Quantum secret sharing (QSS) protocols between $N$ players, for sharing classical secrets, either use multipartite entangled states or use sequential manipulation of single $d$-level states only when $d$ is prime (A. Tavakoli et al., arXiv:1501.05582). We propose a sequential scheme which is valid for any value of $d$. In contrast to A. Tavakoli et al. whose efficiency (number of valid rounds) is $\frac{1}{d}$, the efficiency of our scheme is $\frac{1}{2}$ for any $d$. This, together with the fact that in the limit $d⟶\infty$ the scheme can be implemented by continuous variable optical states, brings the scheme into the domain of present day technology.

We describe a classical model that may serve as an analog for joint and local measurements of an entanglement witness. The analogous experimental procedure and data analysis protocol of the model follow those of a previous experiment to measure an entanglement witness with polarized photons prepared in a mixed state [Phys. Rev. Lett. 91, 227901 (2003)]. Numerical simulations show excellent agreement with both experimental results and quantum-mechanical predictions. This agreement is made possible by the fact that the model exhibits contextuality due to the postselection of coincident detection events.

We present experimental and theoretical results for electron-impact-induced ionization and excitation of the neon valence shell by using a highly sensitive and high-resolution ($e, 2e$) spectrometer. The controversies in previous electron momentum spectroscopic results have been resolved. The satellites at 55.83 and 71.50 eV are mainly attributed to a ${}^{2}P$ manifold, and mixed up with some ${}^{2}S$, not a pure ${}^{2}S$ as were assigned by the earlier electron-momentum spectroscopy. Our experimental momentum distribution for the satellite at 55.83 eV is consistent with that reported by Watanabe et al. [J. Electron Spectrosc. Relat. Phenom 142, 325 (2005)], but not consistent with Samardzic et al.'s results [Phys. Rev. A 48, 4390 (1993)]. The difference between the observed momentum distribution of the satellite at 55.83 eV and the calculations with the plane-wave impulse approximation suggests the need for further improvement of the theoretical methods.

Scattering of beams of light and matter from multielectron atomic targets is formulated in the position representation of quantum mechanics. This yields expressions for the probability amplitude $a\left(\vec{b}\right)$ for a wide variety of processes. Here the spatial parameter $\vec{b}$ is the distance of closest approach of incoming particles traveling on a straight line with the center of the atomic target. The correlated probability amplitude $a\left(\vec{b}\right)$ reduces to a relatively simple product of single-electron probability amplitudes in the widely used independent electron approximation limit, where the correlation effects of the Coulomb interactions between the atomic electrons disappear. As an example in which $a\left(\vec{b}\right)$ has an explicit dependence on $\vec{b}$, we consider transversely finite vortex beams of twisted photons that lack the translational invariance of infinite plane-wave beams. Relatively simple calculations, illustrating the $\vec{b}$ dependence in transition probabilities for photon beams interacting with a two-state degenerate single-electron atomic target, are included. Further application for many-electron systems is discussed. Possible practical uses are briefly considered.

The energies and physical properties of three-electron systems are studied using an explicitly correlated Gaussian basis optimized by the stochastic variational method. The stability of the system as a function of the nuclear charge is analyzed. The role of the Coulomb and magnetic interactions in shaping the structure of these systems is discussed. The accuracy of the energies is substantially improved for high magnetic fields.

We study the interplay between rotating-wave approximation and optimal control. In particular, we show that for a wide class of optimal control problems one can choose the control field such that the Hamiltonian becomes time independent under the rotating-wave approximation. Thus, we show how to recast the functional minimization defined by the optimal control problem into a simpler multivariable function minimization. We provide the analytic solution to the state-to-state transfer of the paradigmatic two-level system and to the more general star configuration of an $N$-level system. We demonstrate numerically the usefulness of this approach in the more general class of connected acyclic $N$-level systems with random spectra. Finally, we use it to design a protocol to entangle Rydberg via constant laser pulse atoms in an experimentally relevant range of parameters.

Time-bin-entangled photons are ideal for long-distance quantum communication via optical fibers. Here we present a source where, even at high creation rates, each excitation pulse generates, at most, one time-bin-entangled pair. This is important for the accuracy and security of quantum communication. Our site-controlled quantum dot generates single polarization-entangled photon pairs, which are then converted, without loss of entanglement strength, into single time-bin-entangled photon pairs.

