We investigate the patterns in distributions of localizable entanglement over a pair of qubits for random multiqubit pure states. We observe that the mean of localizable entanglement increases gradually with increasing the number of qubits of random pure states while the standard deviation of the distribution decreases. The effects on the distributions, when the random pure multiqubit states are subjected to local as well as global noisy channels, are also investigated. Unlike the noiseless scenario, the average value of the localizable entanglement remains almost constant with the increase in the number of parties for a fixed value of noise parameter. We also find that the maximum strength of noise under which entanglement survives can be independent of the localizable entanglement content of the initial random pure states.

We explore the possibility of multiple usage of a single genuine entangled state by considering a scenario consisting of three spin-$\frac{1}{2}$ particles shared between Alice, Bob, and multiple Charlies. Alice performs measurements on the first particle, Bob performs measurements on the second particle, and multiple Charlies perform measurements on the third particle sequentially. Here the choice of measurement settings of each Charlie is independent and uncorrelated with the choices of measurement settings and outcomes of the previous Charlies. In this scenario, we investigate whether more than one Charlie can detect genuine tripartite entanglement, and we answer this question affirmatively. In order to probe genuine entanglement, we use correlation inequalities the violations of which certify genuine tripartite entanglement in a device-independent way. We extend our investigation by using appropriate genuine tripartite entanglement witness operators. Using each of these different tools for detecting genuine tripartite entanglement, we find out the maximum number of Charlies who can detect genuine entanglement in the above scenario.

We calculate theoretically the transverse magneto-optical Kerr effect (TMOKE) in the periodically patterned waveguide made from a diluted magnetic semiconductor. It is demonstrated that the TMOKE is resonantly enhanced when the incident wave is in resonance with the bound state in continuum, arising when the quality factor of the leaky waveguide mode increases due to far-field interference. Our results uncover the potential of all-dielectric and semiconductor nanostructures for resonant magneto-optics.

The achievement of quantum supremacy boosted the need for a robust medium of quantum information. In this task, higher-dimensional qudits show remarkable noise tolerance and enhanced security for quantum key distribution applications. However, to exploit the advantages of such states, we need a thorough characterization of their entanglement. Here, we propose a measure of entanglement which can be computed for either pure or mixed states of a $M$-qudit hybrid system. The entanglement measure is based on a distance deriving from an adapted application of the Fubini-Study metric. This measure is invariant under local unitary transformations and has an explicit computable expression that we derive. In the specific case of $M$-qubit systems, the measure assumes the physical interpretation of an obstacle to the minimum distance between infinitesimally close states. Finally, we quantify the robustness of entanglement of a state through the eigenvalue analysis of the metric tensor associated with it.

Efficient simulation of quantum computers is essential for the development and validation of near-term quantum devices and the research on quantum algorithms. Up to date, two main approaches to simulation have been use, based on either full-state or single-amplitude evaluation. We propose an algorithm that efficiently interpolates between these two possibilities. Our approach elucidates the connection between quantum circuit simulation and partial evaluation of expressions in tensor algebra.

We propose a theoretical framework to quantitatively describe physical unclonable functions (PUFs), including extensions to quantum protocols, so-called quantum readout PUFs (QR-PUFs). (QR-) PUFs are physical systems with challenge-response behavior intended to be hard to clone or simulate. Their use has been proposed in several cryptographic protocols, with particular emphasis on authentication. Here, we provide theoretical assumptions and definitions behind the intuitive ideas of (QR-) PUFs. This allows us to quantitatively characterize the security of such devices in cryptographic protocols. First, by generalizing previous ideas, we design a general authentication scheme which is applicable to different physical implementations of both classical PUFs and (QR-) PUFs. Then, we define the robustness and the unclonability, which allows us to derive security thresholds for (QR-) PUF authentication and paves the way to develop further new authentication protocols.

Although Majorana platforms are promising avenues toward realizing topological quantum computing, they are still susceptible to errors from thermal noise and other sources. We show that the error rate of Majorana qubits can be drastically reduced using a one-dimensional repetition code. The success of the code is due the imbalance between the phase error rate and the flip error rate. We demonstrate how a repetition code can be naturally constructed from segments of Majorana nanowires. We find the optimal lifetime may be extended from a millisecond to over one second.

We explore the quantum Coulomb problem for two-body bound states, in $D=3$ and $D=3-2\epsilon$ dimensions, in detail, and give an extensive list of expectation values that arise in the evaluation of QED corrections to bound-state energies. We describe the techniques used to obtain these expectation values and give general formulas for the evaluation of integrals involving associated Laguerre polynomials. In addition, we give formulas for the evaluation of integrals involving subtracted associated Laguerre polynomials, those with low powers of the variable subtracted off, that arise when evaluating divergent expectation values. We present perturbative results (in the parameter $\epsilon$) that show how bound-state energies and wave functions in $D=3-2\epsilon$ dimensions differ from their $D=3$ dimensional counterparts and use these formulas to find regularized expressions for divergent expectation values such as $〈{\overline{V}}^3〉$ and $〈{\left({\overline{V}}^{\prime }\right)}^2〉$ where $\overline{V}$ is the $D$-dimensional Coulomb potential. We evaluate a number of finite $D$-dimensional expectation values such as $〈r^{-2+4\epsilon }{\partial }_r^2〉$ and $〈r^{4\epsilon }{p}^4〉$ that have $\epsilon \to 0$ limits that differ from their three-dimensional counterparts $〈r^{-2}{\partial }_r^2〉$ and $〈p^4〉$. We explore the use of recursion relations, the Feynman-Hellmann theorem, and momentum-space brackets combined with $D$-dimensional Fourier transformation for the evaluation of $D$-dimensional expectation values. The results of this paper are useful when using dimensional regularization in the calculation of properties of Coulomb bound systems.

