We propose a high security quantum key distribution (QKD) scheme utilizing one mode of spontaneous parametric downconversion gated by a photon number resolving detector. This photon number measurement is possible by using single-photon detectors operating at room temperature and optical fibers. By post selection, the multiphoton probability in this scheme can be reduced to lower than that of a scheme using an attenuated coherent light resulting in improvement of security. Furthermore, if distillation protocol (error correction and privacy amplification) is performed, the gain will be increased. Hence a QKD system with higher security and bit rate than the laser-based QKD system can be attained using present available technologies.

The linearity of quantum operations puts many fundamental constraints on the information processing tasks we can achieve on a quantum system whose state is not exactly known, just as we observe in quantum cloning and quantum discrimination. In this paper we show that in a probabilistic manner, linearity is in fact the only one that restricts the physically realizable tasks. To be specific, if a system is prepared in a state secretly chosen from a linearly independent pure state set, then any quantum state separation can be physically realized with a positive probability. Furthermore, we derive a lower bound on the average failure probability of any quantum state separation.

The natural lifetime of the metastable $4d{}^{2}D_{5∕2}$ state in ${}^{88}\mathrm{Sr}^{+}$ has been measured using a single laser-cooled, trapped ion. The ion was prepared in the $4d{}^{2}D_{5∕2}$ state by laser excitation of the $5s{}^{2}S_{1∕2}-4d{}^{2}D_{5∕2}$ quadrupole transition at 674 nm. The decay time was measured by using Dehmelt’s electron shelving method to monitor the ion’s electronic state. Two separate investigations were conducted under slightly different experimental conditions. 160 000 decay times from the $4d{}^{2}D_{5∕2}$ state were observed in total, and two different methods for determining the statistical value of the measured lifetime have been compared. Systematic effects have also been estimated, and including these effects yields a value of $\tau =390.8\left(1.6\right)\mathrm{ms}$ ($1\sigma$ uncertainty) for the natural lifetime.

The general Feshbach-Fano $R$-matrix procedure proposed recently by Nestmann [J. Phys. B 31, 3929 (1998)] makes it possible to construct resonance metastable states of transient molecular ions and their coupling elements to the background scattering continuum. These quantities are needed for the study of nuclear dynamics in the framework of the nonlocal resonance model. The performance of this approach is carefully studied and its properties analyzed in the field of potential scattering. An improvement of the Nestmann procedure which makes the calculation more stable and robust is proposed.

Positronium (Ps) formation cross sections are calculated for positrons scattered by ground-state potassium in the low-energy region $(0.2–15.0\mathrm{eV})$ using an optical-model approach. Cross sections for Ps formation in $n=3$ states are obtained for the second time and show great discrepancies with the prediction of McAlinden et al. [J. Phys. B 29, 555 (1996)]. Fairly good agreement is obtained with the measurements of Zhou et al. [Phys. Rev. Lett. 73, 236 (1994)] for a total Ps formation cross section when taking Ps $(n=3)$ formation into account. We present here a full description for Ps $(n=1)$, Ps $(n=2)$, and Ps $(n=3)$ formation cross sections.

The multiconfiguration time-dependent Hartree-Fock and the time-dependent configuration interaction singles method are applied to the correlated many-electron dynamics of a one-dimensional jellium model system. We study the scattering of an initially free electron at a model film in the framework of both approaches. In particular, both methods are compared with regard to how they describe the underlying physical processes, namely inelastic electron scattering, inverse photoemission, and electron impact ionization.

We analyze the quantum-to-classical transition (QCT) for coupled bipartite quantum systems for which the position of one of the two subsystems is continuously monitored. We obtain the surprising result that the QCT can emerge concomitantly with the presence of highly entangled states in the bipartite system. Furthermore, the changing degree of entanglement is associated with the backaction of the measurement on the system and is itself an indicator of the QCT. Our analysis elucidates the role of entanglement in von Neumann’s paradigm of quantum measurements comprised of a system and a monitored measurement apparatus.

