Remote information concentration (RIC) in $d$-level systems (qudits) is studied. It is shown that the quantum information initially distributed in three spatially separated qudits can be remotely and deterministically concentrated to a single qudit via an entangled channel without performing any global operations. The entangled channel can be different types of genuine multipartite pure entangled states which are inequivalent under local operations and classical communication. The entangled channel can also be a mixed entangled state, even a bound entangled state which has a similar form to the Smolin state, but has different features from the Smolin state. A common feature of all these pure and mixed entangled states is found; i.e., they have $d^2$ common commuting stabilizers. The differences of qudit-RIC and qubit-RIC ($d=2$) are also analyzed.

Operator-sum or Kraus representations for single-mode bosonic Gaussian channels are developed, and several of their consequences explored. The fact that the two-mode metaplectic operators acting as unitary purification of these channels do not, in their canonical form, mix the position and momentum variables is exploited to present a procedure which applies uniformly to all families in the Holevo classification. In this procedure the Kraus operators of every quantum-limited Gaussian channel can be simply read off from the matrix elements of a corresponding metaplectic operator. Kraus operators are employed to bring out, in the Fock basis, the manner in which the antilinear, unphysical matrix transposition map when accompanied by injection of a threshold classical noise becomes a physical channel, denoted $\mathcal{D}\left(\kappa \right)$ in the Holevo classification. The matrix transposition channels $\mathcal{D}\left(\kappa \right)$, $\mathcal{D}\left({\kappa }^{-1}\right)$ turn out to be a dual pair in the sense that their Kraus operators are related by the adjoint operation. The amplifier channel with amplification factor $\kappa$ and the beam-splitter channel with attenuation factor ${\kappa }^{-1}$ turn out to be mutually dual in the same sense. The action of the quantum-limited attenuator and amplifier channels as simply scaling maps on suitable quasiprobabilities in phase space is examined in the Kraus picture. Consideration of cumulants is used to examine the issue of fixed points. The semigroup property of the amplifier and attenuator families leads in both cases to a Zeno-like effect arising as a consequence of interrupted evolution. In the cases of entanglement-breaking channels a description in terms of rank 1 Kraus operators is shown to emerge quite simply. In contradistinction, it is shown that there is not even one finite rank operator in the entire linear span of Kraus operators of the quantum-limited amplifier or attenuator families, an assertion far stronger than the statement that these are not entanglement breaking channels. A characterization of extremality in terms of Kraus operators, originally due to Choi, is employed to show that all quantum-limited Gaussian channels are extremal. The fact that almost every noisy Gaussian channel can be realized as a product of a pair of quantum-limited channels is used to construct a discrete set of linearly independent Kraus operators for these noisy Gaussian channels, including the classical noise channel, and these Kraus operators have a particularly simple structure.

Despite early experimental tests of the Deutsch-Jozsa (DJ) algorithm, there have been only a very few nontrivial balanced functions tested for register number $n>3$. In this paper, we experimentally demonstrate the DJ algorithm in four- and five-qubit homonuclear spin systems by the nuclear-magnetic-resonance technique, by which we encode the one function evaluation into a long shaped pulse with the application of the gradient ascent algorithm. Our work, dramatically reducing the accumulated errors due to gate imperfections and relaxation, demonstrates a better implementation of the DJ algorithm.

Quantum discord provides a measure for quantifying quantum correlations beyond entanglement and is very hard to compute even for two-qubit states because of the minimization over all possible measurements. Recently a simple algorithm to evaluate the quantum discord for two-qubit $X$ states was proposed by Ali, Rau, and Alber [Phys. Rev. A 81, 042105 (2010)] with minimization taken over only a few cases. Here we shall at first identify a class of $X$ states, whose quantum discord can be evaluated analytically without any minimization, for which their algorithm is valid, and also identify a family of $X$ states for which their algorithm fails. And then we demonstrate that this special family of $X$ states provides furthermore an explicit example for the inequivalence between the minimization over positive operator-valued measures and that over von Neumann measurements.

Multichannel quantum defect theory (MQDT) is shown to be capable of producing quantitatively accurate results for low-energy atom-molecule scattering calculations. With a suitable choice of reference potential and short-range matching distance, it is possible to define a matrix that encapsulates the short-range collision dynamics and is only weakly dependent on energy and magnetic field. Once this has been produced, calculations at additional energies and fields can be performed at a computational cost that is proportional to the number of channels $N$ and not to $N^3$. MQDT thus provides a promising method for carrying out low-energy molecular scattering calculations on systems where full exploration of the energy dependence and the field dependence is currently impractical.

