We present a theoretical model of the quantum decoherence experienced by a pair of polarization-entangled photons, after one of them is sent through a nanohole array, and compare this with the classical depolarization experienced by light with a fixed polarization when this is sent through the same array. We discuss the conditions under which the quantum visibility and the classical degree of polarization are the same. Experimental verification is done with arrays of square and hexagonal symmetry.

It is shown that it is possible to rule out all local and stochastic hidden variable models accounting for the quantum mechanical predictions implied by almost any entangled quantum state vector of any number of particles whose Hilbert spaces have arbitrary dimensions, without resorting to Bell-type inequalities. The present proof makes use of the mathematically precise notion of Bell locality and it involves only simple set theoretic arguments.

A formula for the commutator of tensor product matrices is used to show that, for qubits, compatibility of quantum multiparty observables almost never implies local compatibility at each site, and to predict when this happens/does not happen in a concise manner. In particular, it is shown that two “fully nontrivial” $n$-qubit observables are compatible locally and globally if and only if they are equal up to sign. In addition, the formula gives insight into the construction of paradoxes of the type of the Kochen-Specker theorem, which can then be easily rephrased into proposals for no-hidden-variable experiments of the type of the “Bell theorem without inequalities.”

Bell inequalities, considered within quantum mechanics, can be regarded as nonoptimal witness operators. We discuss the relationship between such Bell witnesses and general entanglement witnesses in detail for the Bell inequality derived by Clauser, Horne, Shimony, and Holt (CHSH) [Phys. Rev. Lett. 23, 880 (1969)]. We derive bounds on how much an optimal witness has to be shifted by adding the identity operator to make it positive on all states admitting a local hidden variable model. In the opposite direction, we obtain tight bounds for the maximal proportion of the identity operator that can be subtracted from such a CHSH witness, while preserving the witness properties. Finally, we investigate the structure of CHSH witnesses directly by relating their diagonalized form to optimal witnesses of two different classes.

We propose an efficient decoy-state protocol for practical quantum key distribution using coherent states. The protocol uses four intensities of different coherent light. A good final key rate is achieved by our protocol with typical parameters of existing practical setups, even with a very low channel transmittance.

Perfect state transfer is possible in modulated spin chains [Phys. Rev. Lett. 92, 187902 (2004)], imperfections, however, are likely to corrupt the state transfer. We study the robustness of this quantum communication protocol in the presence of disorder both in the exchange couplings between the spins and in the local magnetic field. The degradation of the fidelity can be suitably expressed, as a function of the level of imperfection and the length of the chain, in a scaling form. In addition the time signal of fidelity becomes fractal. We further characterize the state transfer by analyzing the spectral properties of the Hamiltonian of the spin chain.

Given a finite group $G$ with a bilocal representation, we investigate the bipartite entanglement in the state constructed from the group algebra of $G$ acting on a separable reference state. We find an upper bound for the von Neumann entropy for a bipartition $(A,B)$ of a quantum system and conditions to saturate it. We show that these states can be interpreted as ground states of generic Hamiltonians or as the physical states in a quantum gauge theory and that under specific conditions their geometric entropy satisfies the entropic area law. If $G$ is a group of spin flips acting on a set of qubits, these states are locally equivalent to 2-colorable (i.e., bipartite) graph states and they include Greenberger-Horne-Zeilinger, cluster states, etc. Examples include an application to qudits and a calculation of the $n$-tangle for 2-colorable graph states.

We show that (1) the violation of the Ekert 1991 inequality is a sufficient condition for certification of the Kochen-Specker (KS) theorem, and (2) the violation of the Bennett-Brassard-Mermin 1992 (BBM92) inequality is, also, a sufficient condition for certification of the KS theorem. Therefore the success in each quantum key distribution protocol reveals the nonclassical feature of quantum theory, in the sense that the KS realism is violated. Further, it turned out that the Ekert inequality and the BBM inequality are depictured by distillable entanglement witness inequalities. Here, we connect the success in these two key distribution processes into the no-hidden-variables theorem and into witness on distillable entanglement. We also discuss the explicit difference between the KS realism and Bell’s local realism in the Hilbert space formalism of quantum theory.

