Consider an $n$-qubit computational basis state corresponding to a bit-string $x$, which has had an unknown local unitary applied to each qubit, and whose qubits have been reordered by an unknown permutation. We show that, given such a state with Hamming weight $\left|x\right|\le \lfloor n/2\rfloor$, it is possible to reconstruct $\left|x\right|$ with success-probability $1-\left|x\right|/\left(n-\left|x\right|+1\right)$, and thus to compute any symmetric function of $x$. We give explicit algorithms for computing whether or not $\left|x\right|\ge t$ for some $t$, and for computing the parity of $x$, and show that these are essentially optimal. These results can be seen as generalizations of the swap test for comparing quantum states.

The ability to accumulate and retrieve entanglement in the fields of two remote cavities with pairs of two-level atoms is discussed. It is shown that this transfer and retrieval can be indeed ideal with a resonant interaction. The case of initial nonmaximally entangled atomic pairs is also considered. This leads to the possibility of concentrating entanglement into a single pair at the retrieval stage. A teleportation protocol based on the same setup is presented. This allows us to achieve teleportation with built-in entanglement concentration.

Continuous-variable cluster states offer a potentially promising method of implementing a quantum computer. This paper extends and further refines theoretical foundations and protocols for experimental implementation. We give a cluster-state implementation of the cubic phase gate through photon detection, which, together with homodyne detection, facilitates universal quantum computation. In addition, we characterize the offline squeezed resources required to generate an arbitrary graph state through passive linear optics. Most significantly, we prove that there are universal states for which the offline squeezing per mode does not increase with the size of the cluster. Simple representations of continuous-variable graph states are introduced to analyze graph state transformations under measurement and the existence of universal continuous-variable resource states.

We have investigated the doubly excited ${{}^{1,3}P}^{\text{e}}$, ${{}^{1,3}D}^{\text{o}}$, and ${{}^{1,3}F}^{\text{e}}$ nonautoionizing states of helium atom with Coulomb and screened Coulomb (Yukawa) potentials in the framework of Ritz variational principle. Highly accurate correlated exponential wave functions with exponents generated by a quasirandom process are used to represent the correlation effect. For the Coulomb case, the metastable bound-excited $2pnp$ ${{}^{1}P}^{\text{e}}$ $\left(3\le n\le 5\right)$, $2pnp$ ${{}^{3}P}^{\text{e}}$ $\left(2\le n\le 5\right)$, $2pnd$ ${{}^{1,3}D}^{\text{o}}$ $\left(3\le n\le 9\right)$, and $2pnf$ ${{}^{1,3}F}^{\text{e}}$ $\left(4\le n\le 9\right)$ states energies are reported. Our upper-bound results for the $2pnd$ ${{}^{1}D}^{\text{o}}$ $\left(3\le n\le 7\right)$, $2pnf$ ${{}^{1}F}^{\text{e}}$ $\left(4\le n\le 8\right)$, ${{}^{3}D}^{\text{o}}$ and ${{}^{3}F}^{\text{e}}$ states are the lowest values up to this date. For the screened Coulomb case, the lower-lying metastable bound states energies for different screening parameters and for each spin states are also reported.

Charge transfer due to collisions of ground-state ${\text{O}}^{3+}\left(2s^{2}2p{}^{2}P\right)$ ions with He is investigated using the quantum-mechanical molecular-orbital close-coupling (QMOCC) method. The ab initio adiabatic potentials and radial couplings utilized in the QMOCC calculations are obtained from the multireference single- and double-excitation configuration interaction approach. State-selective and total charge-transfer cross sections are calculated for collision energies from 0.01 eV/u to 1 keV/u. Comparison with existing data reveals that the present QMOCC calculations are in good harmony with the measured total single-electron charge-transfer cross sections. Excellent agreement with the available experimental data is also found for state-selective cross sections at the measured energy region.

