We derive a semiclassical approximation to the Husimi functions of stationary states of spin systems. We rederive the Bohr-Sommerfeld quantization for spin by locating the poles of the corresponding local Green function. The residues correspond to the Husimi functions, which are seen to agree very well with exact calculations.

A different type of complementarity relation is found between locally accessible information and final average entanglement for a given ensemble. It is also shown that in some well-known distillation protocols, this complementary relation is optimally satisfied. We discuss the interesting trade-off between locally accessible information and distillable entanglement for some states.

A simple model describing depolarization channels with zero-bandwidth environment is presented and exactly solved. The environment is modeled by Lorentzian, telegraphic, and Gaussian zero-bandwidth noises. Such channels can go beyond the standard Markov dynamics and therefore can illustrate the influence of memory effects of the noisy communication channel on the transmitted information. To quantify the disturbance of quantum states the entanglement fidelity between arbitrary input and output states is investigated.

A multimode channel can be utilized to substantially increase the capacity of quantum continuous-variable key distribution. Beyond losses in the channel, an uncontrollable coupling between the modes of the channel typically degrades the capacity of multimode channels. For the key distribution protocol with simultaneous measurement of both complementary quadratures we propose a feasible method to eliminate any undesirable mode coupling by only the receiver’s appropriate measurement and data manipulation. It can be used to substantially increase the capacity of the channel, which has an important application in practical continuous-variable quantum cryptography.

It is shown that generic $N$-party pure quantum states (with equidimensional subsystems) are uniquely determined by their reduced states of just over half the parties; in other words, all the information in almost all $N$-party pure states is in the set of reduced states of just over half the parties. For $N$ even, the reduced states in fewer than $N∕2$ parties are shown to be an insufficient description of almost all states (similar results hold when $N$ is odd). It is noted that real algebraic geometry is a natural framework for any analysis of parts of quantum states: two simple polynomials, a quadratic and a cubic, contain all of their structure. Algorithmic techniques are described which can provide conditions for sets of reduced states to belong to pure or mixed states.

We describe a mechanism for realizing a controlled phase gate for solid-state charge qubits. By augmenting the positionally defined qubit with an auxiliary state, and changing the charge distribution in the three-dot system, we are able to effectively switch the Coulombic interaction, effecting an entangling gate. We consider two architectures, and numerically investigate their robustness to gate noise.

We report calculations of the stopping cross sections of hydrogen atoms for protons and antiprotons at low to intermediate energies and take the difference explicitly to determine the Barkas correction for this system. The calculational method used is the electron-nuclear dynamics formalism which involves the coupled direct dynamics of all nuclei and electrons and thus includes all terms in the Born expansion. The formalism is a nonperturbational, ab initio approach to solve the time-dependent Schrödinger equation, applicable to all the projectile energies under consideration. This is in contrast to the use of different velocity-dependent models for different energy ranges used in other approaches. We find that at high projectile energies, target excitation and ionization are responsible for the projectile energy loss. However, at low projectile energies, the repulsion of the negatively charged projectile and the target electronic structure and its coupling to the target nuclei produce a billiard ball effect which combined with the large ionization and excitation induced by the antiproton is responsible for the large nuclear stopping power, contrary to near-adiabatic dynamics predicted by other models.

The scaled coordinate approach is applied to the problem of $\mathrm{H}{\mathrm{D}}^{+}$ photodissociation in a short, intense, infrared laser pulse. Two- and three-dimensional models for the molecule aligned in the field of a linearly polarized laser are studied. Scaling allows substantial improvements in the numerical accuracy and provides a simple way to calculate the fragments’ energy spectra.

Coulomb explosion imaging has been used to explore anisotropies in the fragment angular distribution associated with the symmetric six-electron Coulomb explosion channel of $\mathrm{C}{\mathrm{O}}_2$ and $\mathrm{N}{\mathrm{O}}_2$ induced by $100\mathrm{fs}$, ${10}^{15}\mathrm{W}∕{\mathrm{cm}}^2$ radiation at $800\mathrm{nm}$ and leading to doubly charged atomic ions. Specific precursor molecular geometries (bond angles prior to explosion) and orientations of the molecular axis (the line connecting the two outer atoms in the system) relative to the polarization axis were isolated for analysis by exploiting the correlation among the atomic ions ejected simultaneously. The effective orientation of the precursor molecular axis is preferentially along the polarization axis for both $\mathrm{C}{\mathrm{O}}_2$ and $\mathrm{N}{\mathrm{O}}_2$ with respective distributions and widths of ${\cos }^{39}\theta (\Delta \theta \simeq 22°)$ and ${\cos }^{25}\theta (\Delta \theta \simeq 27°)$, which are substantially narrower than that of ${\mathrm{H}}_2$, ${\cos }^{19}\theta (\Delta \theta \simeq 31°)$. The widths and distributions are found to be nearly independent of bond angle over a wide range of bond angles (35° and 55° for $\mathrm{C}{\mathrm{O}}_2$ and $\mathrm{N}{\mathrm{O}}_2$, respectively). The narrowing of the width of the distribution from ${\mathrm{H}}_2$ to $\mathrm{C}{\mathrm{O}}_2$, combined with the independence of bond angle are consistent with (1) an increasing moment of inertia, (2) an increasing final charge state, and (3) an increasing precursor molecular ion ionization stage.

