There is now a significant body of results on quantum interactions with closed timelike curves (CTCs) in the quantum information literature, for both the Deutsch model of CTC interactions (D-CTCs) and the projective model (P-CTCs). As a consequence, there is a prima facie argument exploiting entanglement that CTC interactions would enable superluminal and, indeed, effectively instantaneous signaling. In cases of spacelike separation between the sender of a signal and the receiver, whether a receiver measures the local part of an entangled state or a disentangled state to access the signal can depend on the reference frame. We propose a consistency condition that gives priority to either an entangled perspective or a disentangled perspective in spacelike-separated scenarios. For D-CTC interactions, the consistency condition gives priority to frames of reference in which the state is disentangled, while for P-CTC interactions the condition selects the entangled state. Using the consistency condition, we show that there is a procedure that allows Alice to signal to Bob in the past via relayed superluminal communications between spacelike-separated Alice and Clio, and spacelike-separated Clio and Bob. This opens the door to time travel paradoxes in the classical domain. Ralph [T. C. Ralph, arXiv:1107.4675 [quant-ph].] first pointed this out for P-CTCs, but we show that Ralph's procedure for a “radio to the past” is flawed. Since both D-CTCs and P-CTCs allow classical information to be sent around a spacetime loop, it follows from a result by Aaronson and Watrous [S. Aaronson and J. Watrous, Proc. R. Soc. A 465, 631 (2009)] for CTC-enhanced classical computation that a quantum computer with access to P-CTCs would have the power of PSPACE, equivalent to a D-CTC-enhanced quantum computer.

The quantitative assessment of the entanglement in multipartite quantum states is, apart from its fundamental importance, a practical problem. Recently there has been significant progress in developing new methods to determine certain entanglement measures. In particular, there is a method—in principle, analytical—to compute a certified lower bound for the three-tangle. The purpose of this work is to provide a manual for the implementation of this approach and to explicitly discuss several analytically solvable cases in order to gauge the numerical tools. Moreover, we derive a simple analytical bound for the mixed-state three-tangle.

Many important problems in science and engineering can be reduced to the problem of solving linear equations. The quantum algorithm discovered recently indicates that one can solve an $N$-dimensional linear equation in $O(logN)$ time, which provides an exponential speedup over the classical counterpart. Here we report an experimental demonstration of the quantum algorithm when the scale of the linear equation is $2\times 2$ using a nuclear magnetic resonance quantum information processor. For all sets of experiments, the fidelities of the final four-qubit states are all above 96%. This experiment gives the possibility of solving a series of practical problems related to linear systems of equations and can serve as the basis to realize many potential quantum algorithms.

We propose a scheme for realizing quantum logic gates between any pair of ions confined in a linear trap with a pair of laser beams tuned to the carrier. The striking feature of the scheme is that the carrier excitation accompanying the spin-motion coupling does not affect the gate dynamics. As a consequence, the gate not only is much more insensitive to motional heating but also can operate at a higher speed compared to the previous schemes. The other important advantages are that the gate speed does not need to be inversely proportional to the number of ions in the chain, and the accompanying carrier drive results in dynamical decoupling, making the gate performance robust against dephasing noises. We show that for the same error sources the gate infidelity can be decreased by about ten times compared with previous schemes.

We propose a scheme for continuous-variable quantum key distribution (CV-QKD) using the subcarrier multiplexing technique which was employed in microwave photonics. This scheme allows distribution of $N$ channels with independent Gaussian-modulated CV-QKD in parallel with one laser source and several phase modulators. We analyze the influence of nonlinear signal mixing and security in the asymptotic limit. Results indicate that by using this multiplexing technique, each channel will have a non-Gaussian extra source noise, resulting in slight shortening of the maximum transmission distance, while the total secret key rate can be considerably increased. This scheme could also be used for key distribution for multiple users, and combined with wavelength division multiplexing devices it has potential to be used for construction of a CV-QKD network.

We present analytic estimates of the performances of various approximate quantum error-correction schemes for the generalized amplitude-damping (GAD) qubit channel. Specifically, we consider both stabilizer and nonadditive quantum codes. The performance of such error-correcting schemes is quantified by means of the entanglement fidelity as a function of the damping probability and the nonzero environmental temperature. The recovery scheme employed throughout our work applies, in principle, to arbitrary quantum codes and is the analog of the perfect Knill-Laflamme recovery scheme adapted to the approximate quantum error-correction framework for the GAD error model. We also analytically recover and/or clarify some previously known numerical results in the limiting case of vanishing temperature of the environment, the well-known traditional amplitude-damping channel. In addition, our study suggests that degenerate stabilizer codes and self-complementary nonadditive codes are especially suitable for the error correction of the GAD noise model. Finally, comparing the properly normalized entanglement fidelities of the best performant stabilizer and nonadditive codes characterized by the same length, we show that nonadditive codes outperform stabilizer codes not only in terms of encoded dimension but also in terms of entanglement fidelity.

