We explore the connection between quantum brachistochrone (time-optimal) evolution of a three-qubit system and its residual entanglement called three-tangle. The result shows that the entanglement between two qubits is not required for some brachistochrone evolutions of a three-qubit system. However, the evolution between two distinct states cannot be implemented without its three-tangle, except for the trivial cases in which less than three qubits attend evolution. Although both the probability density function of the time-averaged three-tangle and that of the time-averaged squared concurrence between two subsystems become more and more uniform with the decrease in angles of separation between an initial state and a final state, the features of their most probable values exhibit a different trend.

We study the non-Hermitian quantum mechanics for the discrete system. This paper gives an exact analytic single-particle solution for an $N$-site tight-binding chain with two conjugated imaginary potentials $\pm i\gamma$ at two end sites, which Hamiltonian has parity-time symmetry ($\mathcal{P}\mathcal{T}$ symmetry). Based on the Bethe ansatz results, it is found that, in single-particle subspace, this model is comprised of two phases: an unbroken symmetry phase with a purely real energy spectrum in the region $\gamma \prec {\gamma }_c$ and a spontaneously broken symmetry phase with $N-2$ real and two imaginary eigenvalues in the region $\gamma \succ {\gamma }_c$. The behaviors of eigenfunctions and eigenvalues in the vicinity of ${\gamma }_c$ are investigated. It is shown that the boundary of two phases possesses the characteristics of exceptional point. We also construct the equivalent Hermitian Hamiltonian of the present model in the framework of metric-operator theory. We find out that the equivalent Hermitian Hamiltonian can be written as another bipartite lattice model with real long-range hoppings.

We present a comprehensive and self-contained simplified review of the quantum computing scheme of Raussendorf et al. [Phys. Rev. Lett. 98, 190504 (2007); N. J. Phys. 9, 199 (2007)], which features a two-dimensional nearest-neighbor coupled lattice of qubits, a threshold error rate approaching 1%, natural asymmetric and adjustable strength error correction, and low overhead arbitrarily long-range logical gates. These features make it one of the best and most practical quantum computing schemes devised to date. We restrict the discussion to direct manipulation of the surface code using the stabilizer formalism, both of which we also briefly review, to make the scheme accessible to a broad audience.

We use the language of semidefinite programming and duality to derive necessary and sufficient conditions for the optimal Lewenstein-Sanpera decomposition (LSD) of two-qubit states. We first provide a simple and natural derivation of the Wellens-Kuś equations for full-rank states. Then, we obtain a set of necessary and sufficient conditions for the optimal decomposition of rank-3 states. This closes the gap between the full-rank case, where optimality conditions are given by the Wellens-Kuś equations, and the rank-2 case, where the optimal decomposition is analytically known. We also give an analytic expression for the optimal LSD of a special class of rank-3 states. Finally, our formulation ensures efficient numerical procedures to return the optimal LSD for any arbitrary two-qubit state.

Given oracle access to an unknown unitary $C$ from the Clifford group and its conjugate, we give an exact algorithm for identifying $C$ with $O\left(n\right)$ queries, which we prove is optimal. We then extend this to all levels of the Gottesman-Chuang hierarchy (also known as the ${\mathcal{C}}_k$ hierarchy). Further, for unitaries not in the hierarchy itself but known to be close to an element of the hierarchy, we give a method of finding this close element. We also present a Clifford testing algorithm that decides whether a given black-box unitary is close to an element of the Clifford group or far from every element of the Clifford group.

Bipartite maximally entangled states have the property that the largest Schmidt coefficient reaches its lower bound. However, for multipartite states, the standard Schmidt decomposition generally does not exist. We use a generalized Schmidt decomposition and the geometric measure of entanglement to characterize three-qubit pure states and derive a single-parameter family of maximally entangled three-qubit states. The paradigmatic Greenberger-Horne-Zeilinger (GHZ) and $W$ states emerge as extreme members in this family of maximally entangled states. This family of states possesses different trends of entanglement behavior: in going from GHZ to $W$ states, the geometric measure, the relative entropy of entanglement, and the bipartite entanglement all increase monotonically whereas the three-tangle and bipartition negativity both decrease monotonically.

