectly secure secret sharing, and present its necessary and sufficient conditions. We also show that the states are bipartite distillable for all bipartite splits, and hence the states could be distillable into the Greenberger-Horne-Zeilinger state. We finally exhibit a class of secret-sharing states, which have an arbitrarily small amount of bipartite distillable entanglement for a certain split.

It has been established that local lattice spin Hamiltonians can be used for universal adiabatic quantum computation. However, the two-local model Hamiltonians used in these proofs are general and hence do not limit the types of interactions required between spins. To address this concern, the present paper provides two simple model Hamiltonians that are of practical interest to experimentalists working toward the realization of a universal adiabatic quantum computer. The model Hamiltonians presented are the simplest known quantum-Merlin-Arthur-complete (QMA-complete) two-local Hamiltonians. The two-local Ising model with one-local transverse field which has been realized using an array of technologies, is perhaps the simplest quantum spin model but is unlikely to be universal for adiabatic quantum computation. We demonstrate that this model can be rendered universal and QMA-complete by adding a tunable two-local transverse ${\sigma }^x{\sigma }^x$ coupling. We also show the universality and QMA-completeness of spin models with only one-local ${\sigma }^z$ and ${\sigma }^x$ fields and two-local ${\sigma }^z{\sigma }^x$ interactions.

A long-standing open problem in fault-tolerant quantum computation has been to find a universal set of transversal gates. As shown by Zeng et al. (e-print arXiv:0706.1382), such a set does not exist for binary stabilizer codes. Here we generalize our work to show that for subsystem stabilizer codes in $d$-dimensional Hilbert space, such a universal set of transversal gates cannot exist for even one encoded qudit, for any dimension $d$, prime or nonprime. This result strongly supports the idea that other primitives, such as quantum teleportation, are necessary for universal fault-tolerant quantum computation, and may be an important factor for fault-tolerance noise thresholds.

A repeat-until-success (RUS) measurement-based scheme for the implementation of the distributed quantum computation by using single-photon interference at a 50:50 beam splitter is proposed. It is shown that the 50:50 beam splitter can naturally project a suitably encoded matter-photon state to either a desired entangling gate-operated state of the matter qubits or to their initial state when the photon is detected. The recurrence of the initial state permits us to implement the desired entangling gate in a RUS way. To implement a distributed quantum computation we suggest an encoding method by means of the effect of dipole-induced transparency proposed recently [E. Waks and J. Vuckovic, Phys. Rev. Lett. 96, 153601 (2006)]. The effects of the unfavorable factors on our scheme are also discussed.

We present an approach to the correlated dynamics of many-electron systems. We show, that the two-electron reduced density matrix (2RDM) can provide a suitable description of the real time evolution of a system. To achieve this, the hierarchy of equations of motion must be truncated in a practical way. Also, the computational effort, given that the 2RDM is represented by products of two-electron determinants, is discussed, and numerical model calculations are presented.

In this work, we carry out an investigation of high-lying $\mathit{S}$-wave resonances in Ps-H scattering below the ${\text{Ps}}^{-}{\text{-H}}^{+}$ threshold. The method of complex-coordinate rotation is used together with highly correlated wave functions containing all six interparticle coordinates. Using such Hylleraas-type bases up to 6412 terms, the energy positions for the $1S–8S$ states in the Rydberg series converging to the ${\text{Ps}}^{-}$ threshold, as well as the four widths for the $2S–5S$ states, are calculated. The energies for the $5S–8S$ states of this Rydberg series are then used to fit into the quantum defect formula, from which the energy levels for higher members of the Rydberg series can be estimated.

