We propose and study a method for using nonmaximally entangled states to probabilistically implement desired nonlocal gates. Unlike distillation-based protocols, this method does not generate a maximally entangled state at intermediate stages of the process. As a consequence, the method becomes more efficient at a certain range of parameters. Gates of the form $\exp \left[i\xi {\sigma }_{n_A}{\sigma }_{n_B}\right]$ with $\xi ⪡1$ can be implemented with nearly unit probability and with vanishingly small entanglement, while for the distillation-based method, the gate is produced with a vanishing success probability. We also derive an upper bound to the optimal success probability and show that, in the small-entanglement limit, the bound is tight.

This paper constructs a local operation and classical communication protocol that achieves the global optimality of conclusive discrimination of any two pure states with arbitrary a priori probability. This can be interpreted that there is no “nonlocality” in the conclusive discrimination of two multipartite pure states.

We propose a physical scheme for formation of an arbitrary pattern of neutral atoms in an addressable optical lattice. We focus specifically on the generation of a perfect optical lattice of simple orthorhombic structure with unit occupancy, as required for initialization of a neutral atom quantum computer. The scheme employs a compacting process that is accomplished by sequential application of two types of operations: a flip operator that changes the internal state of the atoms, and a shift operator that selectively moves the atoms in one internal state along the lattice principal axis. Realizations of these elementary operations and their physical limitations are analyzed. The complexity of the compacting scheme is analyzed and we show that this scales linearly with the number of lattice sites per row of the lattice.

This paper initiates the study of hidden variables from a quantum computing perspective. For us, a hidden-variable theory is simply a way to convert a unitary matrix that maps one quantum state to another into a stochastic matrix that maps the initial probability distribution to the final one in some fixed basis. We list five axioms that we might want such a theory to satisfy and then investigate which of the axioms can be satisfied simultaneously. Toward this end, we propose a new hidden-variable theory based on network flows. In a second part of the paper, we show that if we could examine the entire history of a hidden variable, then we could efficiently solve problems that are believed to be intractable even for quantum computers. In particular, under any hidden-variable theory satisfying a reasonable axiom, we could solve the graph isomorphism problem in polynomial time, and could search an $N$-item database using $O\left(N^{1∕3}\right)$ queries, as opposed to $O\left(N^{1∕2}\right)$ queries with Grover’s search algorithm. On the other hand, the $N^{1∕3}$ bound is optimal, meaning that we could probably not solve $\mathrm{NP}$-complete problems in polynomial time. We thus obtain the first good example of a model of computation that appears slightly more powerful than the quantum computing model.

A scheme for nonconditional generation of long-living maximally entangled states between two spatially well separated atoms is proposed. In the scheme, $\Lambda$-type atoms pass a resonatorlike equipment of dispersing and absorbing macroscopic bodies giving rise to body-assisted electromagnetic field resonances of well-defined heights and widths. Strong atom-field coupling is combined with weak atom-field coupling to realize entanglement transfer from the dipole-allowed transitions to the dipole-forbidden transitions, whereby the entanglement is preserved when the atoms depart from the bodies and from each other. The theory is applied to the case of atoms passing by a microsphere.

Twirl operations, which convert impure singlet states into Werner states, play an important role in many schemes for entanglement purification. In this paper we describe strategies for implementing twirl operations, with an emphasis on methods suitable for ensemble quantum information processors such as nuclear magnetic resonance (NMR) quantum computers. We implement our twirl operation on a general two-spin mixed state using liquid-state NMR techniques, demonstrating that we can obtain the singlet Werner state with high fidelity.