Decoy states have recently been proposed as a useful method for substantially improving the performance of quantum key distribution (QKD). Here, we present a general theory of the decoy state protocol based on only two decoy states and one signal state. We perform optimization on the choice of intensities of the two decoy states and the signal state. Our result shows that a decoy state protocol with only two types of decoy states—the vacuum and a weak decoy state—asymptotically approaches the theoretical limit of the most general type of decoy state protocol (with an infinite number of decoy states). We also present a one-decoy-state protocol. Moreover, we provide estimations on the effects of statistical fluctuations and suggest that, even for long-distance (larger than 100 km) QKD, our two-decoy-state protocol can be implemented with only a few hours of experimental data. In conclusion, decoy state quantum key distribution is highly practical.

We present high-luminosity experimental investigations of the transfer ionization $(\mathrm{TI}:p+\mathrm{He}\to {\mathrm{H}}^0+{\mathrm{He}}^{2+}+e^{-})$ process in collisions between fast protons and neutral helium atoms in the earlier inaccessibly high-energy range $1.4–5.8\mathrm{MeV}$. The protons were stored in the heavy-ion storage and cooler ring CRYRING, where they intersected a narrow supersonic helium gas jet. We discuss the longitudinal recoil-ion momentum distribution, as measured by means of cold-target recoil-ion momentum spectroscopy and find that this distribution splits into two completely separated peaks at the high end of our energy range. These separate contributions are discussed in terms of the earlier proposed Thomas TI (TTI) and kinematic TI mechansims. The cross section of the TTI process is found to follow a $\sigma \propto v^{-b}$ dependence with $b=10.78\pm 0.27$ in accordance with the expected $v^{-11}$ asymptotic behavior. Further, we discuss the probability for shake-off accompanying electron transfer and the relation of this TI mechanism to photodouble ionization. Finally the influence of the initial-state electron velocity distribution on the TTI process is discussed.

The surface peak of $98\text{‐}\mathrm{keV}$ protons backscattered from a clean Al (110) surface has been studied in detail for three different scattering geometries. The corresponding energy-loss distributions are asymmetric due to the single and double ionization of the Al inner-shell electrons ($L$ shell). Effects beyond the independent-electron model (inner-shell collective effects) have been observed by using Monte Carlo simulations for the ion ballistic and coupled-channel calculations for the inelastic energy loss. These effects decrease the width by up to 10% for the full width at half maximum. Correspondingly, the low-energy tail of the surface peak is reduced in intensity by more than 30% in the case of a large number of near central collisions as in shadowing and blocking geometries.

Vicinage effects in the energy loss and the electron emission spectra are studied in the presence of Coulomb explosion of swift, heavy molecular ions, during their grazing scattering from a solid surface. The dynamic response of the surface is treated by means of the dielectric theory within the specular reflection model using the plasmon pole approximation for the bulk dielectric function, whereas the angle-resolved energy spectra of the electrons emitted from the surface are obtained on the basis of the first-order, time-dependent perturbation theory. The evolution of the charge states of the constituent ions in the molecule during scattering is described by a nonequilibrium extension of the Brandt-Kitagawa model. The molecule scattering trajectories and the corresponding Coulomb explosion dynamics are evaluated for the cases of the internuclear axis being either aligned in the beam direction or randomly oriented in the directions parallel to the surface. Our calculations show that the vicinage effect in the energy loss is generally weaker for heavy molecules than for light molecules. In addition, there is clear evidence of the negative vicinage effect in both the energy loss and the energy spectra of the emitted electrons for molecular ions at lower speeds and with the axis aligned in the direction of motion.

We study a simple model atom that has two bound states and a continuum of free states, interacting with a strong electromagnetic field. In our analysis we assume that only the continuum-continuum transitions occurring between degenerate free states are important for the dynamics of the atomic system; adopting this simplifying hypothesis, we show that it is possible to describe the time evolution of the atom by means of an infinite but discrete set of first-order differential equations describing a formal model atom that has two bound states and a degenerate quasicontinuum of states. Moreover, these equations depend on a small number of parameters of the bare atom and of the external laser pulse. The role of these parameters in the laser-atom dynamics is investigated.