Combining a laser photoelectron source with a triply differentially pumped supersonic beam target and several electron multipliers for simultaneous detection of electrons elastically scattered into the angles 22.5°, 45°, 90°, 112.5°, and 135° and of metastable atoms due to inelastic scattering, we have carried out an improved study of electron-argon scattering over the energy range $11.0–13.7\mathrm{eV}$ with experimental energy widths around $5\mathrm{meV}$. In addition, the Fribourg scattering apparatus has been used for careful remeasurements of the differential cross section and the resonance structure in the energy range of the two lowest anion resonances over the full angular range at a resolution of about $13\mathrm{meV}$. Accurate values for the energies, the widths $(2.3\pm 0.2\mathrm{meV})$, and the fine-structure separation $(172.7\pm 0.2\mathrm{meV})$ of the low-lying ${\mathrm{Ar}}^{-}\left(3p^{5}4s^2{}^{2}P_{3∕2,1∕2}\right)$ Feshbach resonances have been determined from the two experiments by detailed partial-wave analyses of the resonance profiles using several sets of energy-dependent background phase shifts; these include an accurate set obtained with a coupled-cluster calculation involving a soft box potential. Moreover, the excitation function for the production of metastable ${\mathrm{Ar}}^{*}\left(3p^{5}4s{}^{3}P_{2,0}\right)$ atoms has been measured from threshold to $13.7\mathrm{eV}$. From a fit to its onset, the absolute electron energy scale is established to within $\pm 0.3\mathrm{meV}$; in addition, the energies and widths of some higher-lying resonances $(12.9–13.5\mathrm{eV})$ have been determined and are compared with the results of earlier experiments and of a recent $B$-spline $R$-matrix calculation. In connection with calibration experiments involving He atoms, we carried out an improved measurement of the ${\mathrm{He}}^{-}\left(1s2s^2{}^{2}S_{1∕2}\right)$ resonance and deduced a natural width of $10.9\pm 0.3\mathrm{meV}$.

The $B$-spline Breit-Pauli $R$-matrix method is used to investigate electron scattering from singly ionized potassium in the energy range from threshold to $400\mathrm{eV}$. The primary aim of the present work is to resolve discrepancies between the available experimental and theoretical cross sections for excitation of the ${\mathrm{K}}^{+}$ resonance lines. The multiconfiguration Hartree-Fock method with term-dependent nonorthogonal orbitals is employed for an accurate representation of the target wavefunctions. The close-coupling expansion includes 43 bound levels of ${\mathrm{K}}^{+}$ covering all possible terms of the lowest configurations $3p^6$, $3p^{5}4s$, $3p^{5}3d$, $3p^{5}4p$, $3p^{5}5s$, and $3p^{5}4d$. Our results confirm that the apparent cross section for the $(60.1+60.8+61.3)\mathrm{nm}$ emission line from the $3p^5(4s+3d)$ levels in the crossed-beams experiment of Zapesochny et al. {Zh. Eksp. Teor. Fiz. 90, 1972 (1986) [Sov. Phys. JETP 63, 1155 (1986)]} was normalized with an error of about a factor of 4. We also present the cross sections for excitation of the $3p^{5}4p$, $3p^{5}5s$, and $3p^{5}4d$ levels and discuss the cascade contribution from higher excited levels to the $3p^{5}4s$ and $3p^{5}3d$ levels.

Fully differential cross sections for the transfer-ionization process ${\text{H}}^{+}+\text{He}\to {\text{H}}^0+{\text{He}}^{2+}+e^{-}$ are calculated. The theoretical model is an expansion of the transition amplitude through the second order in the projectile-target interaction with highly correlated wave functions for the target. The theoretical results exhibit a strong sensitivity to angular electron correlation in both first- and second-order calculations. The results of the calculations are in sensible agreement with recent COLTRIMS observations.

The influence of transverse relaxation on the resonance soliton ($2\pi$ hyperbolic-secant pulse) in solids is considered. It is shown that memory effects can be considered in terms of generalized non-Markovian optical Bloch equations. The equations of self-induced transparency with a memory function are presented. Explicit forms for the first-order effects of this relaxation on the frequency shift and the pulse height of a resonant $2\pi$ soliton in solids are given and discussed. It is shown that memory effects do lead to a qualitative change in the dynamics of the influence of transverse relaxations on a $2\pi$ pulse in comparison to the McCall-Hahn theory and others. The dynamics of the changes of the inverse width of the pulse are obtained in both the Markovian and the non-Markovian cases with realistic parameters that can be achieved in current experiments.