We propose a method for controlling the decay and decoherence of a driven qubit that is strongly coupled to a reservoir, when the qubit resonance frequency is close to a continuum edge of the reservoir spectrum. This strong-coupling regime is outside the scope of existing methods of decay or decoherence control. We demonstrate that an appropriate sequence of nearly abrupt changes of the resonance frequency can protect the qubit state from decay and decoherence more effectively than the intuitively obvious alternative, which is to fix the resonance well within a forbidden band gap of the reservoir spectrum, as far as possible from the continuum edge. The “counterintuitive” nonadiabatic method outlined here can outperform its adiabatic counterparts in maintaining a high fidelity of quantum logic operations. The remarkable effectiveness of the proposed method, which requires much lower rates of frequency changes than previously proposed control methods, is due to the ability of appropriately alternating detunings from the continuum edge to augment the interference of the emitted and backscattered quanta, thereby helping to stabilize the qubit state against decay. Applications to the control of decay and decoherence near the edge of radiative, vibrational, and photoionization continua are discussed.

We present the positronium formation cross sections for a positron colliding with lithium and sodium for the collision energies from $0.01\mathrm{eV}$ up to $20\mathrm{eV}$ by the hyperspherical close-coupling method. For Li, our results agree with the experimental data and with other calculations. Our results for Na remain in agreement with previous close-coupling calculations, but do not support the latest experimental data for Na below $1\mathrm{eV}$. To validate our model potentials and method in the low-energy regime, the binding energies of positronic lithium and positronic sodium as well as the $s$-wave scattering lengths for positronium scattering from ${\mathrm{Li}}^{+}$ and ${\mathrm{Na}}^{+}$ are also presented.

We present a theoretical treatment of Bragg spectroscopy of an accelerating condensate in a solitary-wave state. Our treatment is based on the Gross-Pitaevskii equation with an optical potential representing the Bragg pulse and an additional external time-dependent potential generating the solitary-wave behavior. By transforming to a frame translating with the condensate, we derive an approximate set of equations that can be readily solved to generate approximate Bragg spectra. Our analytic method is accurate within a well-defined parameter regime and provides physical insight into the structure of the spectra. We illustrate our formalism using the example of Bragg spectroscopy of a condensate in a time-averaged orbiting potential trap.

The behavior of a single molecule driven simultaneously by a laser and by an electric radio frequency field is investigated using a non-Hermitian Hamiltonian approach. Employing the renormalization group method for differential equations, we calculate the average waiting time for the first photon emission event to occur, and determine the conditions for the suppression and enhancement of photon emission. An abrupt transition from localizationlike behavior to delocalization behavior is found.

The minimal number of ${}^3\mathrm{He}$ atoms required to form a bound cluster has been estimated by means of a diffusion Monte Carlo procedure within the fixed-node approximation. Several importance sampling wave functions have been employed in order to consider different shell-model configurations. The resulting upper bound for the minimal number is 32 atoms.

We propose a scheme to teleport an entangled state of two $\mathrm{\Lambda }$-type three-level atoms via photons. The teleportation protocol involves the local redundant encoding protecting the initial entangled state and allowing for repeating the detection until quantum information transfer is successful. We also show how to manipulate a state of many $\mathrm{\Lambda }$-type atoms trapped in a cavity.

We study macroscopic entanglement of various pure states of a one-dimensional $N$-spin system with $N⪢1$. Here, a quantum state is said to be macroscopically entangled if it is a superposition of macroscopically distinct states. To judge whether such superposition is hidden in a general state, we use an essentially unique index $p$: A pure state is macroscopically entangled if $p=2$, whereas it may be entangled but not macroscopically if $p<2$. This index is directly related to fundamental stabilities of many-body states. We calculate the index $p$ for various states in which magnons are excited with various densities and wave numbers. We find macroscopically entangled states $(p=2)$ as well as states with $p=1$. The former states are unstable in the sense that they are unstable against some local measurements. On the other hand, the latter states are stable in the senses that they are stable against any local measurements and that their decoherence rates never exceed $O\left(N\right)$ in any weak classical noises. For comparison, we also calculate the von Neumann entropy $S_{N∕2}\left(N\right)$ of a subsystem composed of $N∕2$ spins as a measure of bipartite entanglement. We find that $S_{N∕2}\left(N\right)$ of some states with $p=1$ is of the same order of magnitude as the maximum value $N∕2$. On the other hand, $S_{N∕2}\left(N\right)$ of the macroscopically entangled states with $p=2$ is as small as $O\left(\log N\right)⪡N∕2$. Therefore larger $S_{N∕2}\left(N\right)$ does not mean more instability. We also point out that these results are partly analogous to those for interacting many bosons. Furthermore, the origin of the huge entanglement, as measured either by $p$ or $S_{N∕2}\left(N\right)$, is discussed to be due to spatial propagation of magnons.

