We study the possibility of using single rare-earth ions coupled to a photonic cavity with high cooperativity for performing nondestructive measurements of photons, which would be useful for global quantum networks and photonic quantum computing. We calculate the achievable fidelity as a function of the parameters of the rare-earth ion and photonic cavity, which include the ion's optical and spin dephasing rates, the cavity linewidth, the single-photon coupling to the cavity, and the detection efficiency. We suggest a promising experimental realization using current state-of-the-art technology in Nd:${\mathrm{YVO}}_4$.

We investigate the self-induced turbulence of high-repetition-rate laser filaments over a wide range of average powers (1 mW to 100 W) and its sensitivity to external atmospheric turbulence. Although both externally imposed and self-generated types of turbulence can have comparable magnitudes, they act on different temporal and spatial scales. While the former drives the shot-to-shot motion at the millisecond time scale, the latter acts on the 0.5-s scale. As a consequence, their effects are decoupled, preventing beam stabilization by the thermally induced low-density channel produced by the laser filaments.

Multiphoton interference results in modulations of output probabilities with phase shift periods that are much shorter than $2\pi$. Here, we investigate the physics behind these statistical patterns in the case of well-defined photon numbers in the input and output modes of a two-path interferometer. We show that the periodicity of the multiphoton interference is related to the weak value of the unobserved intensity difference between the two arms of the interferometer. This means that the operator relations between the photon number differences in input, path, and output can be used to determine the periodicity of the experimentally observed quantum interference, establishing an important link between the classical causality of random phase interference and quantum effects that depend on the superposition of classically distinct possibilities.

Implementations of the quantum phase estimation and quantum counting algorithms with qudits are proposed. The construction of the basic building blocks of the algorithms is described in detail and the fidelity of the quantum counting algorithm with qubits and qudits is simulated numerically. Along with the exponential increase of the size of the target register, the simulations with qudits demonstrate significantly higher probability of finding the number of solutions than qubits and more consistent performance for a different number of solutions.

In quantum information science, the external control of qubits must be balanced with the extreme isolation of the qubits from the environment. Atomic qubit systems typically mitigate this balance through the use of gated laser fields that can create superpositions and entanglement between qubits. Here we propose the use of high-order optical Stark shifts from optical fields to manipulate the splitting of atomic qubits that are insensitive to other types of fields. We demonstrate a fourth-order ac Stark shift in a trapped atomic ion system that does not require extra laser power beyond that needed for other control fields. We individually address a chain of tightly spaced trapped ions and show how these controlled shifts can produce an arbitrary product state of 10 ions as well as generate site-specific magnetic field terms in a simulated spin Hamiltonian.

Recently, a protocol for quantum state discrimination (QSD) in a multiparty scenario has been introduced [Phys. Rev. Lett. 111, 100501 (2013)]. In this protocol, Alice generates a quantum system in one of two predefined nonorthogonal qubit states, and the goal is to send the generated state information to different parties without classical communication exchanged between them during the protocol's session. The interesting feature is that, by resorting to sequential generalized measurements onto this single system, there is a nonvanishing probability that all observers identify the state prepared by Alice. Here, we present the experimental implementation of this protocol based on polarization single-photon states. Our scheme works over an optical network, and since QSD lies in the core of many protocols, it represents a step towards experimental multiparty quantum information processing.

We investigate the static and dynamical patterns of entanglement in an anisotropic $XY$ model with an alternating transverse magnetic field, which is equivalent to a two-component one-dimensional Fermi gas on a lattice, a system realizable with current technology. Apart from the antiferromagnetic and paramagnetic phases, the model possesses a dimer phase which is not present in the transverse $XY$ model. At zero temperature, we find that the first derivative of bipartite entanglement can detect all the three phases. We analytically show that the model has a “factorization line” on the plane of system parameters, in which the zero-temperature state is separable. Along with investigating the effect of temperature on entanglement in a phase plane, we also report a nonmonotonic behavior of entanglement with respect to temperature in the antiferromagnetic and paramagnetic phases, which is surprisingly absent in the dimer phase. Since the time dynamics of entanglement in a realizable physical system plays an important role in quantum information processing tasks, the evolutions of entanglement at small as well as large time are examined. Consideration of large-time behavior of entanglement helps us to prove that in this model, entanglement is always ergodic. We observe that other quantum correlation measures can qualitatively show similar features in zero and finite temperatures. However, unlike nearest-neighbor entanglement, the nearest-neighbor information-theoretic measures can be both ergodic as well as nonergodic, depending on the system parameters.

