It is known that quantum correlations exhibited by a maximally entangled qubit pair can be simulated with the help of shared randomness, supplemented with additional resources, such as communication, postselection or nonlocal boxes. For instance, in the case of projective measurements, it is possible to solve this problem with protocols using one bit of communication or making one use of a nonlocal box. We show that this problem reduces to a distributed sampling problem. We give a new method to obtain samples from a biased distribution, starting with shared random variables following a uniform distribution, and use it to build distributed sampling protocols. This approach allows us to derive, in a simpler and unified way, many existing protocols for projective measurements, and extend them to positive operator value measurements. Moreover, this approach naturally leads to a local hidden variable model for Werner states.

We give a criterion to differentiate between dissipative and diffusive quantum operations. It is based on the classical idea that dissipative processes contract volumes in phase space. We define a quantity that can be regarded as “quantum phase space contraction rate” and which is related to a fundamental property of quantum channels: nonunitality. We relate it to other properties of the channel and also show a simple example of dissipative noise composed with a chaotic map. The emergence of attractor-like structures is displayed.

A Mølmer-Sørensen entangling gate is realized for pairs of trapped ${}^{111}\mathrm{Cd}^{+}$ ions using magnetic-field insensitive “clock” states and an implementation offering reduced sensitivity to optical phase drifts. The gate is used to generate the complete set of four entangled states, which are reconstructed and evaluated with quantum-state tomography. An average target-state fidelity of 0.79 is achieved, limited by available laser power and technical noise. The tomographic reconstruction of entangled states demonstrates universal quantum control of two ion qubits, which through multiplexing can provide a route to scalable architectures for trapped-ion quantum computing.

We present an experimental implementation of the coined discrete-time quantum walk on a square using a three-qubit liquid-state nuclear-magnetic-resonance (NMR) quantum-information processor (QIP). Contrary to its classical counterpart, we observe complete interference after certain steps and a periodicity in the evolution. Complete state tomography has been performed for each of the eight steps, making a full period. The results have extremely high fidelity with the expected states and show clearly the effects of quantum interference in the walk. We also show and discuss the importance of choosing a molecule with a natural Hamiltonian well suited to a NMR QIP by implementing the same algorithm on a second molecule. Finally, we show experimentally that decoherence after each step makes the statistics of the quantum walk tend to that of the classical random walk.

Excitation and charge transfer cross sections for proton collisions with $2s$ excited state hydrogen are calculated using time-dependent lattice, atomic-orbital close-coupling with pseudostates, and classical trajectory Monte Carlo methods. The time-dependent lattice calculation yields $\Delta n=1$ excitation and $\Delta n=0$ and $\Delta n=1$ charge transfer cross sections at 5, 10, and $15\mathrm{keV}$ incident energy. The atomic-orbital close-coupling with pseudostates calculation yields excitation cross sections to $n=3–5$ and charge transfer cross sections to $n=1–5$ at a number of incident energies between 1 and $100\mathrm{keV}$. The time-dependent lattice and close-coupling pseudostates calculations are found to be in good agreement with previous standard close-coupling results. The close-coupling with pseudostates calculations are used to benchmark the classical trajectory Monte Carlo calculations, which are widely used in astrophysical and laboratory plasma modelling.

The double $1s$ ionization of Si induced in collisions with protons was studied by measuring the $K$ x-ray emission of a solid Si target ionized by the impact of 1–3-MeV protons. In order to resolve the hypersatellite contributions corresponding to the radiative decay of the double $1s$ vacancy state, a high-resolution crystal spectrometer was employed yielding sub-eV energy resolution. From the intensity of the measured hypersatellite lines double $1s$ ionization cross sections for the studied collisions were determined. Experimental values were compared with the theoretical ones obtained within the independent electron framework employing single electron ionization probabilities calculated with the semiclassical approach. This comparison suggests a sequential two step model for the double $1s$ ionization which was additionally confirmed by four body classical trajectory Monte Carlo calculations.

The Mott insulating phase of a one-dimensional bosonic gas trapped in an optical lattice is described by a Bose-Hubbard model. A continuous unitary transformation is used to map this model onto an effective model conserving the number of elementary excitations. We obtain quantitative results for the kinetics and for the spectral weights of the low-energy excitations for a broad range of parameters in the insulating phase. By these results, recent Bragg spectroscopy experiments are explained. Evidence for a significant temperature of the order of the microscopic energy scales is found.

We present the classical and quantum theory of time refraction in a generic nonstationary medium. The classical approach leads to expressions for the temporal refraction coefficient, and the temporal Fresnel laws are given. The quantum formulation leads to the derivation of instantaneous Bogoliubov transformations and the evaluation of the number of photon pairs created from vacuum by the temporal changes in the medium. The influence of boundary conditions, the connection of this model with the dynamical Casimir effect, and radiation from superluminal nonaccelerated optical boundaries is also discussed.

We propose a machine for entangling multiple qubits and implementing cloning and anti-cloning. The operation speed increases with the number of qubits without a limitation and thus the operation becomes more and more robust against decoherence with the increase of the number of qubits. This is contrary to usual entangling machines and quantum information processors whose performance would deteriorate with the increase of the number of qubits due to decoherence. We illustrate the idea in the ion trap system, however it can also be realized in other systems, opening a new perspective for building a scalable machine for entanglement generation and quantum information processing.