The nonperturbative effect of interaction can sometimes make interacting bosons behave as though they were free fermions. The system of neutral bosons in a rapidly rotating atomic trap is equivalent to charged bosons coupled to a magnetic field, which has opened up the possibility of a fractional quantum Hall effect for bosons interacting with a short-range interaction. Motivated by the composite fermion theory of a the fractional Hall effect of electrons, we test the idea that the interacting bosons map onto noninteracting spinless fermions carrying one vortex each, by comparing wave functions incorporating this physics with exact wave functions available for systems containing up to 12 bosons. We study here the analogy between interacting bosons at filling factors $\nu =n∕(n+1)$ with noninteracting fermions at ${\nu }^{*}=n$ for the ground state as well as the low-energy excited states and find that it provides a good account of the behavior for small $n$, but interactions between fermions become increasingly important with $n$. At $\nu =1$, which is obtained in the limit $n\to \infty$, the fermionization appears to overcompensate for the repulsive interaction between bosons, producing an attractive interaction between fermions, as evidenced by a pairing of fermions here.

The nonlinear optical response obtained from a model system of a quantum phase gate is investigated. The model system consists of a thin infinite atomic layer of two-level atoms placed in front of a perfect reflecting mirror. The optical response obtained from the model system is semiclassically analyzed using the finite difference time domain method with the optical Bloch equations. It is shown that a nonlinear phase shift of $\pi$ is achieved when the atomic layer is placed at an antinode of the input field. This result is consistent with the theoretical result obtained from a one-dimensional atom model [H. F. Hofmann, K. Kojima, S. Takeuchi, and K. Sasaki, J. Opt. B: Quantum Semiclassical Opt. 5, 218 (2003)]. The dependence of the nonlinear phase shift on the position of the atomic layer is also studied in detail.

A wave function picks up, in addition to the dynamic phase, the geometric (Berry) phase when traversing adiabatically a closed cycle in parameter space. We develop a general multidimensional theory of the geometric phase for (double) cycles around exceptional degeneracies in non-Hermitian Hamiltonians. We show that the geometric phase is exactly $\pi$ for symmetric complex Hamiltonians of arbitrary dimension and for nonsymmetric non-Hermitian Hamiltonians of dimension 2. For nonsymmetric non-Hermitian Hamiltonians of higher dimension, the geometric phase tends to $\pi$ for small cycles and changes as the cycle size and shape are varied. We find explicitly the leading asymptotic term of this dependence, and describe it in terms of interaction of different energy levels.

The classification of stabilizer states under local Clifford (LC) equivalence is of particular importance in quantum error-correction and measurement-based quantum computation. Two stabilizer states are called LC equivalent if there exists a local Clifford operation which maps the first state to the second. We present a finite set of invariants which completely characterizes the LC equivalence class of any stabilizer state. Our invariants have simple descriptions within the binary framework in which stabilizer states are usually described.

We show how atomic coherence can lead to entanglement between two thermal fields at a temperature $T$. We first show that the passage of a three-level atom in $V$ configuration without coherence cannot create entanglement. However, if the excited states are driven by a microwave field, the resulting atomic coherence can lead to entanglement between the thermal fields. We show that, no matter how high the temperature of the fields is, the thermal fields can always be entangled in the presence of atomic coherence.

We describe the calculation of hydrogenic (one-loop) Bethe logarithms for all states with principal quantum numbers $n⩽200$. While, in principle, the calculation of the Bethe logarithm is a rather easy computational problem involving only the nonrelativistic (Schrödinger) theory of the hydrogen atom, certain calculational difficulties affect highly excited states, and in particular states for which the principal quantum number is much larger than the orbital angular momentum quantum number. Two evaluation methods are contrasted. One of these is based on the calculation of the principal value of a specific integral over a virtual photon energy. The other method relies directly on the spectral representation of the Schrödinger–Coulomb propagator. Selected numerical results are presented. The full set of values is available at arXiv.org/quant-ph/0504002.