Recently Costa Filho et al. [Phys. Rev. A 84, 050102(R) (2011)] have introduced a position-dependent infinitesimal translation operator which corresponds to a position-dependent linear momentum and consequently to a quantum particle with position-dependent effective mass. Although there is no doubt about the novelty of the idea and the formalism, we believe that some aspects of the quantum mechanics in their original work could be enhanced. Here in this Brief Report first we address those points and then an alternative is introduced. Finally we apply the formalism for a quantum particle under a null potential confined in a square well, and the results are compared with those in the paper mentioned above.

Entanglement swapping is a process by which two initially independent quantum systems can become entangled and generate nonlocal correlations. To characterize such correlations, we compare them to those predicted by bilocal models, where systems that are initially independent are described by uncorrelated states. We extend in this paper the analysis of bilocal correlations initiated in [Phys. Rev. Lett. 104, 170401 (2010)]. In particular, we derive new Bell-type inequalities based on the bilocality assumption in different scenarios, we study their possible quantum violations, and we analyze their resistance to experimental imperfections. The bilocality assumption, being stronger than Bell's standard local causality assumption, lowers the requirements for the demonstration of quantumness in entanglement-swapping experiments.

A post-Markovian master equation has been recently proposed as a tool to describe the evolution of a system coupled to a memory-keeping environment [A. Shabani and D. A. Lidar, Phys. Rev. A 71, 020101(R) (2005)]. For a single qubit affected by appropriately chosen environmental conditions, the corresponding dynamics is always legitimate and physical. Here we extend such a situation to the case of two qubits, only one of which experiences the environmental effects. We show how, despite the innocence of such an extension, the introduction of the second qubit should be done cum grano salis to avoid consequences such as the breaking of the positivity of the associated dynamical map. This hints at the necessity of using care when adopting phenomenologically derived models for evolutions occurring outside the Markovian framework.

It has been known that one reservoir of driven two-level atoms can establish two-mode interactions and generate bipartite continuous-variable entangled light. Here we show that three-mode interactions can be created by combining two such reservoirs, each of which interacts with two adjacent fields in frequency. It is shown that the van Loock–Furusawa criteria [Phys. Rev. A 67, 052315 (2003)] are well satisfied for a wide range of the relevant parameters. This determines that tripartite continuous-variable Greenberger-Horne-Zeilinger entanglement is obtainable. The scalability to more fields is straightforward, allowing an alternative implementation of a multipartite quantum networks with continuous variables.

An efficient optimal-control theory based on the Krotov method is introduced for a non-Markovian open quantum system with a time-nonlocal master equation in which the control parameter and the bath correlation function are correlated. This optimal-control method is developed via a quantum dissipation formulation that transforms the time-nonlocal master equation to a set of coupled linear time-local equations of motion in an extended auxiliary Liouville space. As an illustration, the optimal-control method is applied to find the control sequences for high-fidelity $Z$ gates and identity gates of a qubit embedded in a non-Markovian bath. $Z$ gates and identity gates with errors less than ${10}^{-5}$ for a wide range of bath decoherence parameters can be achieved for the non-Markovian open qubit system with control over only the ${\sigma }_z$ term. The control-dissipation correlation and the memory effect of the bath are crucial in achieving the high-fidelity gates.

A key goal of quantum communication is to determine the maximum number of bits shared between two quantum systems. An important example of this is in entanglement-based quantum key distribution (QKD) schemes. A realistic treatment of this general communication problem must take account of the nonideal nature of the entanglement source and the detectors. The aim of this paper is to give such a treatment. We obtain analytic expression for the mutual information in terms of experimental parameters. The results are applied to communication schemes that rely on spontaneous parametric down conversion to generate entangled photons. We show that our results can be applied to tasks such as calculating the optimal rate of bits per photon in high-dimensional time-bin-encoded QKD protocols (prior to privacy amplification). A key finding for such protocols is that, by using realistic experimental parameters, one can obtain over 10 bits per photon. We also show how our results can be applied to characterize the capacity of a fiber array and to quantify entanglement using mutual information.

The wide set of control parameters and reduced size scale make semiconductor quantum dots attractive candidates to implement solid-state quantum computation. Considering an asymmetric double quantum dot coupled by tunneling, we combine the action of a laser field and the spontaneous emission of the excitonic state to protect an arbitrary superposition state of the indirect exciton and ground state. As a by-product we show how to use the protected state to solve the Deutsch problem.

In this paper we utilize superoperator formalism to explore the entanglement evolution of four-qubit cluster states in a number of decohering environments. A four-qubit cluster state is a resource for the performance of an arbitrary single-logical-qubit rotation via measurement-based cluster-state quantum computation. We are specifically interested in the relationship between entanglement evolution and the fidelity with which the arbitrary single-logical-qubit rotation can be implemented in the presence of decoherence as this will have important experimental ramifications. We also note the exhibition of entanglement sudden death (ESD) and ask how severely its onset affects the utilization of the cluster state as a means of implementing an arbitrary single-logical-qubit rotation.