We show that entangled photons may be used in coherent multidimensional nonlinear spectroscopy to provide information on matter by scanning photon wave function parameters (entanglement time and delay of twin photons), rather than frequencies and time delays, as is commonly done with classical pulses. Signals are expressed and interpreted intuitively in terms of products of matter and field correlation functions using a diagrammatic close time path loop formalism which reveals the entangled quantum pathways of the fields and matter. The pump-probe signal measured when the pump and the probe are in a twin entangled state shows two-photon resonant contributions which scale linearly rather than quadratically with the incident beam intensity and reveal frequencies of off-resonant transitions. Two-dimensional spectrograms obtained by double Fourier transform of the signal with respect to the entanglement time and delay of the twins could provide detailed information on correlations among states and dynamical processes with high temporal resolution. The analogy with multidimensional time-domain optical techniques which use sequences of short classical pulses and pulse shaping algorithms is pointed out.

We present an ab initio nonperturbative investigation of the frequency comb structure and coherence within each order of the high-order harmonic generation (HHG) of rare-gas atoms by means of the time-dependent density-functional theory (TDDFT) with optimized effective potential (OEP) and self-interaction correction (SIC). The $\text{TDDFT}+\text{OEP}-\text{SIC}$ equations are solved accurately and efficiently by means of the time-dependent generalized pseudospectral technique. We found that a nested comb structure appears within each order of the harmonics, ranging from the first harmonic all the way to the cutoff region. We explore in detail the temporal coherence and robustness of the comb structure by varying the laser-pulse separation $\tau$, the number of pulses $N$, the phase difference between pulses $\Delta \varphi$, and the laser intensity. The frequency comb structure and coherence are preserved in each harmonic regardless of the values of $\tau$ and $N$ used for the case of weak and medium strong incident laser-pulse trains. The time-frequency characteristics of the HHG coherence structure are analyzed in details by means of the wavelet transform of the time-dependent induced dipoles. The interference modulation can be attributed to the constant phase relationship of harmonics among successive pulses. However, under superstrong fields, nonuniform and substantial ionization takes place during each pulse, jeopardizing the temporal coherence of the emitted frequency comb modes. Finally, we found that the dynamical electron correlation, which is included in the present $\text{TDDFT}+\text{OEP}-\text{SIC}$ treatment but not in the single-active-electron model, is significant for the quantitative exploration of the frequency comb structure and coherence of higher harmonics.

We study the tunneling of Bogoliubov excitations through a barrier in a Bose-Einstein condensate. We extend our previous work [S. Tsuchiya and Y. Ohashi, Phys. Rev. A 78, 013628 (2008)] to the case when condensate densities are different between the left and right of the barrier potential. In the framework of the Bogoliubov mean-field theory, we calculate the transmission probability and phase shift, as well as the energy flux and quasiparticle current carried by Bogoliubov excitations. We find that Bogoliubov phonons twist the condensate phase due to a back-reaction effect, which induces the Josephson supercurrent. While the total current given by the sum of quasiparticle current and induced supercurrent is conserved, the quasiparticle current flowing through the barrier potential is shown to be remarkably enhanced in the low-energy region. When the condensate densities are different between the left and right of the barrier, the excess quasiparticle current, as well as the induced supercurrent, remains finite far away from the barrier. We also consider the tunneling of excitations and atoms through the boundary between the normal and superfluid regions. We show that supercurrent can be generated inside the condensate by injecting free atoms from outside. On the other hand, atoms are emitted when the Bogoliubov phonons propagate toward the phase boundary from the superfluid region.

Half-integer-photon resonances in a periodically shaken double well are investigated on the level of the $N$-particle quantum dynamics. Contrary to nonlinear mean-field equations, the linear $N$-particle Schrödinger equation does not contain any nonlinearity which could be the origin of such resonances. Nevertheless, analytic calculations on the $N$-particle level explain why such resonances can be observed even for particle numbers as low as $N=2$. These calculations also demonstrate why fractional photon resonances are not restricted to half-integer values.

