We show that the quantum Zeno effect and the adiabatic change have a close connection even though the former means a halt of the dynamics by frequent measurements and the latter is the dynamics by a slowly changing Hamiltonian. We investigate the motion of a spin under stepping magnetic fields in terms of the (inverse) quantum Zeno effect. The relation between this model and the adiabatic change is studied. Another model is used to integrate the two effects into one formulation which is an extension of the proof of the adiabatic theorem. Despite their good parallelism, the asymptotic behaviors of the transition probability with respect to the total period $T$ have different forms; the former effect shows a $T^{-1}$ behavior while the latter scales $T^{-2}$.

We analyze the effects of inelastic scattering on the tunneling time theoretically, using generalized Nelson’s quantum mechanics. This generalization enables us to describe a quantum system with optical potential and channel couplings in a real-time stochastic approach, which seems to give us a new insight into quantum mechanics beyond Copenhagen interpretation.

It had been widely claimed that quantum mechanics can protect private information during public decision in, for example, the so-called two-party secure computation. If this were the case, quantum smart-cards, storing confidential information accessible only to a proper reader, could prevent fake teller machines from learning the PIN (personal identification number) from the customers’ input. Although such optimism has been challenged by the recent surprising discovery of the insecurity of the so-called quantum bit commitment, the security of quantum two-party computation itself remains unaddressed. Here I answer this question directly by showing that all one-sided two-party computations (which allow only one of the two parties to learn the result) are necessarily insecure. As corollaries to my results, quantum one-way oblivious password identification and the so-called quantum one-out-of-two oblivious transfer are impossible. I also construct a class of functions that cannot be computed securely in any two-sided two-party computation. Nevertheless, quantum cryptography remains useful in key distribution and can still provide partial security in “quantum money” proposed by Wiesner.

We consider the Bennett-Brassard cryptographic scheme, which uses two conjugate quantum bases. An eavesdropper who attempts to obtain information on qubits sent in one of the bases causes a disturbance to qubits sent in the other basis. We derive an upper bound to the accessible information in one basis, for a given error rate in the conjugate basis. Independently fixing the error rates in the conjugate bases, we show that both bounds can be attained simultaneously by an optimal eavesdropping probe. The probe interaction and its subsequent measurement are described explicitly. These results are combined to give an expression for the optimal information an eavesdropper can obtain for a given average disturbance when her interaction and measurements are performed signal by signal. Finally, the relation between quantum cryptography and violations of Bell’s inequalities is discussed.

It is shown that the optimum strategy of the eavesdropper described in the preceding paper can be expressed in terms of a quantum circuit in a way which makes it obvious why certain parameters take on particular values, and why obtaining information in one basis gives rise to noise in the conjugate basis.

It has recently been shown that there are efficient algorithms for quantum computers to solve certain problems, such as prime factorization, which are intractable to date on classical computers. The chances for practical implementation, however, are limited by decoherence, in which the effect of an external environment causes random errors in the quantum calculation. To combat this problem, quantum error correction schemes have been proposed, in which a single quantum bit (qubit) is “encoded” as a state of some larger number of qubits, chosen to resist particular types of errors. Most such schemes are vulnerable, however, to errors in the encoding and decoding itself. We examine two such schemes, in which a single qubit is encoded in a state of $n$ qubits while subject to dephasing or to arbitrary isotropic noise. Using both analytical and numerical calculations, we argue that error correction remains beneficial in the presence of weak noise, and that there is an optimal time between error correction steps, determined by the strength of the interaction with the environment and the parameters set by the encoding.

Recently, we proposed an iteration method for solving the eigenvalue problem of the time-independent Schrödinger equation [H. Meiβner and E. O. Steinborn, Int. J. Quantum Chem. 61, 777 (1997)]. This method, which is based on the generalized Bloch equation, calculates iteratively certain matrix elements of the wave operator which are the wave-function expansion coefficients (WECs). It is valid for boson as well as fermion systems. In this article we show that the WEC-iteration method, together with a renormalization technique, allows us to calculate energy eigenvalues for the ground state and excited states of the quartic, sextic, and octic anharmonic oscillator with very high accuracy. In order to overcome slow convergence in the iteration scheme we use a renormalization technique introduced by F. Vinette and J. Čížek [J. Math. Phys. (N.Y.) 32, 3392 (1991)] and show that this method is equivalent to the renormalization scheme based on the Bogoliubov transformation [N. N. Bogoliubov, Izv. Akad. Nauk SSSR, Ser. Fiz. 11, 77 (1947)] which is frequently used for the treatment of anharmonic oscillators in second quantization.

We show that quantum entanglement can be used as a substitute for communication when the goal is to compute a function whose input data are distributed among remote parties. Specifically, we show that, for a particular function among three parties (each of which possesses part of the function’s input), a prior quantum entanglement enables one of them to learn the value of the function with only two bits of communication occurring among the parties, whereas, without quantum entanglement, three bits of communication are necessary. This result contrasts the well-known fact that quantum entanglement cannot be used to simulate communication among remote parties.

