We propose a robust and efficient approach for tripartite-to-bipartite entanglement localization. By using weak measurements and quantum measurement reversal, an almost maximal entangled state shared by two parties can be generated with the assistance of the third party by local quantum operations and classical communication from a $W$-like state. We show that this approach works well in the presence of losses and phase diffusion. Our method provides an active way to fight against decoherence, and might help for quantum communication and distributed quantum computation.

We present a study of thermalization of a small isolated Hubbard lattice cluster prepared in a pure state with a well-defined energy. We examine how a two-site subsystem of the lattice thermalizes with the rest of the system as its environment. We explore numerically the existence of thermalization over a range of system parameters, such as the interaction strength, system size, and the strength of the coupling between the subsystem and the rest of the lattice. We find thermalization over a wide range of parameters and that interactions are crucial for efficient thermalization of small systems. We relate this thermalization behavior to the eigenstate thermalization hypothesis and quantify numerically the extent to which eigenstate thermalization holds. We also verify our numerical results theoretically with the help of previously established results from random matrix theory for the local density of states, particularly the finite-size scaling for the onset of thermalization.

The superfluid transition temperature $T_c$ of a unitary Fermi gas on a three-dimensional isotropic lattice with an attractive on-site interaction is investigated as a function of density $n$, from half filling down to $5\times {10}^{-7}$ per unit cell, using a pairing fluctuation theory. We show that except at very low densities ($n^{1/3}<0.2$), where $T_c/E_F$ is linear in $n^{1/3}$, $T_c/E_F$ exhibits a significant higher-order nonlinear dependence on $n^{1/3}$. This calls for extra caution against possible significant error in the zero-density-limit value of $T_c/E_F$ from typical quantum Monte Carlo (QMC) simulations, obtained by linearly extrapolating data points at intermediate and high densities. Our result, $T_c/E_F=0.256$, at the $n=0$ limit, is close to, and should be compared with, the maximum $T_c/E_F$ near the Bose-Einstein condensation regime obtained from QMC calculations.

A general framework based on the fluctuation-dissipation theorem has been outlined for the study of the spontaneous thermal fluctuations in optical fibers. The goal is to seek a unified scheme to analyze the two types of intrinsic noises found in fiber lasers and interferometric fiber-optic sensors, namely, the thermoconductive noise and the thermomechanical noise. Some outstanding questions in the current theories are addressed. These include: (a) the underlying relation between the thermoconductive and the thermomechanical noises, (b) the lack of a fully disclosed theory for the thermoconductive noise in passive fibers, and (c) the low-frequency restriction in the current theory of the thermomechanical noise. Specific analyses based on the proposed approach find excellent agreement with existing theories.

We study the generalization of the previous collapse model known as quantum mechanics with universal position localizations (QMUPL), which accounts for both memory and dissipative effects. After deriving the nonlocal action describing the system's dynamics, we solve the equation of motion for a quantum harmonic oscillator via the path integral formalism. We give the explicit expression for the Green's function of the process. We focus on the case of an exponential correlation function and we analyze in detail the behavior Gaussian wave functions. In particular, we study the collapse process, comparing the results with those of related models.

We study, by means of the stabilizer formalism, a quantum error correcting code which is alternative to the standard block codes since it embeds a qubit into a qudit. The code exploits the noncommutative geometry of discrete phase space to protect the qubit against both amplitude and phase errors. The performance of this code is evaluated on Weyl channels by means of the entanglement fidelity as a function of the error probability. A comparison with standard block codes, like five- and seven-qubit stabilizer codes, shows its superiority.

Entanglement-detection criteria are developed within the framework of the majorization formulation of uncertainty. The primary results are two theorems asserting linear and nonlinear separability criteria based on majorization relations, the violation of which would imply entanglement. Corollaries to these theorems yield infinite sets of scalar entanglement-detection criteria based on quasientropic measures of disorder. Examples are analyzed to probe the efficacy of the derived criteria in detecting the entanglement of bipartite Werner states. Characteristics of the majorization relation as a comparator of disorder uniquely suited to information-theoretical applications are emphasized throughout.

