Several proposed techniques for distinguishing between optical coherent states are analyzed under a physically realistic model of photodetection. Quantum error probabilities are derived for the Kennedy receiver, the Dolinar receiver, and the unitary rotation scheme proposed by Sasaki and Hirota for subunity detector efficiency. Monte Carlo simulations are performed to assess the effects of detector dark counts, dead time, signal processing bandwidth, and phase noise in the communication channel. The feedback strategy employed by the Dolinar receiver is found to achieve the Helstrom bound for subunity detection efficiency and to provide robustness to these other detector imperfections making it more attractive for laboratory implementation than previously believed.

The dynamics of the one-tangle and the concurrence is analyzed in the Lipkin-Meshkov-Glick model which describes many physical systems such as the two-mode Bose-Einstein condensates. We consider two different initial states which are physically relevant and show that their entanglement dynamics are very different. A semiclassical analysis is used to compute the one-tangle which measures the entanglement of one spin with all the others, whereas the frozen-spin approximation allows us to compute the concurrence using its mapping onto the spin squeezing parameter.

We analyze the resilience under photon loss of the bipartite entanglement present in multiphoton states produced by parametric down-conversion. The quantification of the entanglement is made possible by a symmetry of the states that persists even under polarization-independent losses. We examine the approach of the states to the set of positive partial transpose states as losses increase, and calculate the relative entropy of entanglement. We find that some bipartite distillable entanglement persists for arbitrarily high losses.

The existing formulations of electron-impact ionization of a hydrogenic target suffer from a number of formal problems including an ambiguous and phase-divergent definition of the ionization amplitude. An alternative formulation of the theory is given. An integral representation for the ionization amplitude which is free of ambiguity and divergence problems is derived and is shown to have four alternative, but equivalent, forms well suited for practical calculations. The extension to amplitudes of all possible scattering processes taking place in an arbitrary three-body system follows. A well-defined conventional post form of the breakup amplitude valid for arbitrary potentials including the long-range Coulomb interaction is given. Practical approaches are based on partial-wave expansions, so the formulation is also recast in terms of partial waves and partial-wave expansions of the asymptotic wave functions are presented. In particular, expansions of the asymptotic forms of the total scattering wave function, developed from both the initial and the final state, for electron-impact ionization of hydrogen are given. Finally, the utility of the present formulation is demonstrated on some well-known model problems.

We develop a dressed-atom picture of the bichromatic force in two standing waves using a Floquet approach. It is based on previous work, but the approach allows for an interpretation of the velocity range of the force. It is limited to two-level atoms and one dimension, and the Floquet frequency is the beat between the two bichromatic optical fields. The force is mediated by Landau-Zener transitions between the dressed states of the Floquet Hamiltonian. Related topics have been addressed before in the literature, but not applied to this particular case.

We study many-qubit generalizations of quantum noise channels that can be written as an incoherent sum of translations in phase space, for which the chord representation results specially useful. Physical descriptions in terms of the spectral properties of the superoperator and the action in phase space are provided. A very natural description of decoherence leading to a preferred basis is achieved with diffusion along a phase space line. The numerical advantages of using the chord representation are illustrated in the case of coarse-graining noise.

We show that the quantum Zeno effect can be used to suppress the failure events that would otherwise occur in a linear optics approach to quantum computing. From a practical viewpoint, that would allow the implementation of deterministic logic gates without the need for ancilla photons or high-efficiency detectors. We also show that the photons can behave as if they were fermions instead of bosons in the presence of a strong Zeno effect, which leads to an alternative paradigm for quantum computation.

We present the wave-packet analysis for two $S$-wave resonances in positron scattering by a helium ion whose existence was predicted by Bhatia and Drachman but has been controversial. The evolution of the wave packet is solved to exhibit temporary formation of the quasistationary state. For both the resonances, the position and width are determined through the resulting time delays in a consideration of a multichannel nature to agree with those by previous variational eigenenergy calculations. It is further found that the lower resonance dominantly forms from, and decays into, the $n=2$ states of the helium ion, while the higher one the $n=3$ states.