We report on measurements of narrow photoassociation lines of ${}^{40}\mathrm{Ca}$ near the ${}^3{P}_1$ + ${}^1{S}_0$ asymptote related to the molecular states ${}^3{\Pi }_u$ and ${}^3{\Sigma }_u^{+}$ at about 1 $\mu$K. From the measured binding energies an accurate description of the long-range interaction potentials was obtained; it was found to be crucial to also include the precisely measured molecular Zeeman splittings. Our analysis is a first step towards application of optical Feshbach resonances in ${}^{40}\mathrm{Ca}$ to modify the scattering length significantly with small losses.

Molecular high-order-harmonic generation and molecular-orbital ionization rates are calculated for the CO, ${\text{H}}_2\text{CO}$, ${\text{CO}}^{+}$, and ${\text{H}}_2{\text{CO}}^{+}$ molecules using numerical solutions of Kohn-Sham equations of time-dependent density-functional theory in the nonlinear nonperturbative regime of laser-molecule interactions. Different laser-molecule orientations (θ = 0, 90°, and 180°) and intensities (8.7 × 10${}^{13}$, 3.5 × 10${}^{14}$, and 1.4 × 10${}^{15}$ W/cm${}^2$) are used. Results show that at wavelength λ = 800 nm, the ionization rate maxima are influenced for each molecular orbital by the interplay between its ionization potential, its geometrical shape, and the laser polarization axis. Molecular high-order-harmonic generation is further studied by a time profile analysis and a time-dependent electron localization function. A comparison of the data between CO and ${\text{H}}_2\text{CO}$ illustrates the importance of the protons on the electron distributions, ionization, and recollision dynamics in intense fields.

The dynamics of a Bose-Einstein condensate of atoms having attractive interactions is studied using quantum many-body simulations. The collapse of the condensate by quantum tunneling is numerically demonstrated, and the tunneling rate is calculated. The correlation properties of the quantum many-body state are investigated.

We present three complementary methods to study stationary nonlinear solutions in one-dimensional nonlinear metal-dielectric structures. Two of them use an approximate treatment of the Kerr-type nonlinear term taking into account only the leading electric-field component, while the third one allows for an exact treatment of the nonlinearity. A direct comparison of the results obtained with all three models is presented and the excellent agreement between them justifies the assumptions that have been used to construct the models. A systematic study of the configurations made of two, three, or four layers that contain a semi-infinite Kerr-type nonlinear dielectric, a metal film, and linear dielectrics is presented. A detailed analysis of properties, type, and number of solutions in these three types of structures is performed. The parameter ranges where plasmon-soliton waves exist are found. Structures with realistic optogeometric parameters where plasmon solitons exist at power levels already used in spatial soliton studies are proposed and studied.

The photoabsorption spectra of the Xe atoms encapsulated at different locations of the C${}_{60}$ have been evaluated using the time-dependent density-functional theory. The calculations are performed in the energy region of the Xe $4d$ giant resonance. The results demonstrate that the main confinement resonances can result only when the Xe atom is located within a very small sphere of radius 0.3 Å around the center of the fullerene. The small resonance peak around 100 eV has now been identified as a shape resonance of the free Xe $4d$-$\epsilon f$ transition; it is not a confinement resonance.

Partition density-functional theory is a formally exact method for solving the ground-state electronic structure problem. It operates by dividing the system into noninteracting fragments along with a global effective potential, which, when solved to self-consistency, yields the exact energy and density (as the sum of the fragment densities) of the interacting system. A recent paper [Phys. Rev. A 86, 012504 (2012)] questions the uniqueness of the fragment occupations and fragment densities. We demonstrate that their analysis is incorrect. We describe some of the technical details of partition density-functional calculations and discuss the relationship to other embedding schemes.

The Comment by Elliott et al. stresses that partition density-functional theory (PDFT) yields a global partition potential and unique occupation numbers. Our reply points out that both of these results can be obtained, numerically, in model calculations, such as those reported previously to illustrate PDFT by shifting the von Weisäcker potentials to achieve zero values in the large-$r$ limit.

We perform time-dependent calculations of strong-field ionization of He by elliptically polarized light in configuration of recent attoclock measurements of Boge et al. [Phys. Rev. Lett. 111, 103003 (2013)]. By solving a three-dimensional time-dependent Schrödinger equation, we obtain the angular offset ${\theta }_m$ of the maximum in the photoelectron momentum distribution in the polarization plane relative to the position predicted by the strong-field approximation. This offset is used in attoclock measurements to extract the tunneling time. Our calculations clearly support the set of experimental angular offset values obtained with the use of nonadiabatic calibration of the in situ field intensity, and disagree with an alternative set calibrated adiabatically. These findings are in contrast with the conclusions of Boge et al. who found a qualitative agreement of their semiclassical calculations with the adiabatic set of experimental data. This controversy may complicate interpretation of the recent attoclock measurements.