We propose a measure for genuine multipartite correlations suited for the study of dynamics in open quantum systems. This measure is contextual in the sense that it depends on how information is read from the environment. It is used to study an interacting collective system of atoms undergoing phase transitions as external parameters are varied. We show that the steady state of the system can have a significant degree of genuine multipartite quantum and classical correlations and that the proposed measure can serve as a witness of critical behavior in quantum systems.

We investigate the lateral Casimir interaction between two corrugated conductors when they enclose a dielectric slab. The magnitude of the lateral Casimir force can be changed due to the presence of a dielectric slab between them, and it strongly depends on the thickness ($d$) and dielectric function of the slab and also on the position of the slab with respect to the conductors. In addition, the distance between the conductors ($H$) and their corrugation wavelengths play important roles in tuning the lateral Casimir interaction. For fixed $d$ and $H$, quite interestingly, the magnitude of the lateral Casimir force varies when the position of the slab with respect to conductors changes, and it has a maximum when the slab is positioned precisely at the center of the space between the conductors. We find that the interaction decreases when the dielectric constant of the slab increases.

We have measured differential cross sections for single and dissociative capture for 25 and 75 keV protons colliding with H${}_2$ and He. Significant differences were found depending on whether the projectile beam was coherent or incoherent. For 75 keV $p$ $+$ H${}_2$ these differences can be mostly associated with molecular two-center interference and possibly some contributions from path interference. For 25 keV (both targets) they are mostly due to path interference between different impact parameters leading to the same scattering angles and, for the H${}_2$ target, possibly some contributions from molecular two-center interference.

The critical value of the atom-field coupling strength for a finite number of atoms is determined by means of both semiclassical and exact solutions. In the semiclassical approach we use a variational procedure with coherent and symmetry-adapted states, while for the exact quantum solution the concept of fidelity is employed. These procedures allow for the determination of the phase transitions in the model and coincide in the thermodynamic limit. For the three cases mentioned above, universal parametric curves are obtained for the expectation values of both the first quadrature of the electromagnetic field and the atomic relative population as implicit functions of the atom-field coupling parameter, valid for the ground and first-excited states.

Heralded noiseless amplification based on single-photon sources and linear optics is ideally suited for long-distance quantum communication tasks based on discrete variables. We experimentally demonstrate such an amplifier, operating at telecommunication wavelengths. Coherent amplification is performed with a gain of $G=1.98\pm 0.20$ for a state with a maximum expected gain $G=2$. We also demonstrate that there is no need for a stable phase reference between the initial signal state and the local auxiliary photons used by the amplifier. We discuss these results in the context of experimental device-independent quantum key distribution based on heralded qubit amplification, and we highlight several key challenges for its realization.

The quantum processes involved in the interaction of matter with, separately, an electron vortex (EV) and an optical vortex (OV) are described, with matter modeled in terms of a neutral two-particle atomic system, allowing for both the internal (electronic-type) motion and the gross (center-of-mass-type) motion of matter to be taken into account. The coupling of the atomic system to the EV is dominated by Coulomb forces, while that of the OV is taken in the $\mathbf{p}·\mathbf{A}$ canonical form which couples $\mathbf{A}$, the transverse vector potential of the optical vortex, to the linear momenta of the two-particle system. An analysis of the dipole active transition matrix element is carried out in each case. The electron vortex is found to be capable of exchanging its orbital angular momentum (OAM) with both the electronic and the center-of-mass motions of the atomic system in an electric dipole transition. In contrast, for electric dipole transitions the optical vortex is found to be capable of exchanging OAM only with the center of mass. The predictions are discussed with reference to recent experiments on electron-energy-loss spectroscopy using EVs traversing magnetized iron thin-film samples and those involving OVs interacting with chiral molecules.

