It was shown that using multiphoton qubits, a nearly deterministic Bell-state measurement can be performed with linear optics and on-off photodetectors [Phys. Rev. Lett. 114, 113603 (2015)]. However, multiphoton qubits are generally more fragile than single-photon qubits under a lossy environment. In this paper, we propose and analyze a scheme to teleport multiphoton-qubit information using hybrid entanglement with a loss-tolerant carrier qubit. We consider three candidates for the carrier qubit: a coherent-state qubit, a single-photon polarization qubit, and a vacuum-and-single-photon qubit. We find that teleportation with the vacuum-and-single-photon qubit tolerates about 10 times greater photon losses than with the multiphoton qubit of the photon number $N\ge 4$ in the high fidelity regime ($F\ge 90\%$). The coherent-state qubit encoding may be even better than the vacuum-and-single-photon qubit as the carrier when its amplitude is as small as $\alpha <0.78$. We further point out that the fidelity of the teleported state by our scheme is determined by loss in the carrier qubit while the success probability depends on loss only in the multiphoton qubit to be teleported. Our study implies that the hybrid architecture may complement the weaknesses of each qubit encoding.

The simple single-channel static-exchange approximation completely ignores correlation between the continuum and molecular ion electrons. In molecular systems with symmetry equivalent atoms, the single-channel approximation can seriously fail in core ionization when using delocalized orbitals to represent the core hole states. We present cross sections and molecular frame photoelectron angular distributions with both localized and delocalized core orbitals in ${\mathrm{CF}}_4$ F $\left(1s\right)$ ionization. We show that only a full coupled-channel calculation can recover an accurate description of the physics of inner-shell photoionization when using delocalized orbitals, whereas nearly the same result can be obtained from independent single-channel static-exchange calculations when localized core orbitals are used. A grid-based variational method described here makes such single-channel calculations possible on larger systems without local-exchange approximations. Illustrative calculations on the core ionization of ${\mathrm{SF}}_6$ are presented to illustrate the power of the grid-based method.

We investigate interactions between the proton spin, the deuteron spin, and the orbital angular momentum in the electronic ground state of the HD molecule. These interactions lead to hyperfine splittings of molecular energy levels. Our numerical results for the first rotational level agree well with the currently most accurate measurement performed by Ramsey et al. [Phys. Rev. 112, 1929 (1958)] in the 1950s. Knowledge of the hyperfine structure of other levels is necessary for the accurate determination of rovibrational transition energies in spectroscopic measurements. We present theoretical predictions and share the numerical code used to perform numerical calculations. This paper sets the groundwork for high-precision spectroscopic tests of hyperfine interactions in molecular systems. In particular we determine the value of the deuteron quadrupole moment $Q=0.2856\left(2\right){\mathrm{fm}}^2$ and give an outlook for improving its accuracy by three orders of magnitude.

We study a system of strongly interacting one-dimensional (1D) bosons on a ring pierced by a synthetic magnetic flux tube. By the Fermi-Bose mapping, this system is related to the system of spin-polarized noninteracting electrons confined on a ring and pierced by a solenoid (magnetic flux tube). On the ring there is an external localized $\delta$-function potential barrier, $V\left(\varphi \right)=g\delta (\varphi -{\varphi }_0)$. We study the Berry phase associated with the adiabatic motion of the $\delta$-function barrier around the ring as a function of the strength of the potential $g$ and the number of particles $N$. The behavior of the Berry phase can be explained via quantum mechanical reflection and tunneling through the moving barrier which pushes the particles around the ring. The barrier produces a cusp in the density to which one can associate a missing charge $\mathrm{\Delta }q$ (missing density) for the case of electrons (bosons, respectively). We show that the Berry phase (i.e., the Aharonov-Bohm phase) cannot be identified with the quantity $\mathrm{\Delta }q/\hslash \oint \mathbf{A}·d\mathbf{l}$. This means that the missing charge cannot be identified as a (quasi)hole. We point out the connection of this result and recent studies of synthetic anyons in noninteracting systems. In addition, for bosons we study the weakly interacting regime, which is related to the strongly interacting electrons via Fermi-Bose duality in 1D systems.