We propose a method for measuring entangled vibronic quantum states of a trapped atom. It is based on the nonlinear dynamics of the system that appears by resonantly driving a weak electronic transition. The proposed technique allows the direct sampling of a Wigner-function matrix, displaying all knowable information on the quantum correlations of the motional and electronic degrees of freedom of the atom. It opens possibilities for testing fundamental predictions of the quantum theory concerning interaction phenomena.

How well can one copy an arbitrary qubit? To answer this question we consider two arbitrary vectors in a two-dimensional state space and an abstract copying transformation which will copy these two vectors. If the vectors are orthogonal, then perfect copies can be made. If they are not, then errors will be introduced. The size of the error depends on the inner product of the two original vectors. We derive a lower bound for the amount of noise induced by quantum copying. We examine both copying transformations which produce one copy and transformations which produce many, and show that the quality of each copy decreases as the number of copies increases.

Motivated by Popescu’s example of hidden nonlocality [Phys. Rev. Lett. 74, 2619 (1995)], we elaborate on the conjecture that quantum states that are intuitively nonlocal, i.e., entangled, do not admit a local causal hidden-variables model. We exhibit quantum states which either (i) are nontrivial counterexamples to this conjecture or (ii) possess a new kind of more deeply hidden irreducible nonlocality. Moreover, we propose a nonlocality complexity classification scheme suggested by the latter possibility. Furthermore, we show that Werner’s [Phys. Rev. A 40, 4277 (1989)] (and similar) hidden-variables models can be extended to an important class of generalized observables. Finally, a result of Fine [Phys. Rev. Lett. 48, 291 (1982)] on the equivalence of stochastic and deterministic hidden variables is generalized to causal models.

We report on a high-resolution photoabsorption study of ${\mathrm{SiH}}_4$ and ${\mathrm{SiD}}_4$ in the excitation region below the Si $2p$ threshold. The spectra can be separated into a lower region from valence excitations and an upper region from Rydberg excitations. In the valence region, intense excitations of vibrational bending modes were observed, reflecting a deviation of the core-excited molecules from the $T_d$ symmetry of ground-state silane. The derived geometry of the core- to -valence-excited molecules was found to be similar to that of the equivalent-cores molecule ${\mathrm{PH}}_4.$ For excitations to higher Rydberg states, symmetric-stretching vibrational modes were exclusively observed, while for the lowest Rydberg states, additional bending-mode vibrational excitations were found to contribute. The latter observation can be explained by a mixing of Rydberg and valence character, causing an increase of the deviation from $T_d$ symmetry with increasing valence character of the core-excited state. The spectral shape of the ${2p}_{3/2}^{-1}5s$ Rydberg state was analyzed by a four-mode Franck-Condon fit, providing insight into the structure of the core-excited molecule. The high instrumental resolution ($\Delta E=15\mathrm{}\mathrm{meV}$ full width at half maximum) allowed the derivation of the natural widths Γ of the Rydberg states, which were found to be identical within the limits of error (with $\Gamma =50\mathrm{}\pm 5\mathrm{meV}$).

Two special variational techniques, the Lehmann-Maehly (LM) method and the Kato method, recently proposed for solving the one-electron Dirac equation without variational collapse are investigated here in detail. Both methods represent significant progress compared to the traditional variational techniques because each of them provides rigorous upper and lower bounds to relativistic binding energies. A careful theoretical examination, however, reveals that only the LM method can be regarded as a radical solution of all the problems related to variational collapse. A numerical application to the Dirac equation for the hydrogen atom in a uniform magnetic field confirms this conclusion and shows as well that the LM method is also capable of yielding extremely accurate results and that the Kato method, in spite of a few limitations, represents in any case a useful approach.

Using a matrix diagonalization method, atomic Rydberg states with large electric-dipole moment states in strong crossed electric and magnetic fields with $\epsilon =0.075\mathrm{}$ $(\epsilon {=EB}^{-4/3}$; we use atomic units) are studied. The characteristics of the states and the influence of the atomic core on the large electric-dipole moment states are discussed.

We show both theoretically and experimentally that a “collective spectroscopy of dense resonances” is able to probe solely the long range electron-electron interaction in planetary atoms. Sequential resonant multiphoton laser excitation induces a characteristic modulation in the dense and unresolved absorption spectrum of $7\mathrm{f}n\mathcal{l}(\mathcal{l}>9)$ planetary states in Sr. The modulation stems from a well-known shake process of the outer electron, which can be described by an overlap integral of the initial- and final-state wave function. The long-range correlation in the final-state wave function, however, introduces characteristic shifts of the minima and asymmetrical heights of the side lobes of the overlap integral, which are absent in the case of pure Coulombic wave functions. For numerical calculations of the overlap integral we derive a local generalized dipole potential for the planetary wave function within an adiabatic approach. It accounts for all long-range electron-electron interactions elucidating the inner dipole structure of a planetary atom. The experimental data are in excellent agreement with the numerical calculations. The results clearly show the overlap integral to be a sensitive probe for long-range interactions, which has been questioned recently based on analytical approximations of the overlap integral.

