We reconsider density matrices of graphs as defined in quant-ph/0406165. The density matrix of a graph is the combinatorial Laplacian of the graph normalized to have unit trace. We describe a simple combinatorial condition (the “degree condition”) to test the separability of density matrices of graphs. The condition is directly related to the Peres-Horodecki partial transposition condition. We prove that the degree condition is necessary for separability, and we conjecture that it is also sufficient. We prove special cases of the conjecture involving nearest-point graphs and perfect matchings. We observe that the degree condition appears to have a value beyond the density matrices of graphs. In fact, we point out that circulant density matrices and other matrices constructed from groups always satisfy the condition and indeed are separable with respect to any split. We isolate a number of problems and delineate further generalizations.

We use techniques for lower bounds on communication to derive necessary conditions in terms of detector efficiency or amount of superluminal communication for being able to reproduce with classical local hidden-variable theories the quantum correlations occurring in Einstein-Podolsky-Rosen (EPR) experiments in the presence of noise. We apply our method to an example involving $n$ parties sharing a Greenberger-Horne-Zeilinger-type state on which they carry out local measurements. For this example, we show that for local hidden-variable theories to reproduce the quantum correlations, the amount of superluminal classical communication $c$ and the detector efficiency $\eta$ are constrained by $\eta 2^{-c∕n}⩽O\left(n^{-1∕6}\right)$. This result holds even if the classical models are allowed to make an error with constant probability.

We study the problem of mapping an unknown mixed quantum state onto a known pure state without the use of unitary transformations. This is achieved with the help of sequential measurements of two noncommuting observables only. We show that the overall success probability is maximized in the case of measuring two observables whose eigenstates define mutually unbiased bases. We find that for this optimal case the success probability quickly converges to unity as the number of measurement processes increases and that it is almost independent of the initial state. In particular, we show that to guarantee a success probability close to one the number of consecutive measurements must be larger than the dimension of the Hilbert space. We connect these results to quantum copying, quantum deleting, and entanglement generation.

We propose a scheme for implementing quantum computation with $N$ atoms trapped in a single-sided cavity. In our scheme, a multiqubit controlled-phase-flip (MCPF) gate as well as a quantum controlled phase flip gate is performed by only one step. The numerical simulations show that the protocol is robust to practical noise. In addition, the scheme can also be extended to achieve other multiqubit controlled unitary gates, and implement MCPF gate on atoms trapped in different cavities.

We show how to perform reversible universal quantum computation on a translationally invariant pure state, using only global operations based on next-neighbor interactions. We do not need to break the translational symmetry of the state at any time during the computation. Since the proposed scheme fulfills the locality condition of a quantum cellular automata, we present a reversible quantum cellular automaton capable of universal quantum computation.

We investigate the relation between the thermalization cross section ${⟨\sigma ⟩}_T$ and the scattering length $a$ of spin-polarized metastable neon $\left({\mathrm{Ne}}^{*}\right)$ in the Doppler-limited temperature regime. We show that a temperature-dependent, quantum-mechanical, five-channel calculation allows one to obtain $a$ consistent with the mass scaling rule between ${}^{20}\mathrm{Ne}^{*}$ and ${}^{22}\mathrm{Ne}^{*}$ from recent data of ${⟨\sigma ⟩}_T$ by Spoden et al. [Phys. Rev. Lett. 94, 223201 (2005)]. We find $a=+{24}_{-5}^{+5}{a}_0$ or $a=-{128}_{-22}^{+16}{a}_0$ for ${}^{20}\mathrm{Ne}^{*}$ and $+115\lesssim a\lesssim +160a_0$ for ${}^{22}\mathrm{Ne}^{*}$, respectively. According to numerical simulations of the evaporative cooling process, these values of $a$ are not large enough to make Bose-Einstein condensation of ${\mathrm{Ne}}^{*}$ feasible for realistic experimental conditions, given the measured ionization rate constants.

The asymptotic wave function derived by Alt and Mukhamedzhanov [Phys. Rev. A47, 2004 (1993)] and Mukhamedzhanov and Lieber [Phys. Rev. A54, 3078 (1996)] has been refined in the region where the pair $(\beta ,\gamma )$ remains close to each other while the third particle $\alpha$ is far away from them $({\rho }_{\alpha }\to \infty ,r_{\alpha }∕{\rho }_{\alpha }\to 0)$. The improved wave function satisfies the Schrödinger equation up to the terms of order $O(1∕{\rho }_{\alpha }^3)$, provides the leading asymptotic terms of the three-body scattering wave function with Coulomb interactions, and gives further insight into the continuum behavior of the three-charged-particle wave function, and helps to obtain the $3\to 3$ scattered wave. This opens up further ways of solving and analyzing the three-body Schrödinger equation by numerical means.