We present a probabilistic scheme for generating and purifying maximally entangled states of two atoms inside an optical cavity via no-photon detection at the cavity output, where ideal detectors are not required. The intermediate mixed states can be continuously purified so as to violate Bell inequalities in a parametrized manner. The scheme relies on an additional strong-driving field that realizes, atypically, simultaneous Jaynes-Cummings and anti-Jaynes-Cummings interactions.

Experiments on nonclassical optical fields have recently been performed. One of the main properties reported is the antibunching effect of photoelectrons, a property that cannot be explained in the framework of the classical theory of optical fields. By carefully studying the random point process of the detection of the optical field, we show that bunching and antibunching effects can be fully explained by a concidence function. In the classical theory, this function is a correlation function which introduces necessarily a bunching effect. But this coincidence function has no reason to be in any case a correlation function. Therefore antibunching effects can simply be derived from the properties of the coincidence function. After having given a precise definition of this coincidence function, some of its properties are discussed and especially its relationship with bunching and antibunching effects. Similarly, its relationship with statistical properties of lifetimes and intervals between points of the process is established. Various examples are presented and analyzed. Several calculations and computer simulations highlight the theoretical results.

We investigate multiparticle entanglement purification schemes which allow one to purify all two colorable graph states, a class of states which includes, e.g., cluster states, Greenberger-Horne-Zeilinger states, and code words of various error correction codes. The schemes include both recurrence protocols and hashing protocols. We analyze these schemes under realistic conditions and observe for a generic error model that the threshold value for imperfect local operations depends on the structure of the corresponding interaction graph, but is otherwise independent of the number of parties. The qualitative behavior can be understood from an analytically solvable model which deals only with a restricted class of errors. We compare direct multiparticle entanglement purification protocols with schemes based on bipartite entanglement purification and show that the direct multiparticle entanglement purification is more efficient and the achievable fidelity of the purified states is larger. We also show that the purification protocol allows one to produce private entanglement, an important aspect when using the produced entangled states for secure applications. Finally we discuss an experimental realization of a multiparty purification protocol in optical lattices which is issued to improve the fidelity of cluster states created in such systems.

We address the question of the multiplicativity of the maximal $p$-norm output purities of bosonic Gaussian channels under Gaussian inputs. We focus on general Gaussian channels resulting from the reduction of unitary dynamics in larger Hilbert spaces. It is shown that the maximal output purity of tensor products of single-mode channels under Gaussian inputs is multiplicative for any $p∊(1,\infty )$ for products of arbitrary identical channels as well as for a large class of products of different channels. In the case of $p=2$, multiplicativity is shown to be true for arbitrary products of generic channels acting on any number of modes.

We consider weakly bound diatomic molecules (dimers) formed in a two-component atomic Fermi gas with a large positive scattering length for the interspecies interaction. We develop a theoretical approach for calculating atom-dimer and dimer-dimer elastic scattering and for analyzing the inelastic collisional relaxation of the molecules into deep bound states. This approach is based on the single-channel zero-range approximation, and we find that it is applicable in the vicinity of a wide two-body Feshbach resonance. Our results draw prospects for various interesting manipulations of weakly bound dimers of fermionic atoms.

The electronic structures of the molecule ${\mathrm{C}}_{50}{\mathrm{Cl}}_{10}$ are studied in the framework of density functional theory (DFT) with the Perdew-Burke-Ernzerhof (PBE) functional. The static polarizability $\alpha$ and second-order hyperpolarizability $\gamma$ are calculated by the use of a finite field approach. Both the average static polarizability $(⟨\alpha ⟩=92.9{\mathrm{\AA }}^3)$ and the second hyperpolarizability $(⟨\gamma ⟩=83.5\times {10}^{-36}\mathrm{esu})$ are larger than those of ${\mathrm{C}}_{60}$. At the same time, the diagonal components of $\alpha$, especially the $\gamma$ in the $xy$ plane, which contains the Cl atoms, are much larger than those in the $z$ direction. The reason is mainly from the distribution of $\pi$ electrons of the HOMO in the planes perpendicular to the $z$ axis. We predict that ${\mathrm{C}}_{50}{\mathrm{Cl}}_{10}$ and its derivatives should be promising nonlinear optical materials.