We present unified, systematic derivations of schemes in the two known measurement-based models of quantum computation. The first model (introduced by Raussendorf and Briegel, [Phys. Rev. Lett. 86, 5188 (2001)]) uses a fixed entangled state, adaptive measurements on single qubits, and feedforward of the measurement results. The second model (proposed by Nielsen, [Phys. Lett. A 308, 96 (2003)] and further simplified by Leung, [Int. J. Quant. Inf. 2, 33 (2004)]) uses adaptive two-qubit measurements that can be applied to arbitrary pairs of qubits, and feedforward of the measurement results. The underlying principle of our derivations is a variant of teleportation introduced by Zhou, Leung, and Chuang, [Phys. Rev. A 62, 052316 (2000)]. Our derivations unify these two measurement-based models of quantum computation and provide significantly simpler schemes.

The problem of quantum state exchange between three coupled quantum harmonic oscillators (which can represent interacting modes of the electromagnetic field in nonlinear crystal or interaction between laser beams and vibrational modes of ions in traps) is considered. We review different definitions of state exchange and find conditions of its possibility for arbitrary initial states in a chain of three oscillators with bilinear resonance coupling (corresponding to the rotating wave approximation), analyzing the structure of integrals of motion and propagators of the Schrödinger equation, as well as the Wigner functions. The influence of different parameters (such as detunings between coupling constants and temperatures of the intermediate oscillator and “receiver”) on the fidelity of exchange is analyzed.

We propose to use laser spectroscopy of ultracold molecules to establish improved limits on the time independence of electron-to-nuclear and nuclear-nuclear mass ratios by comparing, via an optical frequency comb, the frequencies of suitable sets of transitions in the ground electronic state. Hydrogen molecular ions trapped in a radiofrequency trap, sympathetically cooled by atomic ions, are identified as an accessible system. We show that the dipole-allowed rovibrational transition frequencies of $\mathrm{H}{\mathrm{D}}^{+}$ are suitable probes for a time dependence of $m_e∕m_p$ or $m_p∕m_d$. Separate bounds on the time independence of these constants can be obtained from a comparison of $\mathrm{H}{\mathrm{D}}^{+}$ and $\mathrm{H}_2{}^{+}$ transitions frequencies. Spectroscopy of single molecular ions via a quantum jump method is proposed as an approach toward ultrahigh precision.

We report on the anisotropic mass-dependent dispersion coefficients $C_6(M=0,\pm 1)$ for $\mathrm{He}\left(1{}^{1}S\right)\text{–}\mathrm{He}\left(2{}^{3}P\right)$ interaction using two different techniques. The first is a highly accurate Hylleraas basis-set diagonalization, while the second method is a semiempirical assessment based on tabulated oscillator strengths and available photoionization cross sections. The results from the two techniques agree to within 1.5%.

A generalization of the analytical theory of above-threshold ionization in the single active electron approximation is developed while taking into account leading non-dipole and relativistic corrections in the starting Hamiltonian. Special interest is placed on the high energy part of the photoelectron spectrum which consists of a plateau and a characteristic cutoff. It is shown that the correction due to the magnetic component of the laser field gives rise to a decrease of the plateau height, an increase of the maximal cutoff energy, and a drift of the emitted electrons in propagation direction of the laser field. Furthermore, the influence of the relativistic mass shift may become non-neglible by reducing the cutoff energy significantly. Spin effects or the Zitterbewegung play a comparably minor role in the investigated parameter regime of suboptical frequencies and high but not ultra-high laser intensities.