A high-resolution flat-crystal spectrometer was used on the SuperEBIT electron beam ion trap to measure the energies of the $2s_{1/2}-2p_{3/2}$ transitions in lithiumlike through fluorinelike tungsten. These transitions are strongly affected by energy shifts due to quantum electrodynamics (QED). SuperEBIT was run at an electron energy of $103.2\pm 0.5\text{keV}$ and an electron beam current of 150 mA to generate the respective charge states; hydrogenlike aluminum and neonlike krypton were used as calibration elements. The spectra were analyzed with and the results compared to calculations based on the flexible atomic code. Good agreement was found. The measurements yielded line positions with a precision of 1–2 eV, which test QED calculations to 5%–10%.

We describe the measurement and compensation of optical Stark shifts induced by an off-resonant pulse for manipulating the terahertz-separated states $3{{}^{2}D}_{3/2}–3{{}^{2}D}_{5/2}$, in a single trapped ${{}^{40}\text{C}\text{a}}^{+}$ ion. These states can be used as a quantum bit and are coupled by a two-photon stimulated Raman transition with phase-locked light sources bridged by an optical comb generator. The induced optical Stark shift is measured by Ramsey interferometry. We estimate the power ratio of Raman beams that cancel the level shift with an uncertainty of 170 Hz. A shift of the same amount as this uncertainty is estimated to give rise to an infidelity of approximately $7.6\times {10}^{-4}$ during a $\pi /2$ rotation operation.

We show for rotational alignment of diatomic molecules that the crossover from nonadiabatic to adiabatic limits is well described by a convolution of excitation pulse envelope and sinusoidal molecular response and that it takes place in a uniform way in the region between 0.1 and 1 for the ratio of pulse duration to rotational period. In a nonresonant Raman-type excitation, this crossover is used to manipulate the $J$ composition of a rotational wave packet with respect to the initial thermal distribution. By optimizing the duration of a single pulse, arbitrarily narrow distributions at low $J$ levels can be formed. A double-pulse excitation, where a longer second pulse acts as a selective dump pulse, allows to prepare nonthermal distributions centered at high $J$ values. With the alignment signal on top of an isotropic background, experimental techniques sensitive to the induced anisotropy are optimally suited for implementation. To demonstrate the efficiency of the method, numerical simulations are carried out for rotational alignment in ${{}^{14}\text{N}}_2$ at various experimentally relevant laser intensities. The scheme is transferable to quantum systems with a significant variation in transition frequencies between subsequent levels.

We study the quantum phase transition between superfluid and Mott-insulator states for ultracold bosons with two internal states forming two bands of an optical lattice. The two atomic states are resonantly coupled by a coherent field enclosed in a single cavity mode, which mediates transitions between the two bosonic particle modes via absorption or emission of cavity photons. As nonlocal atomic coherence can build up via photon assisted tunneling, this coupling shifts the transition to the Mott-insulator phase toward deeper lattice potentials and stronger on-site interaction. Varying the intra and interband on-site interactions leads to several different atomic phase configurations. There are even parameter regions, where a mean-field approach predicts concurrence of a Mott-insulator state in one band and a superfluid in the other band.

We consider necklace solitons supported by circular waveguide arrays with out-of-phase modulation of nonlinearity and linear refractive index. Such two-dimensional necklace solitons appear as rings of multiple out-of-phase bright spots. We show that necklace solitons are stable if their peak intensity is low or moderate and that the domain of stability shrinks with increasing nonlinearity modulation depth. However, we find that the stability domains expand with increasing number of necklace spots.

We investigate the domain of masses for which a bound state with total orbital momentum $L=1$ and unnatural parity $P=+1$ exists for the Coulomb systems $\left(m_1^{+},m_2^{-},m_3^{-}\right)$.

It is often observed in the ground state of quantum lattice systems with local interactions that the entropy of a large region is proportional to its surface area. In some cases, this area law is corrected with a logarithmic factor. This contrasts with the fact that in almost all states of the Hilbert space, the entropy of a region is proportional to its volume. This paper shows that low-energy states have (at most) an area law with the logarithmic correction, provided two conditions hold: (i) the state has sufficient decay of correlations and (ii) the number of eigenstates with vanishing energy density is not exponential in the volume. These two conditions are satisfied by many relevant systems. The central idea of the argument is that energy fluctuations inside a region can be observed by measuring the exterior and a superficial shell of the region.

We analyze effects of squeezing upon superpositions of coherent states (SCSs) and entangled coherent states for Bell-inequality tests. We find that external squeezing can always increase the degrees of Bell violations, if the squeezing direction is properly chosen, for the case of photon parity measurements. On the other hand, when photon on/off measurements are used, the squeezing operation can enhance the degree of Bell violations only for moderate values of amplitudes and squeezing. We point out that a significant improvement is required over currently available squeezed SCSs in order to directly demonstrate a Bell-inequality violation in a real experiment.