We study the tunneling ionization (TI) of Ni, ${\mathrm{Ni}}^{+}$, and ${\mathrm{Ni}}^{2+}$ with a time-dependent density-functional-theory method and reproduce the puzzling suppression of the TI of Ni and ${\mathrm{Ni}}^{+}$ and the enhancement of TI in ${\mathrm{Ni}}^{2+}$. Numerical results reveal that for all three species the electron tunnels from a $4s$ orbital; that is, excitation precedes tunneling for both of the cations, for which the highest orbitals are $3d$. The effective radial potentials for the $d$ orbitals have a centrifugal barrier, while there is no such barrier for the $s$ orbitals. At the classical turning point for the $3d$ orbital, the $3d$ to $4s$ excitation energy is lower than the centrifugal potential for the $d$ orbitals. Two factors of opposite nature are identified in this work. On the one hand, electrons moving away from the nucleus in the intense laser fields induce an attractive potential that effectively lowers the energy level and thus suppresses tunneling. Excitation, on the other hand, has the opposite effect and enhances tunneling. The energy gap between $4s$ and $3d$ is small for ${\mathrm{Ni}}^{+}$ and therefore suppression wins. As the charge of the cation increases, the excitation energy becomes much greater, and for ${\mathrm{Ni}}^{2+}$ enhancement dominates. Based on a similar analysis, we expect enhanced TI for several transition-metal cations of charge 2 and higher.

We study the dynamics of the many-body atomic kicked rotor with interactions at the mean-field level, governed by the Gross-Pitaevskii equation. We show that dynamical localization is destroyed by the interaction and replaced by a subdiffusive behavior. In contrast to results previously obtained from a simplified version of the Gross-Pitaevskii equation, the subdiffusive exponent does not appear to be universal. By studying the phase of the mean-field wave function, we propose an alternative approximation that describes correctly the dynamics at experimentally relevant times close to the start of subdiffusion, while preserving the reduced computational cost of the former approximation.

The spontaneous parametric down-conversion of photons has been widely applied for generating entangled photon pairs. We theoretically explore the entangled down-converted state of the photon pair, also known as biphoton state, for both degenerate and nondegenerate photon pairs. In particular, the spatial structure of the biphoton state has been expressed in Bessel modes to better understand the correlation with regard to the opening angle ${\vartheta }_k$ of Bessel modes. In fact, the opening angles of the down-converted photon pair are not independent of each other, but rather are correlated. Furthermore, we confirm the experimentally observed conditions concerning the optimization of generating high-degree spatial entanglement by controlling the beam waist of the pump beam. We also introduce a new experimental setup for efficient measurement of the spatial entanglement of the biphoton state using geometrical optics arguments.

We study theoretically the radiative lifetime of bound two-particle excitations in a waveguide with an array of two-level atoms, realizing a one-dimensional Dicke-like model. Recently, Zhang et al. have numerically found an unexpected sharp maximum of the bound pair lifetime when the array period $d$ is equal to $1/12\mathrm{th}$ of the light wavelength ${\lambda }_0$ [Phys. Rev. Research 2, 013173 (2020)]. We uncover a rigorous transformation from the non-Hermitian Hamiltonian with the long-range radiative coupling to the nearest-neighbor coupling model with the radiative losses only at the edges. This naturally explains the puzzle of long lifetime: the effective mass of the bound photon pair also diverges for $d={\lambda }_0/12$, hampering an escape of photons through the edges. We also link the oscillations of the lifetime with the number of atoms to the nonmonotonous quasi-flat-band dispersion of the bound pair.

A non-Hermitian coupled waveguide system with periodically varying parameters, in which the Berry curvature is analogous to a hyperbolic magnetic monopole or antimonopole, is investigated. It is shown to have a purely imaginary Berry connection and is consequently influenced by a geometric multiplier. It is possible for this multiplier to induce net gain or loss in the system, corresponding to the existence of the antimonopole or monopole in parameter space, respectively. For the right choice of parameters, the system will display an apparent nonadiabatic change in behavior, which implies a switch between the dominant eigenstate in the waveguides, leading to a change in parameter space analogous to a charge reversal of the hyperbolic magnetic monopole.

