Generalized measures of quantum correlations are derived by taking Bayes' rule as the only fundamental principle. The resulting quantifiers satisfy several desirable conditions for a measure of quantum correlations and are shown to admit operational interpretation in terms of the difference in efficiency of quantum and classical demons in allowing for the extraction of generalized work from a heat bath. The link with discord is established by adopting the $q$ entropy as entropic principle. This allows us to reproduce, within a one-parameter formalism, both the entropic and the geometric measures of discord and physically distinguish them within the context of the nonextensive thermodynamics. Besides offering a unified view of several measures of correlations in terms of the Bayesian principle and its connection with thermodynamics, our approach unveils a bridge to the nonextensive statistical mechanics.

Photon-number correlation measurements are performed on bright squeezed vacuum states using a standard Bell-test setup, and quantum correlations are observed for conjugate polarization-frequency modes. We further test the entanglement witnesses for these states and demonstrate the violation of the separability criteria, which infers that all of the macroscopic Bell states, containing typically ${10}^6$ photons per pulse, are polarization entangled. The study also reveals the symmetry of macroscopic Bell states with respect to local polarization transformations.

We simulate the implementation of a $T$ gate, or $\frac{\pi }{8}$ gate, for a [7,1,3] encoded logical qubit in a nonequiprobable error environment. We demonstrate that the use of certain non-fault-tolerant methods in the implementation may nevertheless enable reliable quantum computation while reducing basic resource consumption. Reliability is determined by calculating gate fidelities for the one-qubit logical gate. Specifically, we show that despite using a non-fault-tolerant procedure in constructing a logical zero ancilla to implement the $T$ gate, the gate fidelity of the logical gate, after perfect error correction, has no first order error terms. Meaning, any errors that may have occurred during implementation are “correctable” and fault tolerance may still be achieved.

For certain quantum architectures and algorithms, most of the required resources are consumed during the distillation of one-qubit magic states for use in performing Toffoli gates. I show that the overhead for magic-state distillation can be reduced by merging distillation with the implementation of Toffoli gates. The resulting routine distills eight one-qubit magic states directly to a Toffoli state, which can be used without further magic to perform a Toffoli gate.

There are cases where the potentials present in the Schrödinger equation are of long range and have measurable effects as, for instance, for the interaction between atoms at low temperatures or for the calculation of atomic three-body collisions. In these cases, the solution of the Schrödinger equation for the wave functions by finite-difference or finite-element techniques may not achieve the desired accuracy. An iterative method is presented, based on the Lippmann-Schwinger integral equation, that is similar in spirit to the Born approximation but is applied only in the region of the potential tails. This procedure extends the numerical solution obtained for short distances to large distances without loss of accuracy. Numerical examples are presented for atomic van der Waals potentials $C_n/r^n$. For $C_6/r^6$, the size of the radial interval, for which an accuracy of ${10}^{-10}$ is achieved, is $\simeq [100,1000]$ atomic units $a_0$. For the case of $C_3/r^3$, the required interval for the same level of accuracy is [4000,50 000], which, because of its large size, has to be subdivided into smaller partitions. The wave numbers $k$ chosen for these examples correspond to atomic collision energies in the micro-Kelvin range. The larger the wave number $k$, the faster the rate of the convergence, and the limit $k\to 0$ is also investigated. A criterion is given for determining whether the iterations converge in that limit.

Two nonperturbative methods are applied to obtain total and singly differential (in the electron energy) cross sections of electron emission in proton collisions with H${}_2$O at impact energies in the range 10 keV $\le E_{\mathrm{p}}\le$ 5 MeV. Both methods, one classical and one semiclassical, combine an independent particle treatment with a multicenter model potential description of the target. The excellent agreement obtained with experimental data supports the usefulness of the approximations involved and encourages the study of more complex systems.

We consider parity-time ($\mathcal{PT}$) symmetric arrays formed by $N$ optical waveguides with gain and $N$ waveguides with loss. When the gain-loss coefficient exceeds a critical value ${\gamma }_c$, the $\mathcal{PT}$ symmetry becomes spontaneously broken. We calculate ${\gamma }_c\left(N\right)$ and prove that ${\gamma }_c\to 0$ as $N\to \infty$. In the symmetric phase, the periodic array is shown to support $2N$ solitons with different frequencies and polarizations.