The signal half of an entangled twin beam, generated using spontaneous parametric downconversion, interrogates a region of space that is suspected of containing a target and has high loss and high (entanglement-breaking) background noise. A joint measurement is performed on the returned light and the idler beam that was retained at the transmitter. An optimal quantum receiver, whose implementation is not yet known, was shown to achieve 6 dB gain in the error-probability exponent relative to that achieved with a single coherent-state (classical) laser transmitter and the optimum receiver. We present two structured optical receivers that achieve up to 3 dB gain in the error exponent over that attained with the classical sensor. These are designs of quantum-optical sensors for target detection, which can be readily implemented in a proof-of-concept experiment, that appreciably outperform the best classical sensor in the low-signal-brightness, high-loss, and high-noise operating regime.

A proposal for applying nonadiabatic geometric phases to quantum computing, called double-loop method [S.-L. Zhu and Z. D. Wang, Phys. Rev. A 67, 022319 (2003)], is demonstrated in a liquid-state nuclear magnetic-resonance quantum computer. Using a spin-echo technique, the original method is modified so that quantum gates are implemented in a standard high-precision nuclear magnetic-resonance system for chemical analysis. We show that a dynamical phase is successfully eliminated and a one-qubit quantum gate is realized although the gate fidelity is not high.

$K\beta$-to-$K\alpha$ x-ray intensity ratios of Fe, Cr, and Ni have been measured in pure metals and in alloys of ${\text{Fe}}_x{\text{Ni}}_{1-x}$ ($x=0.8$, 0.7, 0.6, 0.5, 0.4, 0.3, and 0.2), ${\text{Ni}}_x{\text{Cr}}_{1-x}$ ($x=0.8$, 0.6, 0.5, 0.4, and 0.2), ${\text{Fe}}_x{\text{Cr}}_{1-x}$ ($x=0.9$, 0.7, and 0.5), and ${\text{Fe}}_x{\text{Cr}}_y{\text{Ni}}_{1-\left(x+y\right)}$ ($x=0.7-y=0.1$, $x=0.5-y=0.2$, $x=0.4-y=0.3$, $x=0.3-y=0.3$, $x=0.2-y=0.2$, and $x=0.1-y=0.2$) following excitation by 22.69 keV x rays from a 10 mCi ${}^{109}\text{C}\text{d}$ radioactive point source. The valence-electron configurations of these metals were determined by corporation of measured $K\beta$-to-$K\alpha$ x-ray intensity ratios with the results of multiconfiguration Dirac-Fock calculation for various valence-electron configurations. Valence-electron configurations of $3d$ transition metals in alloys indicate significant differences with respect to the pure metals. Our analysis indicates that these differences arise from delocalization and/or charge transfer phenomena in alloys. Namely, the observed change of the valence-electron configurations of metals in alloys can be explained with the transfer of $3d$ electrons from one element to the other element and/or the rearrangement of electrons between $3d$ and $4s,4p$ states of individual metal atoms.

For deep potentials with attractive tails proportional to $-1/r^4$, as occur in the interaction between a charged ion and a neutral polarizable atom (or molecule), we present an analytical expression for the tail contribution to the quantization function $F\left(E\right)$ which determines the near-threshold bound-state energies $E_n$ according to the quantization rule $n_{\text{th}}-n=F\left(E_n\right)$. Its usefulness is demonstrated in applications to a model Lennard-Jones potential and to the $\text{H}_2{}^{+}$ molecular ion.

We theoretically investigate the electron dynamics of the high-order harmonics in a wave-form-controlled two-color midinfrared pulse synthesized by a 2000-nm driving pulse and a much weaker 800-nm control pulse. It is shown that the acceleration and the ionization steps can be simultaneously modulated in the few-cycle regime, which not only broadens the bandwidth but also enhances the harmonic yields of the generated supercontinuum with the photon energies of hundreds of eV. The most important result is that the electrons with the highest return kinetic energies, which contribute to the supercontinuum generation near the cutoff, can be ionized near the peak of the electric field where the ionization rate reaches maximum. We also extend this electron dynamic control to the multicycle regime, enabling the generation of a supercontinuum with a bandwidth of 60 eV and an intensity comparable to that of the lower-order harmonics.