Detectors inherently capable of resolving photon numbers have undergone a significant development recently, and this is expected to affect multiplexed periodic single-photon sources where such detectors can find their applications. We analyze various spatially and time-multiplexed periodic single-photon source arrangements with photon-number-resolving detectors, partly to identify the cases when they outperform those with threshold detectors. We develop a full statistical description of these arrangements in order to optimize such systems with respect to maximal single-photon probability, taking into account all relevant loss mechanisms. The model is suitable for the description of all spatial and time multiplexing schemes. Our detailed analysis of symmetric spatial multiplexing identifies a particular range of loss parameters in which the use of the new type of detectors leads to an improvement. Photon number resolution opens an additional possibility for optimizing the system in that the heralding strategy can be defined in terms of actual detected photon numbers. Our results show that this kind of optimization opens an additional parameter range of improved efficiency. Moreover, this higher efficiency can be achieved by using less multiplexed units, i.e., smaller system size as compared to threshold-detector schemes. We also extend our investigation to certain time-multiplexed schemes of actual experimental relevance. We find that the highest single-photon probability is 0.907 that can be achieved by binary bulk time multiplexers using photon-number-resolving detectors.

We study a prototypical model of two coupled two-level systems, where the competition between coherent and dissipative coupling gives rise to a rich phenomenology. In particular, we analyze the case of asymmetric coupling, as well as the limiting case of chiral (or one-way) coupling. We investigate various quantum optical properties of the system, including its steady-state populations, power spectrum, and second-order correlation functions, and outline the characteristic features which emerge in each quantity as one sweeps through the nontrivial landscape of effective complex couplings. Most importantly, we reveal instances of population trapping, unexpected spectral features, and strong emission correlations.

The protocol proposed in the commented-upon article can certify zero discord; however, it fails to quantify nonzero discord for some states. Further, the protocol is less efficient than calculating discord via performing full quantum state tomography.

The authors of the preceding Comment [Kumar and Snizhko, Phys. Rev. A 102, 016401 (2020)] made two critical remarks regarding the protocol for detecting and quantifying quantumness of separable states presented in our paper [Hunt et al., Phys. Rev. A 100, 022321 (2019)]. One is that our protocol is not “experiment friendly” in comparison to full quantum state tomography. The other is that the suggested quantifier fails to distinguish different degrees of quantumness within the family of Werner states. We will show that, while being technically correct, both remarks referred to generalizations of our protocol which had been neither suggested nor intended. We will reiterate why the proposed protocol would be advantageous, compared to full or partial quantum state tomography, for detecting and quantifying discord in many-body bipartite states.

Quantum low-density generator matrix (QLDGM) codes based on Calderbank-Steane-Shor (CSS) constructions have shown unprecedented error correction capabilities, displaying much improved performance in comparison to other sparse-graph codes. However, the nature of CSS designs and the manner in which they must be decoded limit the performance that is attainable with codes that are based on this construction. This motivates the search for quantum code design strategies capable of avoiding the drawbacks associated with CSS codes. In this article, we introduce non-CSS quantum code constructions based on classical LDGM codes. The proposed codes are derived from CSS QLDGM designs by performing specific row operations on their quantum parity check matrices to modify the associated decoding graphs. The application of this method results in performance improvements in comparison to CSS QLDGM codes, while also allowing for greater flexibility in the design process. The proposed non-CSS QLDGM scheme outperforms the best quantum low-density parity check codes that have appeared in the literature.

Correlations and measures of entanglement in ground-state wave functions of relativistic quantum field theories are spatially localized over length scales set by the mass of the field. We utilize this localization to design digital quantum circuits for preparing the ground states of lattice scalar quantum field theories. Controlled rotations that are exponentially localized in their position-space extent are found to provide exponentially convergent wave function fidelity. These angles scale with the correlation between sites and the classical two-point correlation function, as opposed to the more localized mutual information or the hyperlocalized $(1\times 1)$-site negativity. We anticipate that further investigations will uncover quantum circuit designs with controlled rotations dictated by the measures of entanglement. This work is expected to impact quantum simulations of systems of importance to nuclear physics, high-energy physics, and basic energy sciences research.

