The entanglement content of superpositions of pairs of degenerate eigenstates of a bipartite system is considered in the case that both eigenstates are also eigenstates of the $z$ component of the total angular momentum. It is shown that the von Neumann entropy of the state that is obtained tracing out one of the parts of the system has a definite convexity (concavity) as a function of the superposition parameter and that its convexity (concavity) can be predicted using a quantity of information that measures the entropy shared by the states at the extremes of the superposition. Several examples of two-particle systems, whose eigenfunctions and density matrices can be obtained exactly, are analyzed thoroughly.

Variational, nonrelativistic energies have been calculated for the ground state (${}^3{P}_g$) and the lowest quintuplet state (${}^5{S}_u$) of the carbon atom, with wave functions expressed in the basis of symmetry-projected, explicitly correlated Gaussian lobe functions. New exact limits of these energies have been estimated, amounting to $-37.844906\left(4\right)$ and $-37.691751\left(2\right)$ hartree. With finite nuclear masses and leading, scalar relativistic corrections included, respective experimental excitation energy of ${}^{12}\mathrm{C}$ has been reproduced with accuracy of about 7 ${\mathrm{cm}}^{-1}$.

We present measurements of the charge-exchange reaction rate between neutral sodium (Na) and ionized calcium (${\mathrm{Ca}}^{+}$) in a hybrid atom-ion trap, which is comprised of a Na magneto-optical trap concentric with a linear Paul trap. Once the Na and ${\mathrm{Ca}}^{+}$ are co-trapped, the reaction rate is measured by continuously quenching the reaction product ${\mathrm{Na}}^{+}$ from the ion trap, and then destructively measuring the decay of the remaining ion population. The reactants' electronic state and temperature are experimentally controlled, allowing us to determine the four individual reaction rates between $\text{Na}\left[S\text{or}P\right]$ and ${\text{Ca}}^{+}\left[S\text{or}D\right]$ at different collision energies. With the exception of the largest reaction-rate channel ($\text{Na}\left[P\right]+{\text{Ca}}^{+}\left[D\right]$), our rates are consistent with the classical Langevin rate limit. We have also found evidence of reactant collision-energy thresholds associated with two of the four entrance channels.

Recent experiments with strongly interacting, driven Rydberg ensembles have introduced a promising setup for the study of self-organized criticality (SOC) in cold atom systems. Based on this setup, we theoretically propose a control mechanism for the paradigmatic avalanche dynamics of SOC in the form of a time-dependent drive amplitude. This gives access to a variety of avalanche dominated, self-organization scenarios, prominently including self-organized criticality, as well as sub- and supercritical dynamics. We analyze the dependence of the dynamics on external scales and spatial dimensionality. It demonstrates the potential of driven Rydberg systems as a playground for the exploration of an extended SOC phenomenology and their relation to other common scenarios of SOC, such as, e.g., in neural networks and on graphs.

We study conditions for aberration-free imaging of inelastic x-ray-scattering (IXS) spectra with x-ray echo spectrometers. Aberration-free imaging is essential for achieving instrumental functions with high resolution and high contrast. Computational ray tracing is applied to a thorough analysis of a $0.1\mathrm{meV}/0.07-{\mathrm{nm}}^{-1}$-resolution echo-type IXS spectrometer operating with 9-keV x rays. We show that IXS spectra imaged by the x-ray echo spectrometer that uses lenses for the collimating and focusing optics are free of aberrations. When grazing incidence mirrors (paraboloidal, parabolic Kirkpatrick-Baez, or parabolic Montel) are used instead of the lenses, the imaging system reveals some defocus aberration that depends on the inelastic energy transfer. However, the aberration-free images can be still recorded in a plane that is tilted with respect to the optical axis. This distortion can be thus fully compensated by inclining appropriately the x-ray imaging detector, which simultaneously improves its spatial resolution. A full simulation of imaging IXS spectra from a realistic sample demonstrates the excellent performance of the proposed designs.

In this paper we study the minimum error discrimination problem (MED) for ensembles of linearly independent (LI) states. We define a bijective map from the set of those ensembles to itself and we show that the pretty good measurement (PGM) and the optimal measurement for the MED are related by the map. In particular, the fixed points of the map are those ensembles for which the PGM is the optimal measurement. Also, we simplify the optimality conditions for the measurement of an ensemble of LI states.