The exact initial state wave function of an interacting electron pair in a quantum dot under parabolic confinement and neutralization of the dot by the substrate after ejection of electrons is exploited to obtain the fivefold differential cross section $\left(X\right)$ of the $(e,3e)$ process on the dot. The reflections of the center-of-mass (c.m.) motion and relative motion on $X$ are decoupled if the incident and scattered electrons are energetic and the ejected electrons are slow. The results are studied in fixed mutual angle (with zero c.m. momentum $K$) and Bethe ridge modes which allow the “cleanest” analysis of the contribution of the relative motion. The Coulomb interaction between the emitted electrons is found to qualitatively change the angular distribution of $X$. In the mode in which the magnitude of $K$ is equal to the momentum transfer $q$, the angular distribution of $X$ with respect to ${\theta }_{Kq}={\cos }^{-1}(\widehat{K}\bullet \widehat{q})$ leads to a mapping of the initial c.m. wave function of the ejected pair. However, the c.m. motion is found to be best studied in the kinematics where the relative momentum $\vec{k}$ of the ejected pair is equal to $\vec{q}$.

We examine time ordering effects in strongly, suddenly perturbed two-state quantum systems (kicked qubits) by comparing results with time ordering to results without time ordering. Simple analytic expressions are given for state occupation amplitudes and probabilities for singly and multiply kicked qubits. We investigate the limit of no time ordering, which can differ in different representations.

We study a system of $A$ identical interacting bosons trapped by an external field by solving ab initio the many-body Schrödinger equation. A complete solution by using, for example, the traditional hyperspherical harmonics (HH) basis develops serious practical problems due to the large degeneracy of HH basis. Symmetrization of the wave function, calculation of the matrix elements, etc., become an immensely formidable task as $A$ increases. Instead of the HH basis, here we use a new basis, called “potential harmonics” (PH) basis, which is a subset of HH basis. We assume that the contribution to the orbital and grand orbital [in $3(A-1)$-dimensional space of the reduced motion] quantum numbers comes only from the interacting pair. This implies inclusion of two-body correlations only and disregard of all higher-body correlations. Such an assumption is ideally suited for the Bose-Einstein condensate (BEC), which is required, for experimental realization of BEC, to be extremely dilute. Hence three and higher-body collisions are almost totally absent. Unlike the $(3A-4)$ hyperspherical variables in HH basis, the PH basis involves only three active variables, corresponding to three quantum numbers—the orbital $l$, azimuthal $m$, and the grand orbital $2K+l$ quantum numbers for any arbitrary $A$. It drastically reduces the number of coupled equations and calculation of the potential matrix becomes tremendously simplified, as it involves integrals over only three variables for any $A$. One can easily incorporate realistic atom-atom interactions in a straightforward manner. We study the ground and excited state properties of the condensate for both attractive and repulsive interactions for various particle number. The ground state properties are compared with those calculated from the Gross-Pitaevskii equation. We notice that our many-body results converge towards the mean field results as the particle number increases.

Based on the conditional quantum dynamics of laser-ion interactions, we propose an efficient theoretical scheme to deterministically generate quantum pure states of a single trapped cold ion without performing the Lamb-Dicke approximation. An arbitrary quantum state can be created by sequentially using a series of classical laser pulses with selected frequencies, initial phases and durations. As special examples, we further show how to create or approximate several typical macroscopic quantum states, such as the phase state and the even/odd coherent states. Unlike previous schemes operating in the Lamb-Dicke regime, the present one does well for an arbitrary-strength coupling between the internal and external degrees of freedom of the ion. The experimental realizability of this approach is also discussed.

We experimentally demonstrate a crystalline ${\mathrm{CaF}}_2$ optical whispering gallery mode resonator characterized by the quality factor $Q>2\times {10}^{10}$ at $\lambda =1.319\mu \mathrm{m}$. We also report the demonstration of ultrahigh-$Q$ resonators of lithium niobate and lithium tantalate $\left(Q>2\times {10}^8\right)$, and sapphire $\left(Q>{10}^9\right)$. We discuss fundamental limits of the $Q$ factor, and application of such resonators for measurement of ultrasmall optical losses in various materials. We further analyze the observation of thermo-optical instability in whispering gallery modes of crystalline resonators.

We show the formal equivalence between the phase-space representations of transformations and quantum states. We study invariant quantum input-output transformations in phase space and in Hilbert space. We show that all invariant processes are linear transformations while the converse is not true. Some relevant examples of application of these ideas are examined.