The mean lifetimes of the ${}^3$He${}^{20}$Ne${}^{2+}$ and ${}^3$He${}^{22}$Ne${}^{2+}$ isotopes of the HeNe${}^{2+}$ molecular ion have been measured to be $55\pm 10$ ns and $72\pm 14$ ns, respectively. These mean lifetimes are similar to each other and about a factor of 3 smaller than the previously reported mean lifetime of the most abundant ${}^4$He${}^{20}$Ne${}^{2+}$ isotope. The small differences between the mean lifetimes of the different isotopes suggest that the long-lived HeNe${}^{2+}$ decays mainly by dipole electronic transitions to lower dissociating states. We have performed multireference configuration interaction (MRCI) calculations of the HeNe${}^{2+}$ ground state and many excited electronic states. The electronic ground state is found to be metastable and deep enough to sustain a single vibrational state in contrast to previous calculations. However, its calculated mean lifetime is $\sim$11 ps which is too short to be detected in our experiments. Excited states associated with the He + Ne${}^{2+}$ dissociation limits are bound by the long-range interaction between Ne${}^{2+}$ and polarized He. Similarly, the lowest state associated with a He${}^{2+}$+ Ne dissociation limit is also bound by long-range interaction. Due to an avoided crossing, the singlet state correlating with the first excited He${}^{+}$+ Ne${}^{+}$ limit is metastable. These states decay mainly by dipole electronic transitions to lower dissociating states. Decay rate calculations suggest five possible electronic states which are in agreement with the measured values.

We investigate the reliability of the adiabatic approximation in the hyperspherical harmonics formalism. It has been applied to a number of two-electron systems, both compact and loosely bound, with the interaction between the constituent particles being purely Coulombic. The results are compared with the exact ones obtained by solving the set of coupled differential equations numerically. The accuracy of this approximation for two-electron systems is compared with that for systems with nuclear interactions, and we find that the former is better. An explanation has been provided for better agreement with Coulombic systems, particularly for noncompact ones.

Systematic calculations of two-photon decay rates of metastable $2{}^1{S}_0$ and $2{}^3{S}_1$ states are presented for heliumlike ions with nuclear charges in the range $Z=2\mathrm{}–100$. These calculations include retardation and are carried out using relativistic configuration-interaction wave functions that account for the Breit interaction. Photon energy distributions and total rates are given. The relativistic $2{}^1{S}_0$ decay rates agree, to within two standard deviations, with precise measurements for heliumlike Ar, Ni, Br, Kr, and Nb. The calculated $2{}^1{S}_0$ rates are 30% smaller than the corresponding nonrelativistic rates at high $Z$. The $2{}^3{S}_1$ two-photon decay rates remain a factor of about ${10}^{-4}$ of the corresponding $M1\mathrm{}$ rates throughout the helium isoelectronic sequence.

Relativistic correlation energies have been computed for the open-shell ground states of group I B and III A elements up to $Z=79\mathrm{}$ (B, Al, Ga, In, Cu, Ag, Au), as well as their singly ionized closed-shell ions, by means of a recently developed relativistic many-body perturbation theory for open-shell multiplet states. All electrons are included in the correlation calculations. Analytic basis sets of Gaussian spinors are employed to expand the upper and lower components of the Dirac four-spinors in open-shell matrix Dirac-Fock and relativistic many-body perturbation procedures. The state-specific relativistic many-body perturbation theory for open-shell multiplet states involves a full implementation of generalized Møller-Plesset perturbation theory and accounts for both relativistic and electron correlation effects. The ionization energies have been calculated for the atoms, and the effects of relativity, electron correlation, and the nonadditive interplay of these effects on the ionization energies are analyzed.

Quantal calculations are presented for intramultiplet mixing collisions of ${\mathrm{Ne}}^{*}{(2p}^{5}3p)$ with $\mathrm{He}{(}^1{S}_0)$ in the 60–1250 meV collision energy range. The coupled equations are solved in a diabatic representation where the coupling terms are obtained using the model potential calculations of Hennecart and Masnou-Seeuws [J. Phys. B 18, 657 (1985)] for the interaction of the ${\mathrm{Ne}}^{*}$ outer electron with the two cores and values fitted on the spectroscopic data of Dabrowski and Herzberg [Mol. Spectrosc. 73, 183 (1978)] for the core-core interaction. An extensive comparison with the experimental data of the Eindhoven group is presented for absolute polarized cross sections and anisotropy parameters. Very good agreement is obtained with thermal energy data of Manders et al. [Phys. Rev. A 39, 4467 (1989)], while the systematic 30–40 % discrepancy with superthermal data of Boom et al. [Phys. Rev. A 49, 4660 (1994)] might be attributed to a calibration problem in the experiment rather than to an inaccuracy in the long-range potentials.