Qubit, operator, and gate resources required for the digitization of lattice $\lambda {\varphi }^4$ scalar field theories onto quantum computers are considered, building upon the foundational work by Jordan et al. [Quantum Inf. Comput. 14, 1014 (2014); Science 336, 1130 (2012)], with a focus towards noisy intermediate-scale quantum devices. The Nyquist-Shannon sampling theorem, introduced in this context by Macridin et al. [Phys. Rev. A 98, 042312 (2018)] building on the work of Somma [Quantum Inf. Comput. 16, 1125 (2016)], provides a guide with which to evaluate the efficacy of two field-space bases, the eigenstates of the field operator, as used by Jordan et al., and eigenstates of a harmonic oscillator, to describe ($0+1$)- and ($d+1$)-dimensional scalar field theory. We show how techniques associated with improved actions, which are heavily utilized in lattice QCD calculations to systematically reduce lattice-spacing artifacts, can be used to reduce the impact of the field digitization in $\lambda {\varphi }^4$, but are found to be inferior to a complete digitization improvement of the Hamiltonian using a quantum Fourier transform. When the Nyquist-Shannon sampling theorem is satisfied, digitization errors scale as $|log|log|{\epsilon }_{\mathrm{dig}}\left||\right|\sim n_Q$ (number of qubits describing the field at a given spatial site) for the low-lying states, leaving the familiar power-law lattice-spacing and finite-volume effects that scale as $|log|{\epsilon }_{\mathrm{latt}}||\sim N_Q$ (total number of qubits in the simulation). For localized (delocalized) field-space wave functions, it is found that $n_Q\sim 4\left(7\right)$ qubits per spatial lattice site are sufficient to reduce theoretical digitization errors below error contributions associated with approximation of the time-evolution operator and noisy implementation on near-term quantum devices. Only classical computing resources have been used to obtain the results presented in this work.

Quantum cryptographic protocols are typically analyzed by assuming that potential opponents can carry out all physical operations, an assumption which grants capabilities far in excess of present technology. Adjusting this assumption to reflect more realistic capabilities is an attractive prospect, but one that can only be justified with a rigorous, quantitative framework that relates adversarial restrictions to the protocol's security and performance. We investigate the effect of limitations on the eavesdropper's (Eve's) ability to make a coherent attack on the security of continuous-variable quantum key distribution (CV-QKD). We consider a realistic attack in which the total decoherence induced during the attack is modeled by a Gaussian channel. Based on our decoherence model, we propose an optimal hybrid attack, which allows Eve to perform a combination of both coherent and individual attacks simultaneously. We evaluate the asymptotic and composable finite-size security of a heterodyne CV-QKD protocol against such hybrid attacks in terms of Eve's decoherence. We show that when the decoherence is greater than a threshold value, Eve's most effective strategy is reduced to the individual attack. Thus, if we are willing to assume that the decoherence caused by the memory and the collective measurement is large enough, it is sufficient to analyze the security of the protocol only against individual attacks, which significantly improves the CV-QKD performance in terms of both the key rate and maximum secure transmission distance.

Entanglement of formation quantifies the entanglement of a state in terms of the entropy of entanglement of the least entangled pure state needed to prepare it. An analytical expression for this measure exists only for special cases, and finding a closed formula for an arbitrary state remains an open problem. In this work we focus on two-mode Gaussian states, and we derive narrow upper and lower bounds for the measure that get tight for several special cases. Further, we show that the problem of calculating the actual value of the entanglement of formation for arbitrary two-mode Gaussian states reduces to a trivial single parameter optimization process, and we provide an efficient algorithm for the numerical calculation of the measure.

Quantum theory allows for randomness generation in a device-independent setting, where no detailed description of the experimental device is required. Here we derive a general upper bound on the amount of randomness that can be certified in such a setting. Our bound applies to any black-box scenario, thus covering a wide range of scenarios from partially characterized to completely uncharacterized devices. Specifically, we prove that the number of random bits that can be certified is limited by the number of different input states that enter the measurement device. We show explicitly that our bound is tight in the simplest cases. More generally, our paper indicates that the prospects of certifying a large amount of randomness by using high-dimensional (or even continuous variable) systems will be extremely challenging in practice.

