We consider the problem of interconverting a finite amount of resources within all theories whose single-shot transformation rules are based on a majorization relation, e.g., the resource theories of entanglement and coherence (for pure-state transformations), as well as thermodynamics (for energy-incoherent transformations). When only finite resources are available we expect to see a nontrivial trade-off between the rate $r_n$ at which $n$ copies of a resource state $\rho$ can be transformed into $n{r}_n$ copies of another resource state $\sigma$, and the error level ${\epsilon }_n$ of the interconversion process, as a function of $n$. In this work we derive the optimal trade-off in the so-called moderate deviation regime, where the rate of interconversion $r_n$ approaches its optimum in the asymptotic limit of unbounded resources ($n\to \infty$), while the error ${\epsilon }_n$ vanishes in the same limit. We find that the moderate deviation analysis exhibits a resonance behavior which implies that certain pairs of resource states can be interconverted at the asymptotically optimal rate with negligible error, even in the finite $n$ regime.

Reliable entangling gates for qubits encoded in single-photon states represent a major challenge on the road to scalable quantum computing architectures based on linear optics. In this work, we present two approaches to develop high-fidelity, near-deterministic controlled-sign-shift gates based on the techniques of quantum gate teleportation. On the one hand, teleportation in a discrete-variable setting, i.e., for qubits, offers unit-fidelity operations but suffers from low success probabilities. Here, we apply recent results on advanced linear optical Bell measurements to reach a near-deterministic regime. On the other hand, in the setting of continuous variables, associated with coherent states, squeezing, and, typically, Gaussian states, teleportation can be performed in a deterministic fashion, but the finite amount of squeezing implies an inevitable deformation of a teleported single-mode state. Using a new generalized form of the nonlinear-sign-shift gate for gate teleportation, we are able to achieve fidelities of the resulting controlled-sign gate above $90\%$. A special focus is also put on a comparison of the two approaches, not only with respect to fidelity and success probability, but also in terms of resource consumption.

Quantum state teleportation is a protocol where a shared entangled state is used as a quantum channel to transmit quantum information between distinct locations. Here we consider the task of estimating entanglement of the underlying shared state in teleportation protocols. We show that the data accessible in a teleportation experiment allows us to put a lower bound on some entanglement measures, such as entanglement negativity and robustness. Furthermore, we show cases in which the lower bounds are tight. The introduced lower bounds can also be interpreted as quantifiers of the nonclassicality of a teleportation experiment. Thus, our findings provide a quantitative relation between teleportation and entanglement.

The dynamic polarizabilities of the atomic states with angular momentum $j>1/2$ are sensitive to the angle between the quantization axis ${\widehat{e}}_z$ and the polarization vector $\widehat{\epsilon }$ owing to the contribution of anisotropic tensor polarizabilities. The magic wavelength at which the differential Stark shift of an atomic transition nullifies depends on this angle. We identified the magic wavelengths for the $4s_{1/2}\to 3d_{3/2,5/2}$ transitions of ${\mathrm{Ca}}^{+}$ ions at different angles between ${\widehat{e}}_z$ and $\widehat{\epsilon }$ in the case of linearly polarized light. The magic wavelengths near 395.79 nm, which lie between the $4s_{1/2}\to 4p_{1/2}$ and $4s_{1/2}\to 4p_{3/2}$ transition wavelengths, remain insensitive to the angle, while the longest magic wavelength, which is around 1000 nm, for each of the magnetic sublevel transitions is very sensitive to the angle. We suggest that accurate measurements on the longest magic wavelengths for the $4s_{1/2}\to 3d_{5/2}$ and $4s_{1/2}\to 3d_{3/2}$ transitions can be used to determine the oscillator strengths for the $4s_{1/2}\to 4p_{1/2,3/2}, 3d_{5/2}\to 4p_{3/2}$, and $3d_{3/2}\to 4p_{1/2,3/2}$ transitions, and the difference of the static polarizabilities of the $4s_{1/2}$ and $3d_{5/2}$ states, and the tensor polarizability of the $3d_{5/2}$ state.

The collective strong coupling of rubidium atoms in a magneto-optical trap (MOT) to the Laguerre-Gaussian (LG) modes of a Fabry-Pérot cavity is investigated. Bright and dark ${}^{85}\mathrm{Rb}$ MOT atoms are prepared at the geometric center of the cavity, and the vacuum Rabi splitting (VRS) of the collectively coupled atom-cavity system is measured for ${\mathrm{LG}}_{l0}$ ($l=0,1,2,3$) modes. The atom number coupled to the cavity mode depends on the overlap of the atomic density distribution and the specific spatial mode function, which is reflected in the measured VRS spectrum. The known mode function and the measured VRS can then be used to test whether the atomic density distribution in the experiment is Gaussian or uniform. A simple theoretical model for this process is described, and the experimental measurements are found to be in close agreement with the model.