Association rules mining (ARM) is one of the most important problems in knowledge discovery and data mining. Given a transaction database that has a large number of transactions and items, the task of ARM is to acquire consumption habits of customers by discovering the relationships between itemsets (sets of items). In this paper, we address ARM in the quantum settings and propose a quantum algorithm for the key part of ARM, finding frequent itemsets from the candidate itemsets and acquiring their supports. Specifically, for the case in which there are $M_f^{\left(k\right)}$ frequent $k$-itemsets in the $M_c^{\left(k\right)}$ candidate $k$-itemsets ($M_f^{\left(k\right)}\le M_c^{\left(k\right)}$), our algorithm can efficiently mine these frequent $k$-itemsets and estimate their supports by using parallel amplitude estimation and amplitude amplification with complexity $O\left(\frac{k\sqrt{M_c^{\left(k\right)}{M}_f^{\left(k\right)}}}{\epsilon }\right)$, where $\epsilon$ is the error for estimating the supports. Compared with the classical counterpart, i.e., the classical sampling-based algorithm, whose complexity is $O\left(\frac{k{M}_c^{\left(k\right)}}{{\epsilon }^2}\right)$, our quantum algorithm quadratically improves the dependence on both $\epsilon$ and $M_c^{\left(k\right)}$ in the best case when $M_f^{\left(k\right)}\ll M_c^{\left(k\right)}$ and on $\epsilon$ alone in the worst case when $M_f^{\left(k\right)}\approx M_c^{\left(k\right)}$.

We study remote creation of coherence (RCC) for a quantum system, A, with the help of quantum operations on another system, B, and one-way classical communication. We show that all the nonincoherent quantum states are useful for RCC and all the incoherent-quantum states are not. The necessary and sufficient conditions of RCC for the quantum operations on system B are presented for pure states. The upper bound of average RCC is derived, giving a relation among the entanglement (concurrence), the RCC of the given quantum state, and the RCC of the corresponding maximally entangled state. Moreover, for two-qubit systems we find a simple factorization law for the average remote-created coherence.

In recent years, several measures have been proposed for characterizing the coherence of a given quantum state. We derive several results that illuminate how these measures behave when restricted to pure states. Notably, we present an explicit characterization of the closest incoherent state to a given pure state under the trace distance measure of coherence. We then use this result to show that the states maximizing the trace distance of coherence are exactly the maximally coherent states. We define the trace distance of entanglement and show that it coincides with the trace distance of coherence for pure states. Finally, we give an alternate proof to a recent result that the ${\ell }_1$ measure of coherence of a pure state is never smaller than its relative entropy of coherence.

We present theoretical studies of high-order harmonic generation (HHG) driven by plasmonic fields in two-electron atomic systems. Comparing the single- and two-electron active approximation models of the hydrogen negative ion, we provide strong evidence that a nonsequential double-electron recombination mechanism appears to be mainly responsible for the HHG cutoff extension. Our analysis is carried out by means of a reduced one-dimensional numerical integration of the two-electron time-dependent Schrödinger equation, and on investigations of the classical electron trajectories, resulting from the Newton's equation of motion. Additional comparisons between the hydrogen negative ion and the helium atom suggest that the double recombination process depends distinctly on the atomic target. Our research paves the way to the understanding of strong field processes in multielectronic systems driven by spatially inhomogeneous fields.

Using a semiclassical model, we investigate frustrated double ionization (FDI) in ${\mathrm{D}}_3{}^{+}$, a two-electron triatomic molecule, when driven by an intense, linearly polarized, near-infrared (800 nm) laser field. We compute the kinetic energy release of the nuclei and find a good agreement between experiment and our model. We explore the two pathways of FDI and show that, with increasing field strength, over-the-barrier ionization overtakes tunnel ionization as the underlying mechanism of FDI. Moreover, we compute the angular distribution of the ion fragments for FDI and identify a feature that can potentially be observed experimentally and is a signature of only one of the two pathways of FDI.

A density-functional theory is proposed for strongly interacting fermions with arbitrary large negative scattering length. The functional has only two parameters that are directly fixed to reproduce the universal properties of unitary gas: the so-called Bertsch parameter ${\xi }_0$ and a parameter ${\eta }_e$ related to the possible influence of the effective range $r_e$ at infinite scattering length $a$. Using most recent quantum Monte Carlo (QMC) estimates of these two parameters, it is shown that the functional properly reproduces the experimental measurements of interacting Fermi systems not only at unitarity but also away from this limit over a wide range of ${\left(a{k}_F\right)}^{-1}$ values. The functional is applied to obtain an expression of Tan's contact parameter including the effect of $r_e$. Application is finally made to neutron matter. It is shown that most recent QMC results are well reproduced.