We report experimental and theoretical investigations of ultrafast coherent dynamics in a photonic-crystal point-defect nanocavity. The experimental investigations are carried out using a versatile heterodyne pump-probe setup giving access to wavelength and time-resolved dynamics. We find that parametric processes originating from coherent interactions between the pump and the probe lead to characteristic and clearly distinguishable features in the time-resolved dynamics. The parametric process is caused by fast oscillations of spatially trapped carriers, with the nanocavity acting to enhance the optical fields and thereby the strength of these processes. This interpretation is confirmed by the good agreement that is obtained with a theoretical model, which extends previous works by taking into account wave-mixing effects among the probe and pump pulse. The physics behind the parametric process is explained in detail and a simple expression is derived for the conditions under which coherent interactions lead to high-transmission bands for the probe pulses. These results are important for understanding how coherent effects can be used to improve the dynamical properties of nanocavity switches.

We address linear and nonlinear topological interface states in polariton condensates excited at the interface of the honeycomb and Lieb arrays of microcavity pillars in the presence of spin-orbit coupling and Zeeman splitting in the external magnetic field. Such interface states appear only in total energy gaps of the composite structure when parameters of the honeycomb and Lieb arrays are selected such that some topological gaps in the spectrum of one of the arrays overlap with topological or nontopological gaps in the spectrum of the other array. This is in contrast to conventional edge states at the interface of periodic topological and uniform trivial insulators, whose behavior is determined exclusively by the spectrum of the topological medium. The number of emerging interface states is determined by the difference of the Chern numbers of the overlapping gaps. Illustrative examples with one or two coexisting unidirectional interface states are provided. The representative feature of the system is the possibility of wide tuning of the concentration of power of the interface states between two limiting cases when practically all power is concentrated either in the Lieb or the honeycomb array. Localization of the interface states and their penetration depth into arrays drastically vary with Bloch momentum or upon modification of the amplitude of the interface state in the nonlinear regime. We illustrate topological protection of the interface states manifested in the absence of backscattering on interface defects, and study their modulation instability in the nonlinear regime. The latter leads to formation of quasisolitons whose penetration into different arrays also depends on Bloch momentum. In addition, we discuss the impact of losses and coherent pump leading to bistability of the interface states.

Coherent interaction between photons and phonons plays a central role in cavity optomechanics. Additional physical degrees of freedom, such as electrons or atoms, can control the optomechanical interaction and thus serve as a coherent link between photons and phonons. Here, we study cavity optomechanics in a semiconductor gain medium where the inverted carriers interact collectively with the photons and phonons via the carrier relaxation oscillation and optical gain effects. With carrier relaxation oscillation, the carriers are coupled coherently to the mechanical modes via the optical field, which can be used to manipulate the phonon state. With optical gain effect, the inverted carrier population can tune the interaction between photons and phonons, rendering an enhancement of optomechanically induced slow light effect and a transition from optomechanically induced transparency to optomechanically induced absorption. The semiconductor-laser-based optomechanical systems offer substantial flexibility in coherent control of the photons and phonons, which may find wide applications in quantum metrology, information processing, and semiconductor laser engineering.

Coherent x-ray beams with energies $\ge 50\mathrm{keV}$ can potentially enable three-dimensional imaging of atomic lattice distortion fields within individual crystallites in bulk polycrystalline materials through Bragg coherent diffraction imaging (BCDI). However, the undersampling of the diffraction signal due to Fourier-space compression at high x-ray energies renders conventional phase-retrieval algorithms unsuitable for three-dimensional reconstruction. To address this problem, we utilize a phase-retrieval method with a Fourier constraint specifically tailored for undersampled diffraction data measured with coarse-pitched detector pixels that bin the underlying signal. With our approach, we show that it is possible to reconstruct three-dimensional strained crystallites from an undersampled Bragg diffraction data set subject to pixel-area integration without having to physically upsample the diffraction signal. Using simulations and experimental results, we demonstrate that explicit modeling of Fourier-space compression during phase retrieval provides a viable means by which to invert high-energy BCDI data, which is otherwise intractable.