Even though the time reversal is unphysical (it corresponds to the complex conjugation of the density matrix), for some restricted set of states it can be achieved unitarily, typically when there is a common dephasing in a $n$-level system. However, in the presence of multiple phases (i.e., a different dephasing for each element of an orthogonal basis occurs) the time reversal is no longer physically possible. In this paper we derive the channel which optimally approaches in fidelity the time reversal of multiphase equatorial states in arbitrary (finite) dimension. We show that, in contrast to the customary case of the universal-NOT on qubits (or the universal conjugation in arbitrary dimension), the optimal phase covariant time reversal for equatorial states is a nonclassical channel, which cannot be achieved via a measurement-and-preparation procedure. Unitary realizations of the optimal time reversal channel are given with minimal ancillary dimension, exploiting the simplex structure of the optimal maps.

The maximum rates for reliably transmitting classical information over bosonic multiple-access channels (MACs) are derived when the transmitters are restricted to coherent-state encodings. Inner and outer bounds for the ultimate capacity region of the bosonic MAC are also presented. It is shown that the sum-rate upper bound is achievable with a coherent-state encoding and that the entire region is asymptotically achievable in the limit of large mean input photon numbers.

Absolute measurements are presented for the excitation of the ${\nu }_3$ vibrational mode in ${\mathrm{CF}}_4$ by positron and electron impact from 0.1 to 2 eV. To minimize systematic differences, these measurements were made using the same trap-based electron or positron beam, associated experimental apparatus, and procedures. Unlike other vibrational excitation cross sections studied to date, the near-threshold cross section for the ${\nu }_3$ vibrational mode in ${\mathrm{CF}}_4$ is similar, both in magnitude and shape, for positrons and electrons. Comparison of the cross sections with an analytic Born dipole model yields good agreement, while comparison of this model with other measured positron-impact vibrational cross sections indicates that the contribution of this long-range dipole coupling varies widely. The maximum value of the cross section in ${\mathrm{CF}}_4$ is the largest of any positron-impact vibrational excitation cross section measured to date. This provides a likely explanation of the observation that ${\mathrm{CF}}_4$ is very effective when used as a buffer gas to cool positron gases and plasmas.

It is shown by Gea-Banacloche [Phys. Rev Lett. 59, 543 (1987)] that the Laser Phase diffusion rate may be reduced by as much as one-half when laser is coupled out through a partially transmitting mirror to “squeezed vacuum” as opposed to ordinary vacuum. This happens for a particular choice of the phase of the squeezed field. However, phase stability is not achieved for this choice of phase. In this paper, this analysis is extended by including a separate squeezed vacuum reservoir which couples the spontaneous decay between the lasing levels. The results show that, it is possible to obtain the phase stability as well as phase noise quenching in this system.

We show that the phenomenon of superadditivity of distillable entanglement observed in multipartite quantum systems results from the consideration of states created during the execution of the standard end-to-end quantum teleportation protocol [and a few additional local operations and classical communication (LOCC) steps] on a linear chain of singlets. Some of these intermediate states are tensor products of bound entangled (BE) states, and hence, by construction possess distillable entanglement, which can be unlocked by simply completing the rest of the LOCC operations required by the underlying teleportation protocol. We use this systematic approach to construct both new and known examples of superactivation of bound entanglement, and examples of activation of BE states using other BE states. A surprising outcome is the construction of noiseless quantum relay channels with no distillable entanglement between any two parties, except for that between the two end nodes.

In this paper, based on the recent experiment by Roos et al. [Science 304, 1478 (2004)], a theoretical scheme is proposed to create the multipartite entanglement of many trapped ions and implement a two-qubit quantum phase gate between two ions in ion trap. In the scheme, the ion is illuminated by a single laser tuned to the first lower vibrational sideband. We also show that the scheme can be used to directly transfer information between two ions. The scheme has the advantage that it does not use the vibrational mode as the data bus and only requires a single resonant interaction. Thus the scheme is very simple and the quantum dynamics operation can be realized at a high speed. In view of the decoherence mechanism, the simplification for the entangled state preparation and experimental implementation of quantum logic operation may become crucial.

For a system of $N$ qubits, living in a Hilbert space of dimension $d=2^N$, it is known that there exists $d+1$ mutually unbiased bases. Different construction algorithms exist, and it is remarkable that different methods lead to sets of bases with different properties as far as separability is concerned. Here we derive four sets of nine bases for three qubits, and show how they are unitarily related. We also briefly discuss the four-qubit case, give the entanglement structure of 16 sets of bases, and show some of them and their interrelations, as examples. The extension of the method to the general case of $N$ qubits is outlined.

We extend the projected Gross-Pitaevskii equation formalism of Davis et al. [Phys. Rev. Lett. 87, 160402 (2001)] to the experimentally relevant case of thermal Bose gases in harmonic potentials and outline a robust and accurate numerical scheme that can efficiently simulate this system. We apply this method to investigate the equilibrium properties of the harmonically trapped three-dimensional projected Gross-Pitaevskii equation at finite temperature and consider the dependence of condensate fraction, position, and momentum distributions and density fluctuations on temperature. We apply the scheme to simulate an evaporative cooling process in which the preferential removal of high-energy particles leads to the growth of a Bose-Einstein condensate. We show that a condensate fraction can be inferred during the dynamics even in this nonequilibrium situation.

It is experimentally demonstrated that quantum coherences can be efficiently transferred using adiabatic energy-level crossing. In a cluster of six dipolar-coupled proton spins of benzene, oriented by a liquid-crystalline matrix, a single-quantum coherence between one pair of states has been adiabatically transferred to another pair of states, and the superposition survived even after ten successive energy-level crossings.