The slowing down of light pulses with backward-wave four-wave mixing is analyzed for photorefractive crystals with different coupling strengths. The conditions are found for which the delay of a phase-conjugate pulse decreases when the coupling strength increases and can even become negative, switching the pulse deceleration to acceleration. It is shown that for relatively low coupling strength the backward-wave four-wave mixing ensures a longer delay as compared to the two-beam-coupling technique. For coupling strengths tending to zero, the delay of long pulses approaches the response time of the medium. The conclusions of the theoretical analysis are confirmed experimentally with backward-wave four-wave mixing in barium titanate.

We study the equilibration dynamics of closed finite quantum systems and address the question of the time needed for the system to equilibrate. In particular, we focus on the scaling of the equilibration time $T_{\mathrm{eq}}$ with the system size $L$. For clean systems, we give general arguments predicting $T_{\mathrm{eq}}=O\left(L^0\right)$ for clustering initial states, while for small quenches around a critical point we find $T_{\mathrm{eq}}=O\left(L^{\zeta }\right)$ where $\zeta$ is the dynamical critical exponent. We then analyze noisy systems where exponentially large time scales are known to exist. Specifically, we consider the tight-binding model with diagonal impurities and give numerical evidence that in this case $T_{\mathrm{eq}}\sim B{e}^{C{L}^{\psi }}$ where $B,C,\psi$ are observable-dependent constants. Finally, we consider another noisy system whose evolution dynamics is randomly sampled from a circular unitary ensemble. Here, we are able to prove analytically that $T_{\mathrm{eq}}=O\left(1\right)$, thus showing that noise alone is not sufficient for slow equilibration dynamics.

We introduce a multiparty cryptographic protocol, which we call entanglement sharing schemes, wherein a dealer retains half of a maximally entangled bipartite state and encodes the other half into a multipartite state that is distributed among multiple players. In a close analog to quantum secret sharing, some subsets of players can recover maximal entanglement with the dealer whereas other subsets can recover no entanglement (though they may retain classical correlations with the dealer). We find a lower bound on the share size for such schemes and construct two nontrivial examples based on Shor's $\left[\right[9,1,3\left]\right]$ and the $\left[\right[4,2,2\left]\right]$ stabilizer code; we further demonstrate how other examples may be obtained from quantum error correcting codes through classical encryption. Finally, we demonstrate that entanglement sharing schemes can be applied to characterize leaked information in quantum ramp secret sharing.

We report experimental and theoretical cross sections for positron scattering from the fundamental organic-chemistry molecule ethane (C${}_2$H${}_6$). The experimental total cross sections (TCSs) were obtained using a linear transmission technique, for energies in the range 0.1–70 eV and with an energy resolution of $\sim$0.25 eV (full width at half maximum). Agreement, over the common energy range, with the earlier TCS measurements of Floeder et al. [J. Phys. B 18, 3347 (1985)] is excellent, while both the present results and those of Floeder et al. are consistently higher in magnitude than the data of Sueoka and Mori [J. Phys. B 19, 4035 (1986)]. The present calculations employed the Schwinger multichannel method and were performed in the static plus polarization approximation for energies up to 10 eV. Our calculated elastic integral cross sections (ICSs) indicate a Ramsauer-Townsend minimum at around 1.4 eV in the $A_g$ scattering symmetry, and a virtual state. In addition we calculated from our scattering cross section a scattering length of $-$13.83$a_0$. Agreement between our measured TCS and calculated elastic ICS is found to be only qualitative, although this is perhaps not so surprising given the TCS below 10 eV in principle includes contributions from rotational, vibrational, and electronic-state excitation and positronium formation whereas the calculation does not.

We investigate the rotational response of both nondipolar and dipolar Bose-Einstein condensates confined in an annular potential via minimization of the energy in the rotating frame. For the nondipolar case we identify certain phases which are associated with different vortex configurations. For the dipolar case, assuming that the dipoles are aligned along some arbitrary and tunable direction, we study the same problem as a function of the orientation angle of the dipole moment of the atoms.

We study the dynamics of spontaneous generation of coherence and photon–spin-qubit entanglement in a $\Lambda$ system with nondegenerate lower levels. The cases of entanglement in frequency only and frequency and polarization are compared and the reduced density matrix and entanglement entropy are analyzed. We explore in detail how which-path information manifest when the energy difference between the qubit states is larger than the linewidth of the excited state suppresses coherence. A framework is provided to describe the dynamics of spontaneous generation of coherence and (ideal) photodetection in obtaining the postmeasurement qubit density matrix. A simple model of photodetection with a quantum eraser to suppress which-path information in the detection measurement is implemented. It is found that such quantum eraser purifies the qubit density matrix after photodetection; our results are in agreement with those reported in recent experiments.