We investigate whether microscopic cascading of second-order nonlinearities of two molecules in the side-by-side configuration can lead to a third-order molecular nonlinear-optical response that exceeds the fundamental limit. We find that for large values of the second hyperpolarizability, the side-by-side configuration has a cascading contribution that lowers the direct contribution. However, we do find that there is a cascading contribution to the second hyperpolarizability when there is no direct contribution. Thus, while cascading can never lead to a larger nonlinear-optical response than for a single molecule with the same number of electrons, it may provide design flexibility in making large third-order susceptibility materials when the molecular second hyperpolarizability vanishes.

Microscopic cascading of second-order nonlinearities between two molecules has been proposed to yield an enhanced third-order molecular nonlinear-optical response. In this contribution, we investigate the two-molecule cascaded second hyperpolarizability and show that it will never exceed the fundamental limit of a single molecule with the same number of electrons as the two-molecule system. We show the apparent divergence behavior of the cascading contribution to the second hyperpolarizability vanishes when properly taking into account the intermolecular interactions. Although cascading can never lead to a larger nonlinear-optical response than a single molecule, it provides alternative molecular design configurations for creating materials with large third-order susceptibilities that may be difficult to design into a single molecule.

We propose blue-detuned optical traps that are suitable for trapping of both ground-state and Rydberg excited atoms. The addition of a background compensation field or a suitable choice of the trap geometry provides a magic trapping condition for ground-state and Rydberg atoms at the trap center. Deviations from the magic condition at finite temperature are calculated. Designs that achieve less than 200-kHz differential trap shift between Cs ground states and $125s$ Rydberg states for 10 $\mu \mathrm{K}$ Cs atoms are presented. Consideration of the trapping potential and photoionization rates suggests that these traps will be useful for quantum-information experiments with atomic qubits.

Ab initio calculations of two-photon double ionization of helium with photon energies varying from the nonsequential regime to well above the double-ionization threshold are presented. A systematic study of the joint angular distributions of the two ionized electrons at different energy sharing shows that the role of electron correlations is imprinted in the joint angular distribution. In particular, a rather general pattern is identified in the nonsequential regime that is independent of photon energy, pulse length, and energy sharing between the two electrons. Interestingly, the same distribution pattern is found for the equal-energy-sharing case, even when the photon energy is well above the double-ionization threshold. In the case of an extremely uneven energy sharing, the distribution pattern changes drastically as the photon energy is increased. In particular, when the photon energy is greater than the second-ionization threshold, the dominant emission mode of the two electrons switches gradually from “back to back” to “side by side.” Finally, the joint angular distribution is found to provide clear evidence of the role of electron correlations in the initial state.

Using atomic coherence, four-wave-mixing radiation is generated between the excited states of a ladder-type configuration in rubidium atomic vapor. By using all-optical phase control between the two frequency-swept driving beams connecting the two lower levels, the generated signal is phase modulated across its bandwidth. When homodyned with a local oscillator, such phase control looks promising for applications including waveform shaping and high-resolution metrology. Experimental observations of signal line shape symmetrization, linewidth narrowing, and bandwidth switching are demonstrated.

The four two-photon polarization Bell states are one of the main instruments in the toolbox of quantum optics and quantum information. In our experiment we produce their multiphoton counterparts, macroscopic Bell states. These are relevant to applications in quantum technologies because they provide efficient interactions with material quantum objects and with each other via nonlinear interactions. Furthermore, we study the polarization properties of these states using the concept of second-order degree of polarization and its higher-order generalization.

Temporal reshaping of the electric field of few-optical-cycle pulses in a low-density ionizing gas has been used to achieve control of the electron trajectories in the process of high-order harmonic generation. As a result of such a quantum path control mechanism, isolated or multiple attosecond pulses have been produced, depending on the carrier-envelope phase of the driving field. In particular, complete spectral tunability of the harmonic peaks over the whole spectral range has been demonstrated. Experimental results have been interpreted using a nonadiabatic three-dimensional propagation model and a nonadiabatic stationary phase model.

We study the decay process in an open system, emphasizing the relevance of the environment’s spectral structure. Non-Markovian effects are included to quantitatively analyze the degradation rate of the coherent evolution. The way in which a two-level system is coupled to different environments is specifically addressed: multiple connections to a single bath (public environment) or single connections to multiple baths (private environments). We numerically evaluate the decay rate of a local excitation by using the survival probability and the Loschmidt echo. These rates are compared to analytical results obtained from the standard Fermi golden rule (FGR) in wide band approximation, and a self-consistent evaluation that accounts for the bath’s memory in cases where an exact analytical solution is possible. We observe that the correlations appearing in a public bath introduce further deviations from the FGR as compared with a private bath.

The position-momentum Shannon and Rényi uncertainty products of general quantum systems are shown to be bounded not only from below (through the known uncertainty relations), but also from above in terms of the Heisenberg-Kennard product $\langle r^2\rangle \langle p^2\rangle$. Moreover, the Cramér-Rao, Fisher-Shannon, and López-Ruiz, Mancini, and Calbet shape measures of complexity (whose lower bounds have been recently found) are also bounded from above. The improvement of these bounds for systems subject to spherically symmetric potentials is also explicitly given. Finally, applications to hydrogenic and oscillator-like systems are done.