The Gottesman-Knill theorem says that a stabilizer circuit—that is, a quantum circuit consisting solely of controlled-NOT (CNOT), Hadamard, and phase gates—can be simulated efficiently on a classical computer. This paper improves that theorem in several directions. First, by removing the need for Gaussian elimination, we make the simulation algorithm much faster at the cost of a factor of 2 increase in the number of bits needed to represent a state. We have implemented the improved algorithm in a freely available program called CHP (CNOT-Hadamard-phase), which can handle thousands of qubits easily. Second, we show that the problem of simulating stabilizer circuits is complete for the classical complexity class $\oplus \mathsf{L}$, which means that stabilizer circuits are probably not even universal for classical computation. Third, we give efficient algorithms for computing the inner product between two stabilizer states, putting any $n$-qubit stabilizer circuit into a “canonical form” that requires at most $O(n^2∕\log n)$ gates, and other useful tasks. Fourth, we extend our simulation algorithm to circuits acting on mixed states, circuits containing a limited number of nonstabilizer gates, and circuits acting on general tensor-product initial states but containing only a limited number of measurements.

We study the structure of vacuum entanglement for two complimentary segments of a linear harmonic chain, applying the modewise decomposition of entangled Gaussian states discussed by Boteno and Reznik [Phys. Rev. A 67, 052311 (2003)]. We find that the resulting entangled mode-shape hierarchy shows a distinctive layered structure with well-defined relations between the depth of the modes, their characteristic wavelength, and their entanglement contribution. We rederive in the strong coupling (diverging correlation length) regime, the logarithmic dependence of entanglement on the segment size predicted by conformal field theory for the boson universality class and discuss its relation with the mode structure. We conjecture that the persistence of vacuum entanglement between arbitrarily separated finite-size regions is connected with the localization of the highest-frequency innermost modes.

We analyze a quantum network, constructed with ballistic electron waveguides, which can add one-bit binary numbers. We consider two different adder networks, one constructed with Hadamard gates and the other constructed with $\sqrt{\mathrm{NOT}}$ gates. Reflection of electron probability at the gates causes a loss in fidelity of the overall calculation. A fidelity requirement for the implementation of individual rotation gates corresponding to a probability $p>1∕2$ of completing the addition successfully is found.

A quantum-information analysis of how the size and dimensionality of the quantum alphabet affect the critical error rate of the quantum-key-distribution (QKD) protocols is given on an example of two QKD protocols—the six-state and ∞-state (i.e., a protocol with continuous alphabet) ones. In the case of a two-dimensional Hilbert space, it is shown that, under certain assumptions, increasing the number of letters in the quantum alphabet up to infinity slightly increases the critical error rate. Increasing additionally the dimensionality of the Hilbert space leads to a further increase in the critical error rate.

This paper presents the first dissociative recombination (DR) measurement of electrons with rotationally and vibrationally cold $\mathrm{H}_3{}^{+}$ ions. A dc discharge pinhole supersonic jet source was developed and characterized using infrared cavity ringdown spectroscopy before installation on the CRYRING ion storage ring for the DR measurements. Rotational state distributions $\left(T_{\mathrm{rot}}\sim 30\mathrm{K}\right)$ produced using the source were comparable to those in the diffuse interstellar medium. Our measurement of the electron energy dependence of the DR cross section showed resonances not clearly seen in experiments using rotationally hot ions, and allowed calculation of the thermal DR rate coefficient for ions at interstellar temperatures, ${\alpha }_{\mathrm{DR}}\left(23\mathrm{K}\right)=2.6\times {10}^{-7}{\mathrm{cm}}^3{\mathrm{s}}^{-1}$. This value is in general agreement with recent theoretical predictions by Kokoouline and Greene [Phys. Rev. A 68, 012703 (2003)]. The branching fractions of the two breakup channels, $\mathrm{H}+\mathrm{H}+\mathrm{H}$ and $\mathrm{H}+{\mathrm{H}}_2$, have also been measured for rotationally and vibrationally cold $\mathrm{H}_3{}^{+}$.

Two-photon excitation of a quantum ladder system by an ultrashort chirped pulse leads to interferences in the excited-state population, between direct and sequential paths. Experimental results have been obtained in atomic sodium vapor. The presence of several intermediate and final states leads to new phenomena. The interplay between the two sequential paths leads to strongly contrasted oscillations and a large enhancement of the transition probability for precise values of the chirp. A cubic spectral phase modifies significantly the behavior of the quantum interferences and can be used to enhance the two-photon absorption rate.