Ground-plane cloak designs are presented, which minimize scattering of electromagnetic radiation from metallic objects in the visible spectrum. It is showed that simplified ground-plane cloaks made from only a few blocks of all-dielectric isotropic materials, either embedded in a background medium or in free space, can provide considerable cloaking performance while maintaining their broadband nature. A design which operates isolated in free space that cloaks radiation originating from a specified direction is also analyzed. These schemes should be much easier to be demonstrated experimentally compared to full designs.

We present the improved calculations over the results of Korobov [Phys. Rev. A 74, 052506 (2006)] for the energy levels and hyperfine structure of the hydrogen molecular ion $\text{H}_2{}^{+}$, including the relativistic corrections of orders ${\alpha }^2\text{Ry}$ and ${\alpha }^2{m}_e/m_p\text{Ry}$, using variationally constructed basis sets in Hylleraas coordinates. In particular, the computational uncertainty of 3 kHz in Korobov’s calculation for the ${\alpha }^2\text{Ry}$ correction to the two-photon transition frequency $\left(L=0,v=0\right)\to \left(L=0,v=1\right)$ is eliminated.

The final momentum distribution for the scattering of He from a corrugated surface representation of Cu(110) is obtained from semiclassical theory. We derive a formally exact expression for the distribution which involves the absolute value squared of a single overlap of the initial wave function with the final momentum state. This reduces the number of phase-space integrals appearing in the semiclassical expressions and therefore leads to a large reduction in the computational effort. In addition, other energy-dependent observables are directly accessible from the momentum distribution without the need for further simulations. Using this formalism, we compare the quality of results obtained using a classical Wigner approximation and the frozen Gaussian, Herman-Kluk, and thawed Gaussian semiclassical propagators. We find that the thawed Gaussian is not only the best approximation, but it also converges more rapidly than the other semiclassical methods. The frozen Gaussian Herman-Kluk propagator is superior to the frozen Gaussian propagator. In contrast, the classical Wigner approach is qualitatively wrong as it does not properly account for the interference which dominates the angular distribution.

The triple differential cross sections (TDCS) for the photodouble ionization of He, Ne, Ar, and Xe leading to the ${\text{He}}^{2+}\left(1s^0{{}^{1}S}^e\right)$, ${\text{Ne}}^{2+}\left(2s^{0}2p^6{{}^{1}S}^e\right)$, ${\text{Ar}}^{2+}\left(3s^{0}3p^6{{}^{1}S}^e\right)$, and ${\text{Xe}}^{2+}\left(5s^{0}5p^6{{}^{1}S}^e\right)$ states have been measured at about 20 eV above their respective thresholds with the two photoelectrons equally sharing the excess energy. The experimental data are analyzed using a parametrization recently proposed [J. Phys. B 41, 245205 (2008)] which takes into account experimental uncertainties. The parametrization provides a satisfactory representation of the shape of the measured TDCS. The study of the behavior of the gerade amplitude of the TDCS in the different targets gives hints on the dependence of the electron correlation with the principal quantum number $n$ of the ionized $ns$ orbital.

We propose a scheme to identify and separate the contributions from the short and long electron trajectories in the high-order harmonic generation in argon atoms. The modification of the diving laser field by using a diaphragm prior to focusing is demonstrated to be an effective way of controlling the short and long path contributions in harmonic emission since different macroscopic phase-matching conditions are satisfied, respectively. We show that the short and the long path harmonic emission are separated by adjusting the laser focusing geometry and modifying the laser field. This offers a way of selectively probing and controlling the electron dynamics in intense laser fields.