We report an experimental technique for the comparison of ionization processes in ultrafast laser pulses irrespective of pulse ellipticity. Multiple ionization of xenon by $50\mathrm{fs}$ $790\mathrm{nm}$, linearly and circularly polarized laser pulses is observed over the intensity range $10\mathrm{TW}∕{\mathrm{cm}}^2\text{to}10\mathrm{PW}∕{\mathrm{cm}}^2$ using effective intensity matching (EIM), which is coupled with intensity selective scanning (ISS) to recover the geometry-independent probability of ionization. Such measurements, made possible by quantifying diffraction effects in the laser focus, are compared directly to theoretical predictions of multiphoton, tunnel and field ionization, and a remarkable agreement demonstrated. EIM-ISS allows the straightforward quantification of the probability of recollision ionization in a linearly polarized laser pulse. Furthermore, the probability of ionization is discussed in terms of the Keldysh adiabaticity parameter $\gamma$, and the influence of the precursor ionic states present in recollision ionization is observed.

The microscopic foundation of quantum-optical spectroscopy is presented. It is proposed to use this technique to generate and detect quasiparticle states in semiconductors whose quantum-statistical properties are governed by that of the exciting light. While resonant classical excitation induces an optical interband polarization, low-intensity quantum excitation directly seeds a quantum-degenerate exciton state which is characterized by long-range order, anomalous reduction of Coulomb and phonon scattering, as well as strongly enhanced and directional quantum emission.

We analyze methods designed to go beyond the standard quantum limit for a class of atomic interferometers, where the quantity of interest is the difference of phase shifts obtained by two independent atomic ensembles. An example is given by an atomic Sagnac interferometer, where for two ensembles propagating in opposite directions in the interferometer this phase difference encodes the angular velocity of the experimental setup. We discuss methods of separately or jointly squeezing observables of the two atomic ensembles, and compare in detail the advantages and drawbacks of such schemes. In particular, we show that the method of joint squeezing may improve the variance by up to a factor of 2. We take into account fluctuations of the number of atoms in both the preparation and the measurement stage, and obtain bounds on the difference between the numbers of atoms in the two ensembles, as well as on the detection efficiency, which have to be fulfilled in order to surpass the standard quantum limit. Under realistic conditions, the performance of both schemes can be improved significantly by reading out the phase difference via a quantum nondemolition measurement. Finally, we discuss a scheme using macroscopically entangled ensembles.

A simple scheme is proposed to generate an $n$-qubit $W$ state in cavity QED. Conditioned on no photon leakage from the cavity, the $n$-qubit $W$ state can be generated by resonant interaction between atoms and the cavity if the cavity is initially prepared in the single-photon state and all the atoms are in the ground states. We check the time evolution of the system involving decay, and show that, since the required interaction time is very short, with present cavity QED techniques, the success probability of our scheme is almost unity.

We present a physical scheme for entanglement concentration of unknown atomic entangled states via cavity decay. In the scheme, the atomic state is used as a stationary qubit and the photonic state as a flying qubit, and a close maximally entangled state can be obtained from pairs of partially entangled states probabilistically.

To verify the recently calculated intermolecular interaction potentials of the methane dimer within the density functional theory using the (Perdew) local density approximation (LDA) [Chen et al., Phys. Rev. A 69, 034701 (2004)], we have performed a parallel series of calculations using the $\mathrm{LDA}∕6\text{−}311++\mathrm{G}$ (3df, 3pd) level of theory with selected exchange functionals (B, G96, MPW, O, PBE, PW91, S, and XA). None of the above calculated intermolecular interaction potentials from the local density approximation reproduce the results reported in the commented paper. In addition, we point out the inappropriateness of using the Lennard-Jones function to model the long-range parts of the calculated intermolecular interaction potentials, as suggested positively by Chen et al.

The recent experimental result by Nguyen et al. [Phys. Rev. A 71, 062714 (2005)] on the ratio of cross sections for charge exchange processes ${\mathrm{Rb}}^{+}+\mathrm{Rb}\left(5s\right)\to \mathrm{Rb}\left(5p\right)+{\mathrm{Rb}}^{+}$ and ${\mathrm{Rb}}^{+}+\mathrm{Rb}\left(5p\right)\to \mathrm{Rb}\left(5s\right)+{\mathrm{Rb}}^{+}$ is quantitatively derived from simple considerations within the general framework of the quasimolecular theory. Contrary to the expectations, applicability of the Demkov model for charge exchange with small energy defect is not shattered.