We calculate the linear chirp rates of high-order harmonics in argon, generated by intense, $810\mathrm{nm}$ laser pulses, and explore the dependence of the chirp rate on harmonic order, driving laser intensity, and pulse duration. By using a time-frequency representation of the harmonic fields we can identify several different linear chirp contributions to the plateau harmonics. Our results, which are based on numerical integration of the time-dependent Schrödinger equation, are in good agreement with the adiabatic predictions of the strong field approximation for the chirp rates. Extending the theoretical analysis in the recent paper by Mauritsson et al. [Phys. Rev. A 70, 021801(R) (2004)], we also manipulate the chirp rates of the harmonics by adding a chirp to the driving pulse. We show that the chirp rate for harmonic $q$ is given by the sum of the intrinsic chirp rate, which is determined by the new duration and peak intensity of the chirped driving pulse, and $q$ times the external chirp rate.

In a uniform ring-shaped one-dimensional superfluid, quantum fluctuations that unwind the order parameter need to transfer momentum to quasiparticles (phonons). We present a detailed calculation of the leading exponential factor governing the rate of such phonon-assisted tunneling in a weakly coupled Bose gas at a low temperature $T$. We also estimate the preexponent. We find that for small superfluid velocities the $T$ dependence of the rate is given mainly by $\exp (-c_{s}P∕2T)$, where $P$ is the momentum transfer and $c_s$ is the phonon speed. At low $T$, this represents a strong suppression of the rate compared to the nonuniform case. As a part of our calculation, we identify a complex instanton whose analytical continuation to suitable real-time segments is real and describes formation and decay of coherent quasiparticle states with nonzero total momenta.

We demonstrate the onset of strong on-site localization in a many-particle system, with effective localization length smaller than the intersite distance. The localization is obtained by constructing a bounded one-parameter sequence of on-site energies that eliminates resonant hopping between both nearest and remote sites. This sequence leads to quasiexponential decay of the single-particle transition amplitude. It also leads to on-site localization of stationary many-particle states in a finite-length chain. For an infinite many-particle system, we study the time during which all states remain on-site localized. We show that, for any number of particles, this time scales as a high power of the ratio of the bandwidth of on-site energies to the hopping integral. The proposed energy sequence is robust with respect to small errors. The formulation applies to fermions as well as perpetually coupled qubits. The results show viability of quantum computing with time-independent qubit coupling.

We extend the definition of concurrence into a family of entanglement monotones, which we call concurrence monotones. We discuss their properties and advantages as computational manageable measures of entanglement, and show that for pure bipartite states all measures of entanglement can be written as functions of the concurrence monotones. We then show that the concurrence monotones provide bounds on quantum information tasks. As an example, we discuss their applications to remote entanglement distributions (RED) such as entanglement swapping and remote preparation of bipartite entangled states (RPBES). We prove a powerful theorem which states what kind of (possibly mixed) bipartite states or distributions of bipartite states cannot be remotely prepared. The theorem establishes an upper bound on the amount of $G$-concurrence (one member in the concurrence family) that can be created between two single-qudit nodes of quantum networks by means of tripartite RED. For pure bipartite states the bound on the $G$-concurrence can always be saturated by RPBES.

We present a time-dependent non-Hermitian Floquet approach for the precision three-dimensional nonperturbative calculations of high-order harmonic generation (HHG) rates of the hydrogen molecular ions subject to intense laser fields. The procedure involves an extension of the complex-scaling generalized pseudospectral method for nonuniform spatial discretization of the Hamiltonian and non-Hermitian time propagation of the time-evolution operator. The approach is designed for effective and high-precision nonperturbative treatment of high-order multiphoton processes in very intense and/or low-frequency laser fields, which are generally more difficult to treat using the conventional time-independent non-Hermitian Floquet matrix techniques. The method is applied to the multiphoton ionization (MPI) and HHG calculations of $\mathrm{H}_2{}^{+}$ for the wavelength $532\mathrm{nm}$ at the equilibrium internuclear separation $(R=2.0\mathrm{a.u.})$ and several laser intensities, as well as at the laser intensity $5\times {10}^{13}\mathrm{W}∕{\mathrm{cm}}^2$ and various internuclear distances in the range between 3.0 and $17.5\mathrm{a.u.}$ We found that both the MPI and HHG rates are strongly dependent on $R$. Further, at some internuclear separations $R$, the HHG productions are strongly enhanced and this phenomenon can be attributed to the resonantly enhanced MPI at these $R$. Finally, the enhancement of higher harmonics is found to take place mainly at larger $R$. Detailed study of the correlation between the behavior of MPI and HHG phenomena is presented.