Polymer self-consistent field theory techniques are used to find radial electron densities and total binding energies for isolated atoms. Quantum particles are modeled as Gaussian threads with ring-polymer architecture in a four-dimensional thermal space, and a Pauli potential is postulated based on classical excluded volume implemented in the thermal space using Edwards–Flory-Huggins interactions in a mean-field approximation. Other approximations include a Fermi-Amaldi correction for electron-electron self-interactions, a spherical averaging approximation to reduce the dimensionality of the problem, and the neglect of correlations. Polymer scaling theory is used to show that the excluded volume form of Pauli potential reduces to the known Thomas-Fermi energy density in the uniform limit. Self-consistent equations are solved using a bilinear Fourier expansion, with radial basis functions, for the first 18 elements of the periodic table. Radial electron densities show correct shell structure, and the errors on the total binding energies compared to known binding energies are less than $9\%$ for the lightest elements and drop to $3\%$ or less for atoms heavier than nitrogen. More generally, it is suggested that only two postulates are needed within classical statistical mechanics to achieve equivalency of predictions with static, nonrelativistic quantum mechanics: First, quantum particles are modeled as Gaussian threads in four-dimensional thermal space and, second, pairs of threads (allowing for spin) are subject to classical excluded volume in the thermal space. It is shown that these two postulates in thermal space become the same as the Heisenberg uncertainty principle and the Pauli exclusion principle in three-dimensional space.

We simulate the pump-probe experiments of lasing in molecular nitrogen ions with particular interest in the effects of rotational wave-packet dynamics. Our computations demonstrate that the coherent preparation of rotational wave packets in ${\mathrm{N}}_2{}^{+}$ by an intense short nonresonant pulse results in a modulation of the subsequent emission from $B^2{\mathrm{\Sigma }}_u{}^{+}\to X^2{\mathrm{\Sigma }}_g{}^{+}$ transitions induced by a resonant seed pulse. We model the dynamics of such pumping and emission using density-matrix theory to describe the ${\mathrm{N}}_2{}^{+}$ dynamics and the Maxwell wave equation to model the seed pulse propagation. We show that the gain and absorption of a delayed seed pulse is dependent on the pump-seed delay, that is, the rotational coherences excited by the pump pulse can modulate the gain and absorption of the delayed seed pulse. Further, we demonstrate that the coherent rotational dynamics of the nitrogen ions can cause lasing without electronic inversion.

Using numerically exact methods we examine the Fermi-Hubbard model on arbitrary cluster topology. We focus on the question of which systems eventually equilibrate or even thermalize after an interaction quench when initially prepared in a state highly entangled between system and bath. We find that constants of motion in integrable clusters prevent equilibration to the thermal state. We discuss the size of fluctuations during equilibration and thermalization and the influence of integrability. The influence of real-space topology and in particular of infinite-range graphs on equilibration and thermalization is studied.

To achieve the optimal phase sensitivity in two-mode interferometers, one key problem is how to distribute photons between the two input ports, given a fixed total average photon number. In both the $\text{SU}\left(2\right)$ and $\text{SU}(1,1)$ interferometers with a product of coherent and Fock states as inputs, we find there exists a critical value of the total photon number, below which the optimal phase sensitivity can be achieved with the second port being the vacuum state. The critical points can be analytically fixed. We further consider a more general input state as a product of coherent and squeezed Fock states. Then we analytically identify three regions in the parameter space, similar to a phase diagram, and find that critical phenomena occur in two regions. If the total average input photon number is less than the critical value, the optimal distribution tends to minimize the average photon number in the second port. Our finding indicates that, in order to get interferometers with high sensitivity, one must carefully choose the photon number distribution according to the value of the input total average photon number. This central result will be useful in theoretical studies in the field of quantum parameter estimation.