We investigate the problem of arbitrary photonic-Fock-state scattering in a waveguide-QED system which consists of a one-dimensional waveguide coupled to a two-level system. By imposing the open boundary conditions that directly describe the physical settings, we construct a complete set of eigenstates of the system, and elucidate the mathematical structures of the eigenstates. In particular, we show that the eigenstates include a set of multiphoton extended states and multiphoton bound states, formed by all possible partitions of the photon number $N$. The total number of the eigenstates is exactly described by the integer number partition function $Z\left(N\right)$. Using the set of eigenstates, we form the scattering matrix, which facilitates the calculations of the scattered photon states, for the scattering processes. With the scattered photon states, we compute the photon correlation functions that manifestly exhibit the bunching and antibunching behaviors in the scattered photon states. As a concrete example, we discuss in detail with a focus on the three-photon Fock state. Such a capability to generate photonic entanglement from unentangled Fock states will have broad applications in quantum information processing.

The characterization of quantum polarization of light requires knowledge of all the moments of the Stokes variables, which are appropriately encoded in the multipole expansion of the density matrix. We look into the cumulative distribution of those multipoles and work out the corresponding extremal pure states. We find that SU(2) coherent states are maximal to any order whereas the converse case of minimal states (which can be seen as the most quantum ones) is investigated for a diverse range of the number of photons. Taking advantage of the Majorana representation, we recast the problem as that of distributing a number of points uniformly over the surface of the Poincaré sphere.

Mutually unbiased bases (MUB) are useful in a number of research areas. The symmetry of MUB is an elusive and interesting subject. A (complete set of) MUB in dimension $d$ is sharply covariant if it can be generated by a group of order $d(d+1)$ from a basis state. Such MUB, if they exist, would be most appealing to theoretical studies and practical applications. Unfortunately, they seem to be quite rare. Here we prove that no MUB in odd prime dimensions is sharply covariant, by virtue of clever applications of Mersenne primes, Galois fields, and Frobenius groups. This conclusion provides valuable insight about the symmetry of MUB and the geometry of quantum state space. It complements and strengthens the earlier result of the author that only two stabilizer MUB are sharply covariant. Our study leads to the conjecture that no MUB other than those in dimensions 2 and 4 is sharply covariant.

Microwave fields can be used to drive local spin transitions in quantum gases and for outcoupling of cold atomic beams from magnetic traps. In this paper, we derive an analytic theory for the outcoupling rate as a response to weak microwave fields of varying frequency and power. The theory holds for thermal clouds and Bose-Einstein condensates. It allows for calculating transition rates in arbitrary magnetic trap geometries and includes the effect of gravity. We verify our theory by measuring the flux of outcoupled atoms at the single-particle level. The derived spectral response is important for magnetic noise spectroscopy with quantum gases, and for probing quantum gas dynamics with single atom detectors in real time.

A simple formula is derived for the maximum squeezing rate which occurs at the initial stages of the squeezing process: the rate only depends on the second partial derivatives of a classical Hamiltonian. Rules for optimum rotation of the phase space are found to keep the state optimally located and oriented for fastest squeezing. These operations transform the phase-space point of interest into a saddle point with opposite principal curvatures. Similar results are found for the Bloch-sphere phase space and spin squeezing. Application of the general formulas is illustrated by several model examples including parametric down conversion, Kerr nonlinearity, Jaynes-Cummings interaction, and spin squeezing by one-axis twisting and two-axis countertwisting.

We analyze an entanglement-based quantum key distribution (QKD) architecture that uses a linear chain of quantum repeaters employing photon-pair sources, spectral-multiplexing, linear-optic Bell-state measurements, multimode quantum memories, and classical-only error correction. Assuming perfect sources, we find an exact expression for the secret-key rate, and an analytical description of how errors propagate through the repeater chain, as a function of various loss-and-noise parameters of the devices. We show via an explicit analytical calculation, which separately addresses the effects of the principle nonidealities, that this scheme achieves a secret-key rate that surpasses the Takeoka-Guha-Wilde bound—a recently found fundamental limit to the rate-vs-loss scaling achievable by any QKD protocol over a direct optical link—thereby providing one of the first rigorous proofs of the efficacy of a repeater protocol. We explicitly calculate the end-to-end shared noisy quantum state generated by the repeater chain, which could be useful for analyzing the performance of other non-QKD quantum protocols that require establishing long-distance entanglement. We evaluate that shared state's fidelity and the achievable entanglement-distillation rate, as a function of the number of repeater nodes, total range, and various loss-and-noise parameters of the system. We extend our theoretical analysis to encompass sources with nonzero two-pair-emission probability, using an efficient exact numerical evaluation of the quantum state propagation and measurements. We expect our results to spur formal rate-loss analysis of other repeater protocols and also to provide useful abstractions to seed analyses of quantum networks of complex topologies.