Optical high-order sideband generation, creating new frequencies with equal spectral separation, has developed potential applications in optical communication and metrology. Here, we investigate the generation of optomechanically induced high-order optical sideband spectra in an optical parity-time ($\mathcal{PT}$) -symmetric system. The system consists of an active optical mode, a passive optical mode, and a mechanical mode, where the mechanical mode is optomechanically coupled with the passive optical mode. Based on numerical analysis, the $\mathcal{PT}$-symmetric system enhances sideband spectra in both amplitude and number of sidebands. With certain parameters, forty sidebands head up on both sides of the control field near the exceptional point. The capability to generate optical high-order sidebands and control light propagation in micro- and nanomechanical systems may open up a promising perspective for complex integrated $\mathcal{PT}$ devices.

We study how the feature of chiral edge transport changes in photonic Floquet topological insulators when the driving is not perfectly periodic and the system is under the effect of disorders. Assuming that the aperiodicity is caused by fluctuations in the driving, we find that the fluctuations with finite correlation time can cause leakage of chiral edge excitations into the bulk of the system. For fluctuations with short correlation time, an effective master equation that captures the leakage of edge excitations is derived. When the correlation time of the fluctuations is longer than the typical time of the system, the lifetime of chiral edge excitations increases as a power of the correlation time. The lifetime of chiral edge excitations is insensitive to disorders with short correlation time, though when the disorder is strong enough, the lifetime of pointlike edge excitations can be several orders of magnitude longer than the lifetime of chiral edge excitations. The loss of photons into environment cannot stop the leakage of photons into the bulk of the system, but it eventually determines the lifetime of the excitation in the system. On the contrary, the chiral edge transport is robust against the quasirandom fluctuations.

We propose a curious protocol for swapping the intraphoton entanglement between path and polarization degrees of freedom of a single photon to interphoton entanglement between two distance photons that have never interacted. This is accomplished by using an experimental setup consisting of three suitable Mach-Zehnder interferometers along with number of beam splitters, polarization rotators, and detectors. Using the same setup, we have also demonstrated an interesting quantum state transfer protocol, symmetric between Alice and Bob. Importantly, the Bell-basis discrimination is not required in both the swapping and state transfer protocols. Our proposal can be implemented using linear optical devices.

An important application for near-term quantum computing lies in optimization tasks, with applications ranging from quantum chemistry and drug discovery to machine learning. In many settings, most prominently in so-called parametrized or variational algorithms, the objective function is a result of hybrid quantum-classical processing. To optimize the objective, it is useful to have access to exact gradients of quantum circuits with respect to gate parameters. This paper shows how gradients of expectation values of quantum measurements can be estimated using the same, or almost the same, architecture that executes the original circuit. It generalizes previous results for qubit-based platforms, and proposes recipes for the computation of gradients of continuous-variable circuits. Interestingly, in many important instances it is sufficient to run the original quantum circuit twice while shifting a single gate parameter to obtain the corresponding component of the gradient. More general cases can be solved by conditioning a single gate on an ancilla.

Polar diatomic molecules that have, or are expected to have, a ${}^2\mathrm{\Sigma }_{1/2}$-ground state are studied systematically with respect to simultaneous violation of parity $\mathcal{P}$ and time-reversal $\mathcal{T}$ with numerical methods and analytical models. Enhancements of $\mathcal{P},\mathcal{T}$-violating effects due to an electric dipole moment of the electron (eEDM) and $\mathcal{P},\mathcal{T}$-odd scalar-pseudoscalar nucleon-electron current interactions are analyzed by comparing trends within columns and rows of the periodic table of the elements. For this purpose electronic structure parameters are calculated numerically within a quasirelativistic zeroth order regular approximation (ZORA) approach in the framework of complex generalized Hartree-Fock (cGHF) or Kohn-Sham (cGKS). Scaling relations known from analytic relativistic atomic structure theory are compared to these numerical results. Based on this analysis, problems of commonly used relativistic enhancement factors are discussed. Furthermore, the ratio between both $\mathcal{P},\mathcal{T}$-odd electronic structure parameters mentioned above is analyzed for various groups of the periodic table. From this analysis an analytic measure for the disentanglement of the two $\mathcal{P},\mathcal{T}$-odd electronic structure parameters with multiple experiments in dependence of electronic structure enhancement factors is derived.

We present a theoretical study of the shaping of the time evolution of field-free orientation of linear molecules. We show the extent to which the degree of orientation can be steered along a desired periodic time-dependent signal. The objective of this study is not to optimize molecular orientation but to propose a general procedure to precisely control rotational dynamics through the first moment of the molecular axis distribution. Rectangular and triangular signals are taken as illustrative examples. At zero temperature we compute the quantum states leading to such field-free dynamics. A tera-Hertz laser pulse is designed to reach these states by using optimal control techniques. The investigation is extended to the case of nonzero temperature. Due to the complexity of the dynamics, the control protocol is derived with a Monte Carlo simulated annealing algorithm. A figure of merit based on the Fourier coefficients of the degree of orientation is used. We study the robustness of the control process against temperature effects and amplitude variations of the electric field.