We investigate two models of a quantum system under rapid measurement performed to detect whether the system is in a given state $|{\psi }_{\mathrm{d}}\rangle$. In the first, the detection process is modeled via an imaginary potential $2i\hslash |{\psi }_{\mathrm{d}}\rangle \langle {\psi }_{\mathrm{d}}|/\tau$. In the second approach, repeated strong projective measurements are performed on the otherwise unitarily evolving system with a fixed high frequency $1/\tau$. We compare the statistics of the random time $T$ of first successful detection for the two models, considering both its probability density function $F\left(t\right)$ and the moments $\langle T^m\rangle$. We show, by a direct comparison of the two solutions, that both approaches yield the same results for $F\left(t\right)$ (and so the moments) in the small-$\tau$ limit, also called the Zeno limit, as long as the initial state $|{\psi }_{\mathrm{in}}\rangle$ is not parallel to the detection state, so that $|\langle {\psi }_{\mathrm{d}}|{\psi }_{\mathrm{in}}\rangle |<1$. When this condition is violated, however, the low probability density to detect the state on timescales much larger than $\tau$ is precisely a factor of 4 smaller in the non-Hermitian model. We express the solution of the Zeno limit of both problems formally in terms of an electrostatic analogy. Our results are corroborated by numerical simulations.

A quantum random-number generator (QRNG) can theoretically generate unpredictable random numbers with perfect devices and is an ideal and secure source of random numbers for cryptography. However, the practical implementations always contain imperfections, which will greatly influence the randomness of the final output and even open loopholes to eavesdroppers. Recently, Thewes et al. experimentally demonstrated a continuous-variable eavesdropping attack, based on heterodyne detection, on a trusted continuous-variable QRNG in Phys. Rev. A 100, 052318 (2019), yet like in many other practical continuous-variable QRNG studies, they always supposed the local oscillator was stable and ignored its fluctuation, which might lead to security threats such as wavelength attack. In this work, based on the theory of the conditional min-entropy, imperfections of the practical security of continuous-variable QRNGs are systematically analyzed, especially the local oscillator fluctuation under imbalanced homodyne detection. Experiments of a practical QRNG based on vacuum fluctuation are demonstrated to show the influence of local oscillator fluctuation on the total measurement noise variances and the practical conditional min-entropy with beam splitters of different transmittances. Moreover, a local oscillator monitoring method is proposed for the practical continuous-variable QRNG, which can be used to calibrate the practical conditional min-entropy.

We theoretically investigate the use of fast pulsed two-qubit gates for trapped ion quantum computing in a two-dimensional microtrap architecture. In one dimension, such fast gates are optimal when employed between nearest neighbors, and we examine the generalization to a two-dimensional geometry. We demonstrate that fast pulsed gates are capable of implementing high-fidelity entangling operations between ions in neighboring traps faster than the trapping period, with experimentally demonstrated laser repetition rates. Notably, we find that without increasing the gate duration high-fidelity gates are achievable even in large arrays with hundreds of ions. To demonstrate the usefulness of this proposal, we investigate the application of these gates to the digital simulation of a 40-mode Fermi-Hubbard model. This also demonstrates why shorter chains of gates required to connect arbitrary pairs of ions make this geometry well suited for large-scale computation.

A theoretical study is performed for the excitation of a single atom localized in the center of twisted light modes. Here we present the explicit dependence of excitation rates on critical parameters, such as the polarization of light, its orbital angular momentum projection, and the orientation of its propagation axis with respect to the atomic quantization axis. The effect of a spatial spread of the atom is also considered in detail. The expressions for transition rates obtained in this work can be used for any atom of arbitrary electronic configuration. For definiteness we apply them to the specific case of the ${}^{2}S_{1/2}(F=0)\to {}^{2}F_{7/2}(F=3,M=0)$ electric octupole (E3) transition in ${{}^{171}\mathrm{Yb}}^{+}$ ion. Our analytical and numerical results are suitable for the analysis and planning of future experiments on the excitation of electric-dipole-forbidden transitions by twisted light modes in optical atomic clocks.