We compare harmonic spectra from hydrogen based on the numerical solution of the time-dependent Schrödinger equation and three approximate models: (i) the strong field approximation (SFA), (ii) the Coulomb-Volkov modified strong field approximation (CVA), and (iii) the strong field approximation with the stationary phase approximation applied to the momentum integrals (SPSFA). At laser intensities in the range of $(1-3)\times {10}^{14}{\mathrm{W}/\mathrm{cm}}^2$ we find good agreement when comparing the SFA and CVA with exact results. In general the CVA displays an overall better agreement with ab initio results, which reflects the role of the Coulomb field in the ionization as well as in the recombination process. Furthermore, it is found that the widely used SPSFA breaks down for low-order harmonic generation; i.e., the approximation turns out to be accurate only in the outer part of the harmonic plateau region as well as in the cutoff region. We trace this deficiency to the singularity of the SPSFA associated with short trajectories, i.e., short return times. When removing these, we obtain a version of the SPSFA which works rather well for the entire harmonic spectrum.

The generation of two-mode broadband squeezed light is investigated in cascading double-cavity optomechanical systems. The cavities are driven by amplitude-modulated lasers with two frequency tones, one of which is red detuning and other blue detuning from the cavity fields. It is shown that a two-mode squeezed field can be generated in a single double-cavity system via dissipation of the mechanical resonator. To generate broadband and strong squeezing of the cavity fields, many identical double-cavity optomechanical systems are connected together in a cascading way. The vacuum noise fed into the cavities and the thermal noise coupled to the mechanical resonator can be greatly depressed in the cascading system. As a result, the very strong and constant squeezing can be achieved in a large frequency range when the number of cascaded optomechanical systems becomes large.

Are the electromagnetic scalar and vector potentials dispensable? Vaidman [Phys. Rev. A 86, 040101(R) (2012)] has suggested that local interactions of gauge-invariant quantities, e.g., magnetic torques, suffice for the description of all quantum electromagnetic phenomena. We analyze six thought experiments that challenge this suggestion. All of them have explanations in terms of local interactions of gauge-dependent quantities, and, in addition, some have explanations in terms of nonlocal interactions of gauge-invariant quantities. We claim, however, that two of our examples have no gauge-invariant formal description and that, in general, no local description can dispense with electromagnetic potentials.

The preceding Comment challenged my claim that potentials might be just auxiliary mathematical tools and that they are not necessary for explaining physical phenomena. The Comment did not confront my explanation without the potentials of the Aharonov-Bohm effects that appeared in the original article, but stated that I cannot apply this explanation for seven other examples. In my reply, using my method, I provide explanations of one of the examples, show that two other examples are not relevant, and agree that the remaining examples require further analysis. However, I argue that none of the examples provides robust counterexamples to my claim, similar to the original Aharonov-Bohm setups which were explained in my article, so the Comment does not refute my claim.

Anomalous motional heating is a major obstacle to scalable quantum information processing with trapped ions. Although the source of this heating is not yet understood, several previous studies suggest that noise due to surface contaminants is the limiting heating mechanism in some instances. We demonstrate an improvement by a factor of 4 in the room-temperature heating rate of a niobium surface electrode trap by in situ plasma cleaning of the trap surface. This surface treatment was performed with a simple homebuilt coil assembly and commercially available matching network and is considerably gentler than other treatments, such as ion milling or laser cleaning, that have previously been shown to improve ion heating rates. We do not see an improvement in the heating rate when the trap is operated at cryogenic temperatures, pointing to a role of thermally activated surface contaminants in motional heating whose activity may freeze out at low temperatures.

The puzzling properties of quantum mechanics, i.e., wave-particle duality, entanglement, and superposition, have been dissected experimentally over the past decades. However, hidden-variable (HV) models based on three classical assumptions of wave-particle objectivity, determinism, and independence strive to explain the same experiments or even defeat quantum mechanics. Meanwhile, the steady development of quantum technologies continues to enable us to test experimentally the predictions of quantum mechanics and HV theories. We report an experimental demonstration of an entanglement-assisted quantum delayed-choice scheme using a liquid nuclear magnetic resonance quantum-information processor. This experiment is based on the recently proposed scheme [R. Ionicioiu et al., Nat. Commun. 5. 3997 (2014)], which predicted different results for quantum mechanics and HV theories. In our experiments, the intensities and the visibilities of the interference are consistent with the theoretical predictions of quantum mechanics. The results show that a contradiction with the experiments is indeed appearing when all three assumptions of the HV models are combined, though any two of those assumptions are compatible with the experiments.