We study the ground state of a bosonic ring ladder under a gauge flux in the vortex phase, corresponding to the case where the single-particle dispersion relation has two degenerate minima. By combining exact diagonalization and an approximate fermionization approach we show that the ground state of the system evolves from a fragmented state of two single-particle states at weak interparticle interactions to a fragmented state of two Fermi seas at large interactions. Fragmentation is inferred from the study of the eigenvalues of the reduced single-particle density matrix as well as from the calculation of the fidelity of the states. We characterize these nonclassical states by the momentum distribution, the chiral currents, and the current-current correlations.

An eigenmode analysis is presented of the electromagnetic field which occurs between two complementary surface impedances. The analysis is based on the generalized reflection method which is a generalization of the Sommerfeld-Maliuzhinets technique. Numerical results are presented and validated against independent comsol simulations. Also, the characteristic impedance and phase velocity are defined and calculated for further investigation of the structure.

We provide a comprehensive analysis of the differences between two important standards for randomized benchmarking (RB): the Clifford-group RB protocol proposed originally in Emerson et al. [J. Opt. B 7, S347 (2005)] and Dankert et al. [Phys. Rev. A 80, 012304 (2009)], and a variant of that RB protocol proposed by the NIST group in Knill et al. [Phys. Rev. A 77, 012307 (2008)]. While these two protocols are frequently conflated or presumed equivalent, we prove that they produce distinct exponential fidelity decays leading to differences of up to a factor of 3 in the estimated error rates under experimentally realistic conditions. These differences arise because the NIST RB protocol does not satisfy the unitary two-design condition for the twirl in the Clifford-group protocol and thus the decay rate depends on noninvariant features of the error model. Our analysis provides an important first step toward developing definitive standards for benchmarking quantum gates and a more rigorous theoretical underpinning for the NIST protocol and other RB protocols lacking a group-structure. We conclude by discussing the potential impact of these differences for estimating fault-tolerant overheads.

We investigate a general class of dissipative quantum circuit capable of computing arbitrary conjunctive normal form (CNF) Boolean formulas. In particular, the clauses in a CNF formula define a local generator of Markovian quantum dynamics which acts on a network of qubits. Fixed points of this dynamical system encode the evaluation of the CNF formula. The structure of the corresponding quantum map partitions the Hilbert space into sectors, according to decoherence-free subspaces (DFSs) associated with the dissipative dynamics. These sectors then provide a natural and consistent way to classify quantum data (i.e., quantum states). Indeed, the attractive fixed points of the network allow one to learn the sector(s) for which some particular quantum state is associated. We show how this structure can be used to dissipatively prepare quantum states (e.g., entangled states) and outline how it may be used to generalize certain classical computational learning tasks.

We consider higher-order finite-nuclear-size (FNS) contributions to the energy levels of light ordinary and muonic hydrogenlike atoms. Relativistic corrections to the leading FNS term have been known in terms of an integration in coordinate space. The related results are model dependent. In the meantime, if the data on the nuclear structure are obtained from electron-nucleus scattering, it is a representation of the electric charge form factor in momentum space rather than the charge density. An example is the case of a proton as a nucleus. Often the electric form factor is presented in terms of a dispersion integral or a Padé approximation. We present explicit results for such representations for leading finite-nuclear-size higher-order (in $Z\alpha$ and in $Z\alpha m{R}_N$) corrections beyond the leading FNS term.

The strong-field ionization behavior when a Rydberg atom is exposed to a terahertz single-cycle pulse is studied. Fully three-dimensional time-dependent Schrödinger equations and classical trajectory Monte Carlo calculations are performed. Results from stationary eigenstates and Rydberg wave packets are presented, and it is found that the ionization properties can be different for the two cases. All of the pulse parameters and physical quantities are scaled versus the principal quantum number $n$. The ionized electron's scaled radial, energy, and angular distributions are investigated for different $n$, and the quantum results are interpreted using a semiclassical method. The scaling relations of quantum interference amplitudes are discussed.

Collective oscillations of superfluid mixtures of ultracold fermionic and bosonic atoms are investigated while varying the fermion-boson scattering length. We study the dynamics with respect to excited center of mass modes and breathing modes in the mixture. Parametric resonances are also analyzed when the scattering length varies periodically in time, by comparing partial differential equation models and ordinary differential equation models for the dynamics. An application to the recent experiment with fermionic ${}^6\mathrm{Li}$ and bosonic ${}^7\mathrm{Li}$ atoms, which approximately have the same masses, is discussed.

We study, within the classical fields approximation, a two-dimensional weakly interacting uniform Bose gas of a finite number of atoms. By using a grand canonical ensemble formalism we show that such systems exhibit, in addition to the Berezinskii-Kosterlitz-Thouless (BKT) and thermal phases, an intermediate region. This intermediate region is characterized by a decay of current-current correlations at low momenta and by an algebraic decay of the first-order correlations with an exponent being larger than the critical value predicted by the BKT theory. The density of the superfluid fraction at the temperature which separates the BKT phase from the intermediate region approaches the one found by Nelson and Kosterlitz for two-dimensional superfluids while the number of atoms is increased.