We show quantitatively the influence of the dipole density on the resolving capability of a negative-refractive-index slab. A numerical solution for scatter with a model that represents a locally periodic array of electric and magnetic dipoles provides a means for evaluating the influence of periodicity. A Fourier transform of the spatial field solution gives access to the plane wave transfer function in relation to the degree of granularity. Throughout, a quasistatic homogenization procedure is used to ensure that correctly matched effective medium parameters are achieved. The results provide a measure of the fabrication technology necessary to achieve substantially subwavelength resolution.

To reply to the Comment on our original paper entitled “Arbitrated quantum-signature scheme” [Phys. Rev. A 65, 042312 (2002)], we present more detailed presentations and proofs of the quantum-signature scheme in our paper. We feel our further investigation has shown that the original quantum-signature scheme is secure and operationally well defined. In addition, proofs illustrate that the quantum-signature scheme with unknown quantum states is also suitable in principle.

We describe various results related to the random-party distillation of multiparty entangled states—that is, conversion of such states into entangled states shared between fewer parties, where those parties are not predetermined. In previous work we showed that certain output states (namely Einstein-Podolsky-Rosen pairs) could be reliably acquired from a prescribed initial multipartite state [namely the W state $|\text{W}⟩=\frac{1}{\sqrt{3}}\left(|100⟩+|010⟩+|001⟩\right)$] via random-party distillation that could not be reliably created between predetermined parties. Here we provide a more rigorous definition of what constitutes “advantageous” random-party distillation. We show that random-party distillation is always advantageous for W-class three-qubit states (but only sometimes for Greenberger-Horne-Zeilinger class states). We show that the general class of multiparty states known as symmetric Dicke states can be readily converted to many other states in the class via random-party distillation. Finally we show that random-party distillation is provably not advantageous in the limit of multiple copies of pure states.

We study the local entanglement remaining after filtering operations corresponding to imperfect measurements performed by one or both parties, such that the parties can only determine whether or not the system is located in some region of space. The local entanglement in pure states of general bipartite multidimensional continuous-variable systems can be completely determined through simple expressions. We apply our approach to semiclassical Wentzel-Kramers-Brillouin-Jeffreys (WKB) systems, multidimensional harmonic oscillators, and a hydrogen atom as three examples.

Quantum repeaters promise to deliver long-distance entanglement overcoming loss in realistic quantum channels. A promising class of repeaters, based on atomic ensemble quantum memories and linear optics, follows the proposal by L.-M. Duan et al., Nature (London) 414, 413 (2001). Here we analyze this protocol in terms of a very general model for the quantum memories employed. We derive analytical expressions for scaling of entanglement with memory imperfections, dark counts, loss, and distance, and we apply our results to two specific quantum memory protocols. Our methods apply to any quantum memory with an interaction Hamiltonian at most quadratic in the mode operators and are in principle extendible to more recent modifications of the original proposal of Duan, Lukin, Cirac, and Zoller.

Relativistic configuration-interaction calculations have been performed for anion states representing $6p$ attachments to all lanthanides with $4f^{n}6s^2$ ground states. The complexity of these systems requires a corelike treatment of the $4f$ subshell (same occupancy in all correlation configurations), and the methodology of creating $jls$ restrictions on the $4f^n$ subgroup has been improved to include the mixing of $LS$ terms from individual neutral $J$ calculations. Results show a nearly linear decrease in electron affinity with $n$ for these lanthanides from $177\mathrm{meV}$ for ${\mathrm{Pr}}^{-}$ $(n=3)$ to $22\mathrm{meV}$ for ${\mathrm{Tm}}^{-}$ $(n=13)$.

Parity violation (PV) effects at the Dirac-Hartree-Fock and Dirac-Kohn-Sham level of theory are presented for the chiral molecule SeOClI. The PV energy contribution to the $S$ enantiomer of SeOClI ranges between $-7.1$ and $-9.2\mathrm{Hz}$, depending on the level of theory applied. For the Se-O fundamental stretching mode, which lies within the $\mathrm{C}{\mathrm{O}}_2$ laser frequency range, we obtain PV energy differences of $110\mathrm{mHz}$ between the two enantiomers, which is twice as large compared to the previously investigated C-F stretching mode of CHFBrI.