We study the nonequilibrium dynamics of a Bose-Einstein condensate that is split in a harmonic trap by turning up a periodic optical lattice potential. We evaluate the dynamical evolution of the phase coherence along the lattice and the number fluctuations in individual lattice sites within the stochastic truncated Wigner approximation when several atoms occupy each site. We show that the saturation of the number squeezing at high lattice strengths, which was observed in recent experiments by Orzel et al. [Science 291, 2386 (2001)] can be explained by the nonadiabaticity of the splitting.

Causal quantum theory is an umbrella term for ordinary quantum theory modified by two hypotheses: state vector reduction is a well-defined process, and strict local causality applies. The first of these holds in some versions of Copenhagen quantum theory and need not necessarily imply practically testable deviations from ordinary quantum theory. The second implies that measurement events which are spacelike separated have no nonlocal correlations. To test this prediction, which sharply differs from standard quantum theory, requires a precise definition of state vector reduction. Formally speaking, any precise version of causal quantum theory defines a local hidden variable theory. However, causal quantum theory is most naturally seen as a variant of standard quantum theory. For that reason it seems a more serious rival to standard quantum theory than local hidden variable models relying on the locality or detector efficiency loopholes. Some plausible versions of causal quantum theory are not refuted by any Bell experiments to date, nor is it evident that they are inconsistent with other experiments. They evade refutation via a neglected loophole in Bell experiments—the collapse locality loophole—which exists because of the possible time lag between a particle entering a measurement device and a collapse taking place. Fairly definitive tests of causal versus standard quantum theory could be made by observing entangled particles separated by $\approx 0.1$ light seconds.

We discuss a deterministic model of detector coupled to a two-level system (a qubit). The detector is a quasiclassical object whose dynamics is described by the kicked rotator Hamiltonian. We show that in the regime of quantum chaos the detector acts as a chaotic bath and induces decoherence of the qubit. We discuss the dephasing and relaxation rates and demonstrate that the main features of single-qubit decoherence due to a heat bath can be reproduced by our fully deterministic dynamical model. Moreover, we show that, for strong enough qubit-detector coupling, the dephasing rate is given by the rate of exponential instability of the detector’s dynamics, that is, by the Lyapunov exponent of classical motion. Finally, we discuss the measurement in the regimes of strong and weak qubit-detector coupling. For the case of strong coupling the detector performs a measurement of the up∕down state of the qubit. In the case of weak coupling, due to chaos, the dynamical evolution of the detector is strongly sensitive to the state of the qubit. However, in this case it is unclear how to extract a signal from any measurement with a coarse-graining in the phase space on a size much larger than the Planck cell.

We derive the optimal trade-off between the estimation fidelity and the fidelity of the state after the estimation for a single copy of an unknown pure state of a $d$-level system belonging to a specific subset of the set of all pure states. The set of states to be considered here is formed by all pure states of a $d$-level system produced by $d$-independent phase shifts of some reference state. We also propose a measurement scheme realizing such an optimal partial estimation of multiple phases in which the trade-off between the fidelities can be controlled by the state of the ancilla.

The impulse approximation is used to calculate cross sections for fragmentation of $\mathrm{Ps}\left(1s\right)$ in collision with He, Ne, Ar, Kr, and Xe. Triple, double, single, and total cross sections are evaluated. Reasonably good agreement is found with the measurements of Armitage et al. [Phys. Rev. Lett. 89, 173402 (2002)] on $\mathrm{Ps}\left(1s\right)+\mathrm{He}\left(1{}^{1}S\right)$ scattering. These absolute measurements comprise the total Ps ionization cross section and the cross section differential with respect to the longitudinal energy of the ejected positron. Characteristics of free electron and free positron scattering are explored in the double and triple differential cross sections for $\mathrm{Ps}\left(1s\right)+\mathrm{Xe}$ scattering.

Charge-state-correlated total cross sections for projectile-electron loss, capture, and target ionization in ${\mathrm{C}}^{3+}\text{−}\mathrm{Ne}$ collisions have been measured and calculated at absolute energies in the few MeV regime. The calculations are based on a recently proposed coupled mean-field approach which combines a set of nonperturbative single-particle calculations for the initial projectile electrons with another one for the initial target electrons. The basis generator method has been used to solve these equations. Very good overall agreement between experimental and theoretical data is found, which provides further evidence for the applicability of the approach to rather complex many-electron collision systems. One notable exception is the cross section for elastic projectile-electron loss associated with no change of the target charge state. In this case, the theoretical and experimental results differ qualitatively.