We describe an efficient DQC1 (deterministic quantum computation with one quantum qubit) algorithm to quantify the amount of geometric quantum discord present in the output state of a DQC1 computation. DQC1 is a model of computation that utilizes separable states to solve a problem with no known efficient classical algorithm and is known to contain quantum correlations as measured by the discord. For the general case of a $(1+n)$-qubit DQC1 state we provide an analytical expression for the geometric quantum discord and find that its typical (and maximum) value decreases exponentially with $n$. This is in contrast to the standard quantum discord whose value for typical DQC1 states is known to be independent of $n$. We experimentally demonstrate the proposed algorithm on a four-qubit liquid-state nuclear magnetic resonance quantum information processor. In the special case of a two-qubit DQC1 model, we also provide an expression for the quantum discord that only requires the outcome of the DQC1 algorithm.

A complex-scaled multireference configuration interaction method (CMR-CI) is proposed, which employs the multireference orbitals optimized with complex-scaled multiconfiguration self-consistent field for the specific state. First applications for the 1$s$2$s^2$2$p$ ${}^{1,3}$$P^{\mathrm{o}}$ Auger resonances of Be and Be-like cations (B, C, N, O, Mg) show that present results agree very well with the available experimental and theoretical results. For example, our CMR-CI 1$s$2$s^2$2$p$ ${}^1{P}^{\mathrm{o}}$ resonance position and linewidth for C${}^{2+}$ are (294.031 eV, 61.5 meV), which is in excellent agreement with the high-resolution advanced light source latest experiment result (293.94 $\pm$ 0.03 eV, 65 $\pm$ 12 meV) [Scully et al., J. Phys. B 38, 1967 (2005)]. Our calculations show that this CMR-CI method is a practical and important tool to study resonant states.

We investigate the strong-field ionization for the ground state of H${{}_2}^{+}$ by numerically solving the three-dimensional (3D) time-dependent Schrödinger equation (TDSE), and comparisons have been made among the TDSE, the different versions of molecular strong-field approximation (MO-SFA) and the molecular Ammosov-Delone-Krainov (MO-ADK) approximation. The study shows that, for the TDSE results, the ratio of ionization rates between perpendicular and parallel alignments displays a step-like structure against the Keldysh parameter $\gamma$. For small internuclear distances, the transition between the steps are found to be around $\gamma \approx 1$ and is recognized as the competition between the multiphoton ionization (MPI) and tunneling ionization (TI). The ionization is more isotropic in the MPI regime. For large internuclear distances, the transition position shifts to larger $\gamma$ due to the charge-resonance-enhanced ionization (CREI). Different versions of strong-field ionization theories are compared against the TDSE results.

The shear viscosity of a two-dimensional Fermi gas interacting via a short-range potential with scattering length $a_{2\mathrm{d}}$ in kinetic theory is computed. It is found that classical kinetic theory predicts that the shear viscosity to entropy density ratio of a strongly interacting two-dimensional gas is comparable to that of the three-dimensional unitary gas. Results are applied to the damping of collective modes of a trapped Fermi gas, and compared to experimental data recently obtained by Vogt et al. [Phys. Rev. Lett. 108, 070404 (2012)].

We clarify an interpretation of transmittance signals in ladder-type atomic systems by discriminating the contributions of one-photon resonance, two-photon resonance, and a mixed term of both in the calculated spectra for these ladder-type multilevel atoms. When the two-photon-resonance effect is distinguished from an accurate spectrum calculated by modeling ladder-type electromagnetically-induced transparency for the $5S_{1/2}-5P_{3/2}-5D_{5/2}$ transitions of ${}^{87}$Rb atoms, we find that the transmittance signals for the $5D_{5/2}(F^{\prime \prime }=2,3)$ states are mainly composed of the mixed term related not to pure-two-photon atomic coherence but to the optical-pumping effect whereas the transmittance signal for the $5D_{5/2}(F^{\prime \prime }=4)$ state originates from both the pure-two-photon-resonance term and the mixed term.