The propagation of a pair of quantized fields inside a medium of three-level atoms in the $\Lambda$ configuration is analyzed. We calculate the stationary quadrature noise spectrum of the field after propagating through the medium in the case where the field has a general (but small) noise spectrum and the atoms are in a coherent population trapping state and show electromagnetically induced transparency. Although the mean values of the field remain unaltered as the field propagates, there is an oscillatory interchange of noise properties between the probe and pump fields. Also, as the field propagates, there is an oscillatory creation and annihilation of correlations between the probe and pump quadratures. We further study the field propagation of squeezed states when there is two-photon resonance, but the field has a detuning $\delta$ from atomic resonance. We show that the field propagation is very sensitive to $\delta$. The propagation in this case can be explained as a combination of a frequency-dependent rotation of maximum squeezed quadrature with an interchange of noise properties between pump and probe fields. It is also shown that the effect of the Doppler width in a squeezed state propagation is considerable.

We give a sufficient criterion that guarantees that a many-body quantum system can be controlled by properly manipulating the (local) Hamiltonian of one of its subsystems. The method can be applied to a wide range of systems: it does not depend on the details of the couplings but only on their associated topology. As a special case, we prove that Heisenberg and Affleck-Kennedy-Lieb-Tasaki chains can be controlled by operating on one of the spins at their ends. In principle, arbitrary quantum algorithms can be performed on such chains by acting on a single qubit.

We argue that it is possible in principle to reduce the uncertainty of an atomic magnetometer by double passing a far-detuned laser field through the atomic sample as it undergoes Larmor precession. Numerical simulations of the quantum Fisher information suggest that, despite the lack of explicit multibody coupling terms in the system’s magnetic Hamiltonian, the parameter estimation uncertainty in such a physical setup scales better than the conventional Heisenberg uncertainty limit over a specified but arbitrary range of particle number. Using the methods of quantum stochastic calculus and filtering theory, we demonstrate numerically an explicit parameter estimator (called a quantum particle filter) whose observed scaling follows that of our calculated quantum Fisher information. Moreover, the quantum particle filter quantitatively surpasses the uncertainty limit calculated from the quantum Cramér-Rao inequality based on a magnetic coupling Hamiltonian with only single-body operators. We also show that a quantum Kalman filter is insufficient to obtain super-Heisenberg scaling and present evidence that such scaling necessitates going beyond the manifold of Gaussian atomic states.

We consider the distinguishability of Gaussian states from the viewpoint of continuous-variable quantum cryptography using postselection. Specifically, we use the probability of error to distinguish between two pure coherent (squeezed) and two particular mixed symmetric coherent (squeezed) states where each mixed state is an incoherent mixture of two pure coherent (squeezed) states with equal and opposite displacements in the conjugate quadrature. We show that the two mixed symmetric Gaussian states (where the various components have the same real part) never give an eavesdropper more information than the two pure Gaussian states. Furthermore, when considering the distinguishability of squeezed states, we show that varying the amount of squeezing leads to a “squeezing” and “antisqueezing” of the net information rates.

This paper characterizes a quantum correlation formed in an ensemble of atomic two-level systems that stores a narrow-band squeezed state of light by coherently trapping an electron in an atomic superposed state $a|1⟩+b|0⟩$. In the storage process, a photonic quantum correlation in the squeezed light is transformed into an atomic quantum correlation between $N$ atoms in an adiabatic way. If we regard the atomic superposed state as a 1/2-spin state and adopt the framework of a pairwise spin entanglement to analyze the atomic quantum correlation, we can identify a certain entangled state of a spin pair as the atomic signature of the squeezed light. The pairwise spin entangled state reflects all the physical properties of the squeezed light. By following the dissipative time evolution in the pairwise entangled state, we can describe the degraded properties of the squeezed light in retrieval.

We study a $\left(k,m\right)$-threshold controlling scheme for controlled quantum teleportation. A standard polynomial coding over $\text{GF}\left(p\right)$ with prime $p>m-1$ needs to distribute a $d$-dimensional qudit with $d\ge p$ to each controller for this purpose. We propose a scheme using $m$ qubits (two-dimensional qudits) for the controllers’ portion, following a discussion on the benefit of a quantum control in comparison to a classical control of a quantum teleportation.