In their study of superluminal propagation, rotary drag, and surface polaritons [Khan et al., Phys. Rev. A 96, 013848 (2017); Phys. Rev. A 96, 049906(E) (2017)], the authors consider a four-level atomic arrangement with transitions in the optical domain. In fact, the values they give to the parameters lead to a probe wavelength lying in the decimeter band and we point out that, in such conditions, all their results are irrelevant.

Hereby, we amend several spectral parameters reported in our earlier work [N. Khan et al., Phys. Rev. A 96, 013848 (2017); Phys. Rev. A 96, 049906(E) (2017)], which led to unphysical predictions to be tested experimentally. In particular, the resulting probe wavelength was in the decimeter band, as pointed out in a Comment by Macke and Ségard [B. Macke and B. Ségard, preceding Comment, Phys. Rev. A 99, 057801 (2019)]. After incorporating the corrected parameters, the predictions of our theoretical demonstration on the gain-assisted superluminal propagation and rotary drag of photon and that of surface plasmon polaritons are improved to a good degree of accuracy and expected to be tested realistically. In particular, even the minimum values of rotary drag for both photon and surface plasmon polaritons are on the order of few microradians, thus falling within the range of experimental testability.

We analytically calculate the leading quantum corrections of the ground-state energy of two- and one-dimensional weakly interacting Rabi-coupled Bose-Bose mixtures in the frame of the Bogoliubov approximation. We show that to repulsive intraspecies and attractive interspecies interactions, the effect of quantum fluctuations favors the formation of self-bound droplets. These liquidlike states are crucially affected by the Rabi coupling, leading thus to the appearance of a quantum instability. We derive meaningful formulas to describe the droplet phase in the one-dimensional case.

We address the breakdown of the bulk-boundary correspondence observed in non-Hermitian systems, where open and periodic systems can have distinct phase diagrams. The correspondence can be completely restored by considering the Hamiltonian's singular-value decomposition instead of its eigendecomposition. This leads to a natural topological description in terms of a flattened singular decomposition. This description is equivalent to the usual approach for Hermitian systems and coincides with a recent proposal for the classification of non-Hermitian systems. We generalize the notion of the entanglement spectrum to non-Hermitian systems, and show that the edge physics is indeed completely captured by the periodic bulk Hamiltonian. We exemplify our approach by considering the chiral non-Hermitian Su-Schrieffer-Heger and Chern insulator models. Our work advocates a different perspective on topological non-Hermitian Hamiltonians, paving the way to a better understanding of their entanglement structure.

The dynamics of an open quantum system is non-Markovian when memory effect is non-negligible. The quantum memory effect is a very complex issue and presently there is no universally accepted method to quantify it. By examining the memory kernel of the Nakajima-Zwanzig master equation, we study the memory effect in a theoretical model consisting of a spin coupled to an environment of an Ising spin chain subject to a transverse field. We find that it can be dictated by either the time correlation in the environment, or the system-environment correlation, depending on the strength of the transverse field and the state of the environment. We analyze the information loss to the environment and backflow from it, and discover that the information flow is not always a reliable indicator for the nature of the dynamics.

We study the possibility of observing Schwinger pair production enhanced by a thermal bath of photons. We consider the full range of temperatures and electric field intensities from pure Schwinger production to pure thermal production, and identify the most promising and interesting regimes. In particular, we identify temperatures of $\sim 20\mathrm{keV}/k_B$ and field intensities of $\sim {10}^{23}\mathrm{W}{\mathrm{cm}}^{-2}$ where pair production would be observable. In this case, the thermal enhancement over the Schwinger rate is exponentially large and due to effects which are not visible at any finite order in the loop expansion. Pair production in this regime can thus be described as more nonperturbative than the usual Schwinger process, which appears at one loop. Unfortunately, such high temperatures appear to be out of reach of foreseeable technologies, though nonthermal photon distributions with comparable energy densities are possible. We suggest the possibility that similar nonperturbative enhancements may extend out of equilibrium and propose an experimental scheme to test this.