Through numerical simulations we reveal the scenario of $3.9-\mu \mathrm{m}$ filament spectrum enrichment in the atmosphere in the cases of linear and circular polarization of the incident pulse. The discrete spectrum of odd harmonics transforms into the two-octave plateau in the case of linear polarization. In contrast, in the case of circular polarization of the incident pulse, the harmonic-free flat supercontinuum appears with the plasma onset, reaching the tenth harmonic of the input radiation. We identify the energy balance specific to the filamentation near 4 $\mu \mathrm{m}$: the absorption on ${\mathrm{CO}}_2$ lines in the atmosphere is accelerated by the self-phase modulation in the Kerr nonlinearity early before the plasma channel is formed. This nonlinearly enhanced linear absorption overwhelms the plasma losses and conversion of the input pulse energy to the higher harmonics as well as the plateau.

The quantum steering ellipsoid can be used to visualize 2-qubit states, and thus provides a generalization of the Bloch picture for the single qubit. Recently, a monogamy relation for the volumes of steering ellipsoids has been derived for pure 3-qubit states and shown to be stronger than the celebrated Coffman-Kundu-Wootters inequality. We first demonstrate the close connection between this volume monogamy relation and the classification of pure 3-qubit states under stochastic local operations and classical communication. We then show that this monogamy relation does not hold for general mixed 3-qubit states and derive a weaker monogamy relation that does hold for such states. We also prove a volume monogamy relation for pure 4-qubit states (further conjectured to hold for the mixed case), and generalize our 3-qubit inequality to $n$ qubits. Finally, we study the effect of noise on the quantum steering ellipsoid and find that the volume of any 2-qubit state is nonincreasing when the state is exposed to arbitrary local noise. This implies that any volume monogamy relation for a given class of multiqubit states remains valid under the addition of local noise. We investigate this quantitatively for the experimentally relevant example of isotropic noise.

We derive a general criterion to detect entangled states in multipartite systems based on the symmetric logarithmic derivative quantum Fisher information. This criterion is a direct consequence of the fact that separable states do not improve the accuracy upon estimating the one-parameter family of quantum channels. Our result is a generalization of the previously known criterion for the one-parameter unitary channel to any one-parameter quantum channel. Several variants of the proposed criterion are also given, and then the general structure is revealed behind this sort of entanglement criteria based on quantum Fisher information. We discuss several examples to illustrate our criterion. In the last part, we briefly show how the proposed criterion can be extended to a more general setting that is applicable for a certain class of open quantum systems, and we discuss how to detect entangled states even in the presence of decoherence.

We have investigated systematically the $K\alpha$ x-ray spectra in elements from Ca to Ge within Berger's two-Lorentzian functions model, using a high-resolution antiparallel double-crystal x-ray spectrometer, in order to obtain in detail the physical meaning of the asymmetry in the spectral profiles. The overall tendency of the corrected full width at half maximum of the $K{\alpha }_1$ and $K{\alpha }_2$ lines as a function of $Z$, as well as the linewidths, are in good agreement with the data reported in the literature. It is found, from both the experiments and calculation, that satellite lines arising from shake-off appear between the $K{\alpha }_1$ and $K{\alpha }_2$ lines. The asymmetry index of $K{\alpha }_1$ in $3d$ elements from Sc to Zn is ascribed to the existence of a $3d$ spectator hole. Moreover, the observed Sc $K{\alpha }_1$ line shows a symmetric profile unlike the Ti $K{\alpha }_1$ line profile, this discrepancy being explained by the existence of satellite lines on both sides of the Sc profile. Our experimental results yielded around 25% probability for the probability of shake processes creating a second hole in the $3p$ or $3d$ subshells in Sc and around 18% probability for creating a second hole the in the $3p$ in Ca. For the latter process our calculated value, using multiconfiguration Dirac-Fock wave functions and the sudden approximation yielded a 10% probability.

We describe a protocol to prepare clusters of ultracold bosonic atoms in strongly interacting states reminiscent of fractional quantum Hall states. Our scheme consists in injecting a controlled amount of angular momentum to an atomic gas using Raman transitions carrying orbital angular momentum. By injecting one unit of angular momentum per atom, one realizes a single-vortex state, which is well described by mean-field theory for large enough particle numbers. We also present schemes to realize fractional quantum Hall states, namely, the bosonic Laughlin and Moore-Read states. We investigate the requirements for adiabatic nucleation of such topological states, in particular comparing linear Landau-Zener ramps and arbitrary ramps obtained from optimized control methods. We also show that this protocol requires excellent control over the isotropic character of the trapping potential.