Bell’s theorem implies that the outcomes of local measurements on two maximally entangled systems cannot be simulated without classical communication between the parties. The communication cost is finite for $n$ Bell states, but it grows exponentially in $n$. Three simple protocols are presented that provide approximate simulations for low-dimensional entangled systems and require a linearly growing amount of communication. We have tested them by performing some simulations for a family of measurements. The maximal error is less than $1\%$ in three dimensions and grows sublinearly with the number of entangled bits in the range numerically tested. One protocol is the multidimensional generalization of the exact Toner-Bacon [Phys. Rev. Lett. 91, 187904 (2003)] model for a single Bell state. The other two protocols are generalizations of an alternative exact model, which we derive from the Kochen-Specker [J. Math. Mech. 17, 59 (1967)] scheme for simulating single-qubit measurements. These protocols can give some indication for finding optimal one-way communication protocols that classically simulate entanglement and quantum channels. Furthermore they can be useful for deciding if a quantum communication protocol provides an advantage on classical protocols.

An entanglement bound based on local measurements is introduced for multipartite pure states. It is the upper bound of the geometric measure and the relative entropy of entanglement. It is the lower bound of the minimal-measurement entropy. For pure bipartite states, the bound is equal to the entanglement entropy. The bound is applied to pure tripartite qubit states and the exact tripartite relative entropy of entanglement is obtained for a wide class of states.

In equilibrium, forces induced by fluctuations of the electromagnetic field between electrically polarizable objects (microscopic or macroscopic) in vacuum are generically attractive. The force may, however, become repulsive for microscopic particles coupled to thermal baths with different temperatures. We demonstrate that this nonequilibrium repulsion can be realized also between macroscopic objects, as planar slabs, if they are kept at different temperatures. It is shown that repulsion can be enhanced by (i) tuning of material resonances in the thermal region and by (ii) reducing the dielectric contrast due to “dilution.” This can lead to stable equilibrium positions. We discuss the realization of these effects for aerogels, yielding repulsion down to submicron distances at realistic porosities.

We report measured and calculated cross sections for elastic scattering of low-energy electrons by isopropanol (propan-2-ol). The experimental data were obtained using the relative flow technique with helium as the standard gas and a thin aperture as the collimating target gas source, which permits use of this method without the restrictions imposed by the relative flow pressure conditions on helium and the unknown gas. The differential cross sections were measured at energies of 1.5, 2, 3, 5, 6, 8, 10, 15, 20, and 30 eV and for scattering angles from 10${}^{\circ }$ to 130${}^{\circ }$. The cross sections were computed over the same energy range employing the Schwinger multichannel method in the static-exchange plus polarization approximation. Agreement between theory and experiment is very good. The present data are compared with previously calculated and measured results for $n$-propanol, the other isomer of C${}_3$H${}_7$OH. Although the integral and momentum transfer cross sections for the isomers are very similar, the differential cross sections show a strong isomeric effect: In contrast to the $f$-wave behavior seen in scattering by $n$-propanol, $d$-wave behavior is observed in the cross sections of isopropanol. These results corroborate our previous observations in electron collisions with isomers of C${}_4$H${}_9$OH.

We study a dilute sample of cold atoms to achieve efficient population transfer from a ground state to a Rydberg state. This sample is approximately divided into many independent microspheres containing only two atoms. Each pair of atoms in a microsphere may become quantum correlated via the dipole-dipole interaction characterized by a van der Waals potential. Our numerical results show that, by modulating detunings of a pump pulse and a Stokes pulse applied in the counterintuitive order, we can drive the dilute sample either into the blockade regime or into the antiblockade regime. In the blockade regime, only one atom is allowed to be coherently transferred into the Rydberg state in a microsphere, which then results in a maximal entangled state. In the antiblockade regime, however, both atoms in a microsphere can be efficiently excited into the Rydberg state, which is not accompanied by quantum entanglement. A second maximal entangled state may also be generated if we work between the blockade regime and the antiblockade regime. Note that the existence of a quasidark state is essential for exciting both atoms in a microsphere into the Rydberg state when the van der Waals potential is nonzero.

We study the ground-state configurations of few interacting bosons confined in two dimensions by anisotropic harmonic potentials. By means of variational calculations, including correlation effects, we show that the arrangement of bosons strongly depends on the strength of the repulsive interaction and the anisotropy of the confinement. We compute the condensate fraction of the system and found that by increasing the anisotropy of the potential a weaker interaction suffices to destroy the condensate and favors the emergence of a crystal-like structure.