The temporal response of resonances in nanoplasmonic structures typically converts an incoming few-cycle field into a much longer near-field at the spot where nonlinear physical phenomena including electron emission, recollision, and high-harmonic generation can take place. We show that for practically useful structures pulse shaping of the incoming pulse can be used to synthesize the plasmon-enhanced field and enable single-cycle-driven nonlinear physical phenomena. Our method is demonstrated for the generation of an isolated attosecond pulse by plasmon-enhanced high harmonic generation. We furthermore show that optimal control techniques can be used even if the response of the plasmonic structure is not known a priori.

We investigate numerically the effect of long-range interaction on the transverse localization of light. To this end, nonlinear zigzag optical waveguide lattices are applied, which allows precise tuning of the second-order coupling. We find that localization is hindered by coupling between next-nearest lattice sites. Additionally, (focusing) nonlinearity facilitates localization with increasing disorder, as long as the nonlinearity is sufficiently weak. However, for strong nonlinearities, increasing disorder results in weaker localization. The threshold nonlinearity, above which this anomalous result is observed, grows with increasing second-order coupling.

The spontaneous emission of a two-level atom in a anisotropic photonic crystal is investigated without making use of the rotating wave approximation (RWA). Similar to the RWA case, there exist two characteristic atomic transition frequencies which separate the radiation field from the localized and propagated fields. Unlike the RWA calculation, these two characteristic frequencies are shifted due to a full calculation of the energy shifts.

Energy levels and the radiative and Auger transition rates of the 1$s$2$p^4$ ${}^{2,4}L$ ($L=S$, $P$, $D$) resonances in the boron isoelectronic sequence are calculated using the saddle-point variation and saddle-point complex-rotation methods. Large-scale wave functions are used to saturate the functional space. Relativistic and mass polarization corrections are included by the first-order perturbation theory. The Auger branching ratios of the important decay channels for these core-excited states are calculated. The reliable transition wavelengths and Auger electron energies are used to identify available x-ray spectra and Auger electron spectra. Identifications of several unknown experimental lines from 1$s$2$p^4$ resonances are reported. The total radiative rates and total Auger rates of these 1$s$2$p^4$ resonances are also reported and discussed along with the increase of atomic number $Z$. It is found that the total Auger rates are several orders of magnitude greater than the total radiative rates in these low-$Z$ ions.

We calculate the time-of-flight patterns of strongly interacting bosons confined in a two-dimensional square lattice in the presence of an artificial magnetic field, using a quantum rotor model that is inherently combined with the Bogoliubov approach. We consider various geometries of the magnetic flux, which are expected to be realizable, or have already been implemented in experimental settings. The flexibility of the method allowed us to study cases where the artificial magnetic field is uniform or staggered or forms a checkerboard configuration. The effects of additional temporal modulation of the optical potential that results from application of Raman lasers driving particle transitions between lattice sites are also included. The time-of-flight patterns presented may serve as a verification of the chosen gauge in experiments, but also provide important hints on unconventional, nonzero-momentum condensates, or the possibility of observing graphenelike physics resulting from the occurrence of Dirac cones in artificial magnetic fields in systems of ultracold bosons in optical lattices. Also, we elucidate the differences between the effects of magnetic fields in solids and of artificial magnetic fields in optical lattices, which can be controlled on a much higher level, leading to effects not possible in condensed matter physics.

In this work, we propose a parity-time- ($\mathcal{PT}$-) symmetric optical coupler whose arms are birefringent waveguides as a realistic physical model which leads to a so-called quadrimer, i.e., a four-complex-field setting. We seek stationary solutions of the resulting linear and nonlinear model, identifying its linear point of $\mathcal{PT}$-symmetry breaking and examining the corresponding nonlinear solutions that persist up to this point, as well as so-called ghost states that bifurcate from them. We obtain the relevant symmetry-breaking bifurcations between symmetric (circularly polarized) and asymmetric (elliptically polarized) states and numerically follow the associated dynamics which give rise to growth or decay even within the $\mathcal{PT}$-symmetric phase. Our symmetric stationary nonlinear solutions are found to terminate in saddle-center bifurcations which are analogous to the linear $\mathcal{PT}$ phase transition. We found that the $\mathcal{PT}$ symmetry significantly changes the stability and dynamical properties of the modes with different polarizations.