We study the preparation of coherent quantum states in a two-photon micromaser for applications in quantum metrology. While this setting can be in principle realized in a host of physical systems, we consider atoms interacting with the field of a cavity. We focus on the case of the interaction described by the Jaynes-Cummings Hamiltonian, which cannot be achieved by the conventional approach with three-level atoms coupled to the cavity field at two-photon resonance. We find that additional levels are required in order to cancel Stark shifts emerging in the leading order. Once this is accomplished, the dynamics of the cavity features a degenerate stationary state manifold of pure states. We derive the analytic form of these states and show that they include Schrödinger cat states with a tunable mean photon number. We also confirm these states can be useful in phase estimation protocols with their quantum Fisher information exceeding the standard limit. To account for realistic imperfections, we consider single-photon losses from the cavity, finite lifetime of atom levels, and higher order corrections in the far-detuned limit, which result in metastability of formerly stationary cavity states and long-time dynamics with a unique mixed stationary state. Despite being mixed, this stationary state can still feature quantum Fisher information above the standard limit. Our work delivers a comprehensive overview of the two-photon micromaser dynamics with particular focus on application in phase estimation and, while we consider the setup with atoms coupled to a cavity, the results can be directly translated to optomechanical systems.

Photons are useful quantum systems for investigating the fundamental and practical aspects of dephasing, decoherence, and other types of open quantum dynamics. However, descriptions of open dynamics of photonic systems are usually in terms of decoherence functions and in many cases an explicit master-equation-based description is not available. This is particularly true when considering multipartite photonic open systems having possibly correlated environments. We obtain generic master equations for the reduced dephasing dynamics of a two-photon polarization state coupled to respective frequency degrees of freedom when the frequency degrees of freedom that form the environment are initially correlated. Our results show the explicit dependence of the operator form of the master equation and the decay rates on these correlations as well as on various types of frequency distributions. Furthermore, we use the recently developed bath-positive decomposition method to treat an initially correlated polarization-frequency state of a photon and demonstrate how this allows us to gain new insight and detailed information on how the contributions of different origins influence the photonic dephasing.

The no-signaling principle preventing superluminal communication is a limiting paradigm for physical theories. Within the information-theoretic framework it is commonly understood in terms of admissible correlations in composite systems. Here we unveil its complementary incarnation—the ”dynamical no-signaling principle”—which forbids superluminal signaling via measurements on simple physical objects (e.g., particles) evolving in time. We show that it imposes strong constraints on admissible models of dynamics. The posited principle is universal; it can be applied to any theory (classical, quantum, or postquantum) with well-defined rules for calculating detection statistics in spacetime. As an immediate application we show how one could exploit the Schrödinger equation to establish a fully operational superluminal protocol in the Minkowski spacetime. This example illustrates how the principle can be used to identify the limits of applicability of a given model of quantum or postquantum dynamics.

We design and implement an atomic frequency comb quantum memory for 793-nm wavelength photons using a monolithic cavity based on a thulium- (Tm-) doped ${\mathrm{Y}}_3{\mathrm{Al}}_5{\mathrm{O}}_{12}$ crystal. Approximate impedance matching results in the absorption of 90% of input photons and a memory efficiency of $(27.5\pm 2.7)\%$ over a 500-MHz bandwidth. The cavity enhancement leads to a significant improvement over the previous efficiency in Tm-doped crystals using a quantum memory protocol. In turn, this allows us to store and recall quantum states of light in such a memory. Our results demonstrate progress toward efficient and faithful storage of single-photon qubits with a large time-bandwidth product and multimode capacity for quantum networking.

In the present study we have investigated the ionization threshold behavior of neon cluster ions ${\mathrm{Ne}}^{n+}$ (with $n=2-6$) formed upon the electron ionization of small neon clusters. The clusters were formed by supersonic expansion of cold neon gas through a pinhole nozzle. The appearance energies for these cluster ions were subsequently determined using a nonlinear least-squares fitting procedure. The obtained thresholds turned out to be only slightly lower than the ionization energy of the single neon atom. The present results are compared with previous electron impact and photoionization results. In addition, we investigated the electron ionization of neon clusters doped with $\mathrm{C}{\mathrm{O}}_2$ molecules. The mass spectrum at the electron energy of 70 eV showed predominantly bare cluster ions of $\mathrm{C}{\mathrm{O}}_2$. Charged clusters with fragments of $\mathrm{C}{\mathrm{O}}_2$ were observed as well, though in weaker abundance than the intact cluster ions. The relative abundance of these fragment ions was different from the ratios previously reported for electron ionization of bare $\mathrm{C}{\mathrm{O}}_2$ clusters and indicated increased formation of ${\left(\mathrm{C}{\mathrm{O}}_2\right)}_4{{\mathrm{O}}_2}^{+}$ due to a neon matrix effect. We further investigated the ionization mechanisms in the cluster by measuring the ion yields of ${{\left(\mathrm{C}{\mathrm{O}}_2\right)}_4}^{+}$ as a function of the electron energy close to the threshold. Direct ionization by the incoming electron, Penning ionization, and charge-transfer ionization were identified as possible processes, with varying contributions for different initial mean neon cluster sizes.