In this paper, we prove that the unconditionally secure key can be surprisingly extracted from multiphoton emission part in the photon polarization-based quantum key distribution. One example is shown by explicitly proving that one can indeed generate an unconditionally secure key from Alice’s two-photon emission part proposed by Scarani [ et al. Phys. Rev. Lett. 92, 057901 (2004)]. Which is called the Scarani-Acin-Ribordy-Gisin (SARG04) protocol. This protocol uses the same four states as in Bennett-Brassard 1984 (BB84) and differs only in the classical postprocessing protocol. It is, thus, interesting to see how the classical postprocessing of quantum key distribution might qualitatively change its security. We also show that one can generate an unconditionally secure key from the single to the four-photon part in a generalized SARG04 protocol that uses six states. Finally, we also compare the bit error rate threshold of these protocols with the one in the BB84 protocol and the original six-state protocol assuming a depolarizing channel.

The $M$-shell ionization in high-$Z$ atoms by low-energy light ${}_1{}^1\mathrm{H}$, ${}_1{}^2\mathrm{H}$, ${}_2{}^3\mathrm{He}$, and ${}_2{}^4\mathrm{He}$ ions have been studied systematically in the energy range $0.1–1.0\mathrm{MeV}∕\mathrm{amu}$ in order to verify the available theoretical approaches describing the $M$-shell ionization by charged particles in asymmetric collisions. The present low-energy data, combined with our earlier results reported for $M$-shell ionization by hydrogen and helium ions for higher energies, form a systematic experimental basis to test the theoretical predictions of $M$-shell ionization based on the plane-wave Born approximation (PWBA), the semiclassical approximation (SCA), and the binary-encounter approximation (BEA). In the PWBA based approaches the energy loss (E), Coulomb deflection (C), perturbed stationary state (PSS), and relativistic (R) effects were considered within the ECPSSR theory and its recent modification, called the ECUSAR theory, in which a description of the PSS effect was corrected to account for the united- and separated-atom (USA) electron binding energy limits. In the SCA calculations with relativistic wave functions the binding effect was included only in the limiting cases of separated-atom and united-atom limits. Possible contribution of the electron capture, multiple ionization, and recoil ionization to the $M$-shell vacancy production, which is dominated for light ions impact by direct single ionization process, are also discussed. The universal scaling of measured $M$-shell x-ray production and ionization cross sections was investigated in detail. Using the present data the isotopic effect has been studied by comparing the measured $M$-shell ionization cross-section ratios for equal-velocity hydrogen ${}_1{}^1\mathrm{H}$ and ${}_1{}^2\mathrm{H}$ as well as helium ${}_2{}^3\mathrm{He}$ and ${}_2{}^4\mathrm{He}$ isotopes. In addition, the ratios of measured ionization cross sections for ${}_1{}^2\mathrm{H}$ and ${}_2{}^4\mathrm{He}$ were used to investigate the role of the binding effect. The present results are of practical importance for the application of particle-induced x-ray emission technique in trace element studies.

A fully quantal approach to proton collisions with hydrogen based on the atomic-orbital close-coupling method is presented. The method leads to a system of coupled three-dimensional momentum-space integral equations for the scattering amplitudes. These equations are reduced to two-dimensional ones using an on-shell approximation. Furthermore, by considering the symmetry of the problem, we demonstrate that these can be reduced to just one dimension. The resulting equations are solved without partial-wave expansion. Cross sections for electron transfer in proton collisions with the ground state of atomic hydrogen are calculated and shown to agree well with experiment over a wide energy range.

We report cross sections for elastic scattering of low-energy electrons by fullerene, ${\mathrm{C}}_{60}$, calculated within the static-exchange approximation. The calculations are carried out via the Schwinger multichannel (SMC) method, equivalent in this case to the standard Schwinger variational principle. Combining the high parallel efficiency of the SMC method with a quadrature specially adapted to the high symmetry of ${\mathrm{C}}_{60}$ facilitates the most demanding step of the calculation and so permits the use of a large basis set. We analyze the structure of the cross section with reference to a simple spherical-shell model, and we compare our results to prior measurements and calculations.

Time-dependent density-functional theory is used to calculate quantum-size effects in the energy loss of antiprotons interacting with a confined two-dimensional electron gas. The antiprotons follow a trajectory normal to jellium circular clusters of variable size, crossing every cluster at its geometrical center. Analysis of the characteristic time scales that define the process is made. For high-enough velocities, the interaction time between the projectile and the target electrons is shorter than the time needed for the density excitation to travel along the cluster. The finite-size object then behaves as an infinite system, and no quantum-size effects appear in the energy loss. For small velocities, the discretization of levels in the cluster plays a role and the energy loss does depend on the system size. A comparison to results obtained using linear theory of screening is made, and the relative contributions of electron-hole pair and plasmon excitations to the total energy loss are analyzed. This comparison also allows us to show the importance of a nonlinear treatment of the screening in the interaction process.