Six years ago, by using operator techniques and path-integral methods, it was shown that the complex non-Hermitian $PT$-symmetric Hamiltonian $p^2-g{x}^4$ is equivalent to a conventional Hermitian Hamiltonian $p^2+4g{x}^4-2\hslash \sqrt{g}x$. Further it was revealed that the linear term in the Hermitian Hamiltonian is anomalous in the sense that it has no classical analog. In this paper we show that the complex non-Hermitian $\mathit{PT}$-symmetric Hamiltonian $p^2-g{x}^4+4i\hslash \sqrt{g}x$ and the conventional Hermitian Hamiltonian $p^2+4g{x}^4+6\hslash \sqrt{g}x$ have the same eigenspectra. In this case, the anomalous terms in both Hamiltonians are different from the previous one and vanish in the semiclassical limit. Further these equivalent Hamiltonians have zero-energy ground states. The exact ground-state wave functions and supersymmetric partner potentials are derived.

We extend to any maximally entangled state of a bipartite system whose constituents are arbitrarily (but finite) dimensional the result, recently derived for maximally entangled states of two-dimensional constituents, that hidden variable theories cannot have local parts, i.e., that their local averages cannot differ from the quantum-mechanical ones. Our result applies also to contextual theories not included in the former analysis.

We present a theoretical study of minimum error probability discrimination, using quantum-optical probe states, of $M$ optical phase shifts situated symmetrically on the unit circle. We assume ideal lossless conditions and full freedom for implementing quantum measurements and for probe-state selection, subject only to a constraint on the average energy, i.e., photon number. In particular, the probe state is allowed to have any number of signal and ancillary modes and to be pure or mixed. Our results are based on a simple criterion that partitions the set of pure probe states into equivalence classes with the same error probability performance. Under an energy constraint, we find the explicit form of the state that minimizes the error probability. This state is an unentangled but nonclassical single-mode state. The error performance of the optimal state is compared with several standard states in quantum optics. We also show that discrimination with zero error is possible only beyond a threshold energy of $(M-1)/2$. For the $M=2$ case, we show that the optimum performance is readily demonstrable with current technology. While transmission loss and detector inefficiencies lead to a nonzero erasure probability, the error rate conditional on no erasure is shown to remain the same as the optimal lossless error rate.

We study the entanglement of tripartite quantum states and provide analytical lower bounds of concurrence in terms of the concurrence of substates. The lower bound may improve all of the existing lower bounds of concurrence. The approach is generalized to arbitrary dimensional multipartite systems.

We present relativistic coupled-cluster (CC) calculations of energies, magnetic-dipole hyperfine constants, and electric-dipole transition amplitudes for low-lying states of atomic boron. The trivalent boron atom is computationally treated as a monovalent system. We explore performance of the CC method at various approximations. Our most complete treatment involves single, double, and the leading valence triple excitations. The calculations are done using several approximations in the CC method. The results are within 0.2$\%$–0.4$\%$ of the energy benchmarks. The hyperfine constants are reproduced with 1$\%$–2$\%$ accuracy.

Three different measurements have been reported for the ground-state quadrupole polarizability in singly ionized barium (Ba${}^{+}$) which disagree with each other. Our calculation of this quantity using the relativistic coupled-cluster method disagrees with two of the experimental values and is within the error bars of the other. We discuss the issues related to the accuracy of our calculations and emphasize the need for further experiments to measure the quadrupole polarizability for this state and/or the $5D$ states.

Single charge exchange in collisions between fast bare projectiles and heliumlike atomic systems is investigated by means of the four-body boundary-corrected first Born approximation. An extensive analytical study of the general transition amplitude for electron capture into the arbitrary $n^f{l}^f{m}^f$ final states of the projectile is carried out. The quantum-mechanical transition amplitude for both symmetric and asymmetric collisions is derived in terms of a two-dimensional numerical quadrature over real variables. An illustrative computation is performed involving state-selective and total single-capture cross sections for $p$-He and ${\mathrm{Li}}^{3+}$-He collisions at intermediate and high impact energies. Detailed comparisons with the available measurements are reported with the purpose of further assessing the validity and utility of the four-body corrected first Born method in various applications ranging from fusion research to radiotherapy.