We propose two experimental schemes to generate the cluster states in the context of microwave cavity quantum electrodynamics (QED). In the first scheme to prepare many cavities into the cluster states, we encode the vacuum state and one-photon state of the microwave cavity as the logic zero and one of the qubits. The second scheme is to prepare many atoms into the cluster states, where qubits are represented by the states of Rydberg atoms. Both schemes require the resonant atom-cavity interaction so that the quantum dynamics operates at a high speed, which is important in view of decoherence.

We analyze the interaction of a two-level superconducting quantum interference device (SQUID) qubit with a classical microwave pulse. The rf-SQUID is characterized by an asymmetric double well potential that gives rise to diagonal matrix elements. The diagonal matrix elements are accounted for in the interaction of the microwave pulse with the SQUID. We present analytical results that correctly describe the system’s dynamics.

We study entanglement in mixed bipartite quantum states which are invariant under simultaneous SU(2) transformations in both subsystems. Previous results on the behavior of such states under partial transposition are substantially extended. The spectrum of the partial transpose of a given SU(2)-invariant density matrix $\rho$ is entirely determined by the diagonal elements of $\rho$ in a basis of tensor-product states of both spins with respect to a common quantization axis. We construct a set of operators which act as entanglement witnesses on SU(2)-invariant states. A sufficient criterion for $\rho$ having a negative partial transpose is derived in terms of a simple spin correlator. The same condition is a necessary criterion for the partial transpose to have the maximum number of negative eigenvalues. Moreover, we derive a series of sum rules which uniquely determine the eigenvalues of the partial transpose in terms of a system of linear equations. Finally we compare our findings with other entanglement criteria including the reduction criterion, the majorization criterion, and the recently proposed local uncertainty relations.

It is shown that the decoherence-free subspace (DFS) of practical multiphoton polarization cannot avoid exponential decoherence even in the same extra environment if the photons are frequency anticorrelated. The reason lies in the fact that the condition of collective decoherence is not satisfied in this case. As an example, the evolution of a biphoton decoherence-free state is given. A possible solution for a feasible multiphoton DFS state is also given.

We analyze and further develop a method to represent the quantum state of a system of $n$ qubits in a phase-space grid of $N\times N$ points (where $N=2^n$). The method, which was recently proposed by Wootters and co-workers (Gibbons et al., Phys. Rev. A 70, 062101 (2004).), is based on the use of the elements of the finite field $\mathrm{GF}\left(2^n\right)$ to label the phase-space axes. We present a self-contained overview of the method, we give insights into some of its features, and we apply it to investigate problems which are of interest for quantum-information theory: We analyze the phase-space representation of stabilizer states and quantum error-correction codes and present a phase-space solution to the so-called mean king problem.

In this work we present the main results concerning an accurate line shape analysis on acetylene lines in the spectral region around $3\mu \mathrm{m}$. We clearly demonstrate the influence of Dicke narrowing as well as correlations between velocity-changing and dephasing collisions and the speed-dependent effects on Xe-broadened lines. In the low pressure regime the correlations are the main effect responsible for the line asymmetry while for high pressure (several hundred Torr) the speed-dependent effects predominate. This work constitutes the experimental evidence of the influence of such kind of effects on the line profiles of a nonpolar molecule, except ${\mathrm{H}}_2$. The influence of the choice of the theoretical profile describing the line shape on the fitted line parameters is also discussed and the Xe-broadening and shift parameters were found for six ${\mathrm{C}}_2{\mathrm{H}}_2$ lines.

It is shown that third order (second order in the interelectron interaction and first order in the interaction with the electromagnetic field) contributions to transition amplitudes in heliumlike ions with one negative-energy intermediate state (NES) vanish in QED but not in relativistic many-body perturbation theory (RMBPT) in which the summation over NES states replaces one summation over positive-energy states with the same sign. An all-order RMBPT procedure based on QED for evaluating transition amplitudes in heliumlike ions that takes this result into account is formulated and used to evaluate $1s2s{}^{3}S_1\to 1s3s{}^{3}S_1$ $M1$ transitions for heliumlike ions with $Z=2–10$.