We derive the ultimate bounds on the performance of nonlinear measurement schemes in the presence of noise. In particular, we investigate the precision of the second-order estimation scheme in the presence of the two most detrimental types of noise, photon loss and phase diffusion. We find that the second-order estimation scheme is affected by both types of noise in an analogous way as the linear one. Moreover, we observe that for both types of noise the gain in the phase sensitivity with respect to the linear estimation scheme is given by a multiplicative term $O(1/N)$. Interestingly, we also find that under certain circumstances, a careful engineering of the environment can, in principle, improve the performance of measurement schemes affected by phase diffusion.

We present a comprehensive theoretical treatment of supcode, a method for generating dynamically corrected quantum gate operations, which are immune to random noise in the environment, by using carefully designed sequences of soft pulses. supcode enables dynamical error suppression even when the control field is constrained to be positive and uniaxial, making it particularly suited to counteracting the effects of noise in systems subject to these constraints such as singlet-triplet qubits. We describe and explain in detail how to generate supcode pulse sequences for arbitrary single-qubit gates and provide several explicit examples of sequences that implement commonly used gates, including the single-qubit Clifford gates. We develop sequences for noise-resistant two-qubit gates for two exchange-coupled singlet-triplet qubits by cascading robust single-qubit gates, leading to a 35% reduction in gate time compared to previous works. This cascade approach can be scaled up to produce gates for an arbitrary-length spin qubit array and is thus relevant to scalable quantum computing architectures. To more accurately describe real spin qubit experiments, we show how to design sequences that incorporate additional features and practical constraints such as sample-specific charge noise models and finite pulse rise times. We provide a detailed analysis based on randomized benchmarking to show how supcode gates perform under realistic $1/f^{\alpha }$ noise and find a strong dependence of gate fidelity on the exponent $\alpha$, with best performance for $\alpha >1$. Our supcode sequences can therefore be used to implement robust universal quantum computation while accommodating the fundamental constraints and experimental realities of singlet-triplet qubits.

We study the emergence of Faraday waves in cigar-shaped collisionally inhomogeneous Bose-Einstein condensates subject to periodic modulation of the radial confinement. Considering a Gaussian-shaped radially inhomogeneous scattering length, we show through extensive numerical simulations and detailed variational treatment that the spatial period of the emerging Faraday waves increases as the inhomogeneity of the scattering length gets weaker, and that it saturates once the width of the radial inhomogeneity reaches the radial width of the condensate. In the regime of strongly inhomogeneous scattering lengths, the radial profile of the condensate is akin to that of a hollow cylinder, while in the weakly inhomogeneous case the condensate is cigar shaped and has a Thomas-Fermi radial density profile. Finally, we show that when the frequency of the modulation is close to the radial frequency of the trap, the condensate exhibits resonant waves which are accompanied by a clear excitation of collective modes, while for frequencies close to twice that of the radial frequency of the trap, the observed Faraday waves set in forcefully and quickly destabilize condensates with weakly inhomogeneous two-body interactions.

In open resonators the energy associated with a localized photonic excitation is lost in the form of a radiated wave, in the same manner that a classical charged particle in a curved orbit loses energy in the form of electromagnetic radiation. As a consequence, photonic modes in conventional spatially bounded open resonators have finite decay times. Here, we theoretically show that, surprisingly, in the limit of vanishing material loss, plasmons give the opportunity to have light localization in open spatially bounded systems with infinitely large lifetimes.

We theoretically investigated a microtoroidal cavity quantum electrodynamics system in which radiation from the emitter is nearly perfectly guided into a fiber mode, and analyzed the resonance fluorescence from the emitter after pulsed excitation. We derived analytic formulas to rigorously evaluate the photon statistics of the pulse emitted into the fiber, and clarified the conditions needed for the excitation pulse to generate single- and two-photon pulses.

We study the slowing, storing, and releasing of microwave pulses in a superconducting circuit composed of two coplanar waveguide resonators and a superconducting transmon-type qubit. The quantum interference analogy to electromagnetically induced transparency is created in two coupled resonators. By tuning the resonance frequency of the transmon, we dynamically tune the effective coupling between the resonators. Via the modulation of the coupling, we show the tunable true time delay of microwave pulses at the single-photon level. We also store the microwave field in a high-$Q$ resonator and release the signal from it to the output port. Our scheme promises applications in both quantum information processing and classical wireless communications.