The counting statistics give insight into the properties of quantum states of light and other quantum states of matter such as ultracold atoms or electrons. The theoretical description of photon counting was derived in the 1960s and was extended to massive particles more recently. Typically, the interaction between each particle and the detector is assumed to be limited to short time intervals, and the probability of counting particles in one interval is independent of the measurements in previous intervals. There has been some effort to describe particle counting as a continuous measurement, where the detector and the field to be counted interact continuously. However, the formalism based on continuous measurements does not provide a formula applicable to general time- and space-dependent fields. In our work, we derive a fully time- and space-dependent description of the counting process for linear quantum many-body systems, taking into account the back-action of the detector on the field. We apply our formalism to an expanding Bose-Einstein condensate of ultracold atoms, and show that it describes the process correctly, whereas the standard approach gives unphysical results in some limits. The example illustrates that, in certain situations, the back-action of the detector cannot be neglected and has to be included in the description.

We theoretically analyze pulse propagation in a medium of inhomogeneously broadened two-level quantum systems, which have a vibrational degree of freedom with respect to the center-of-mass coordinate. This system mimics local mode oscillations of rare-earth-metal-ion dopants in dielectric crystals that are coupled to electronic transitions. We show the emergence of various nonlinear optical phenomena, such as self-induced transparency or the nonlinear interaction between two pulses coupling to different electrovibrational transitions. Interaction between the pulses makes it possible to generate various Raman sidebands of the incident fields and to tune the location where they are generated. We also demonstrate controlled population transfer between electrovibrational states of the ions at specific points along the propagation axis. Similarities and differences between our results and other pulse propagation phenomena of few-level quantum systems are discussed.

We have studied the modulational instability (MI) of the higher-order nonlinear Schrödinger (HNLS) equation with non-Kerr nonlinearities in an optical context and presented an analytical expression for MI gain to show the effects of non-Kerr nonlinearities and higher-order dispersions on MI gain spectra. In our study, we demonstrate that MI can exist not only for the anomalous group-velocity dispersion (GVD) regime, but also in the normal GVD regime in the HNLS equation in the presence of non-Kerr quintic nonlinearities. The non-Kerr quintic nonlinear effect reduces the maximum value of the MI gain and bandwidth and plays a sensitive role over the Kerr nonlinearity, which leads to continuous wave breaking into a number of stable wave trains of ultrashort optical pulses that can be used to generate the stable supercontinuum white-light coherent sources.

In their recent paper, Assafräo et al. [D. Assafräo, H. R. J. Walters, F. Arretche, A. Dutra, and J. R. Mohallem, Phys. Rev. A 84, 022713 (2011)] use a scaled adiabatic potential to calculate total and differential cross sections for positron scattering from a variety of targets. They claimed that the results are “very close to experimental and best theoretical data.” A brief examination of the recent literature on this subject demonstrates, however, that comparisons with several important and recent results have not been made, and that such comparisons clearly affect the accuracy of their conclusions.

We analyze the evolution of the Gaussian discord between two resonant harmonic oscillators coupled to a common environment. For this, we use the same tools we applied before to fully characterize the evolution of the entanglement in this system [Paz and Roncaglia, Phys. Rev. Lett. 100, 220401 (2008)]. The asymptotic value of Gaussian discord is obtained as a function of parameters characterizing the environment (temperature, couplings, etc.) and the initial state of the system (initial squeezing, initial purity, etc.) The type of Gaussian measurement optimizing the extraction of information between the oscillators is fully characterized by means of a phase diagram. Such a diagram (with phases corresponding to homodyne or heterodyne measurements) has similar topology to the one describing dynamical phases for the entanglement. We present evidence pointing to the fact that Gaussian discord is not always a good approximation of true discord as the asymptotic value of the former is shown to be a nondecreasing function of temperature (in the high-temperature regime), reaching an asymptotic value of $\ln \left(2\right)$ for a pure initial state (and lower values for mixed initial states).

One-way quantum computation by utilizing multipartite cluster states paves the way for the realization of universal quantum computation. However, quantum memory should be implemented in the practical systems to ensure the operations could be timed appropriately. A scheme of the controlled-$X$ gate with a cache function for one-way quantum computation is proposed here. Due to the generation of a hybrid cluster state based on the interaction of light-atoms, the atom stations will not only be treated as the submodes of cluster states, but also implement the function of quantum memory.

Revivals of quantum correlations have often been explained in terms of back-action on quantum systems by their quantum environment(s). Here we consider a system of two independently evolving qubits, each locally interacting with a classical random external field. The environments of the qubits are also independent, and there is no back-action on the qubits. Nevertheless, entanglement, quantum discord, and classical correlations between the two qubits may revive in this model. We explain the revivals in terms of correlations in a classical-quantum state of the environments and the qubits. Although classical states cannot store entanglement on their own, they can play a role in storing and reviving entanglement. It is important to know how the absence of back-action, or modeling an environment as classical, affects the kind of system time evolutions one is able to describe. We find a class of global time evolutions where back-action is absent and for which there is no loss of generality in modeling the environment as classical. Finally, we show that the revivals can be connected with the increase of a parameter used to quantify non-Markovianity of the single-qubit dynamics.