We analyze von Neumann-like quantum measurements in terms of simultaneous virtual paths constructed for two noncommuting variables. The approach is applied to measurements of operator functions of conjugate variables and to the joint measurements of such variables. The limits of applicability of the restricted phase space path integral are studied. We demonstrate that, for a simple joint measurement, using entangled meter states allows one to manipulate the order in which the measurements are conducted. The effects of “weakening” a measurement by choosing unsharp meter states are also discussed.

To understand how entangled states behave under local quantum operations is an open problem in quantum-information theory. The Jamiolkowski isomorphism provides a natural way to study this problem in terms of quantum states. We introduce the Schmidt number for quantum operations by this duality and clarify how the Schmidt number of a quantum state changes under a local quantum operation. Some characterizations of quantum operations with Schmidt number $k$ are also provided.

We investigate the relation between the entanglement properties of a quantum state and its energy for macroscopic spin models. To this aim, we develop a general method to compute energy bounds for states without certain forms of multipartite entanglement. Violation of these bounds implies the presence of these types of multipartite entanglement. As examples, we investigate the Heisenberg model in different dimensions, the Ising model and the $XX$ model in the presence of a magnetic field. Finally, by studying the Heisenberg model on a triangular lattice, we demonstrate that our techniques can be applied also to frustrated systems.

We investigate decoherence effects in the recently suggested quantum-computation scheme using weak nonlinearities, strong probe coherent fields, detection, and feedforward methods. It is shown that in the weak-nonlinearity-based quantum gates, decoherence in nonlinear media can be made arbitrarily small simply by using arbitrarily strong probe fields, if photon-number-resolving detection is used. On the contrary, we find that homodyne detection with feedforward is not appropriate for this scheme because in this case decoherence rapidly increases as the probe field gets larger.

Implementation of a linear optics quantum multibit half-adder that could show potential scalability is discussed. Parametric down-conversion sources are assumed that are pumped by a mode carrying orbital angular momentum $l$. A single photon from a pair is prepared by detection of its twin. This preparation of a single photon defines two bits to be summed and the starting carry control bit. This hyperentangled single photon enters a sequence of optical gates that acts on this photon and ancilla photons. At the adder output, each single photon detected gives the sum operation plus carry. The photons belong to a hyperentangled system with a $2^3$ Hilbert space describing each photon. Conditions to have a scalable system for quantum computation define the requirements for construction of this photon source.

We consider the bipartite spin entanglement between two identical fermions generated in spin-independent scattering. We show how the spatial degrees of freedom act as ancillas for the creation of entanglement to a degree that depends on the scattering angle $\theta$. The number of Slater determinants generated in the process is greater than 1, corresponding to genuine quantum correlations between the identical fermions. The maximal entanglement attainable of 1 ebit is reached at $\theta =\pi ∕2$. We also analyze a simple $\theta$-dependent Bell’s inequality, which is violated for $\pi ∕4<\theta ⩽\pi ∕2$. This phenomenon is unrelated to the symmetrization postulate but does not appear for unequal particles.

In this work we report on the first experimental demonstration of selection of the long electron quantum paths in the process of high-order harmonic generation by phase-stabilized multiple-cycle light pulses. A complete experimental investigation of the role of intensity and carrier-envelope phase of the driving pulses on the spectral characteristics of the long quantum paths is performed. Simulations based on the nonadiabatic saddle-point method and on a complete nonadiabatic three-dimensional model reproduce the main features of the experimental results. The use of phase-stabilized driving pulses allows one to control, on an attosecond temporal scale, the spectral and temporal characteristics associated with the electron quantum paths involved in the harmonic generation process.

We derive the dynamic and thermodynamic stability conditions for dilute multicomponent Bose-Einstein condensates (BECs). These stability conditions, generalized for $n$-component BECs, are found to be equivalent and are shown to be consistent with the phase diagrams of two- and three-component condensates that are derived from energetic arguments.

We consider a Raman photoassociation model in a field configuration in which a Gaussian and a first-order Laguerre Gaussian laser field are applied between the bound-bound and free-bound transitions, respectively. We show that such a configuration can lead to a coherent population trapping superposition of an atomic condensate and a ground molecular vortex of unit winding number. We develop stimulated Raman adiabatic passages that minimize the effect of mean-field shifts due to collisions, for optimal conversion of an atomic condensate into a ground molecular vortex.

We investigate the feasibility of simulating different model Hamiltonians used in high-temperature superconductivity. We briefly discuss the most common models and then focus on the simulation of the so-called $t\text{−}J\text{−}U$ Hamiltonian using ultra-cold atoms in optical lattices. For this purpose, previous simulation schemes to realize the spin interaction term $J$ are extended. We especially overcome the condition of a filling factor of exactly one, which otherwise would restrict the phase of the simulated system to a Mott-insulator. Using ultra-cold atoms in optical lattices allows simulation of the discussed models for a very wide range of parameters. The time needed to simulate the Hamiltonian is estimated and the accuracy of the simulation process is numerically investigated for small systems.

We investigated theoretically the emission spectrum for a harmonically trapped two-level atom; our study is not limited in Lamb-Dicke approximation. We have shown that the effects of the atomic motion on the emission spectrum are dependent on the initial state of the system, the Lamb-Dicke parameter $\eta$, and the detuning parameter.

We present a linear optical scheme for error-free distribution of two-photon polarization-entangled Bell states over noisy channels. The scheme can be applied to an elementary quantum repeater protocol with potentially significant improvements in efficiency and system complexity. The scheme is based on the use of polarization and time-bin encoding of photons and can perform single-pair, single-step purification with currently available technology.

This paper presents the results obtained using a genetic algorithm (GA) to search for stable structures of medium-size silicon clusters. This is the third report in which a GA coupled with the MSINDO semiempirical molecular orbital program is used to find stable atomic cluster structures. The structures selected by the GA-MSINDO method were further optimized using the density functional theory (DFT). This combination of GA-MSINDO global optimization followed by DFT local optimization proves to be very effective for searching the structures of medium-size Si clusters. For most of the clusters studied here we report different structures with significant lower energy than those previously found using limited search approaches on common structural motifs. This demonstrates the need for global optimization schemes when searching for stable structures of medium-size silicon clusters.

The $R$-matrix Floquet theory is used to study laser-assisted electron-helium scattering in the energy range from 0.2 to $2.5\mathrm{eV}$. Differential cross sections and signals for scattering through $156°$ in a ${\mathrm{CO}}_2$ laser field are calculated over a range of intensities from ${10}^6$ to ${10}^8\mathrm{W}{\mathrm{cm}}^{-2}$ and compared with those obtained experimentally. Similar calculations for scattering in a Nd:YAG laser field are also presented in order to assess the validity of the Kroll-Watson low-frequency approximation when the scattering energy is less than the photon energy.

In this paper, I numerically investigate the propagation of ultrashort pulses through an extended collection of multilevel systems under the condition of electromagnetically induced transparency. The transparency of a weak probe pulse is induced by a much stronger coupling pulse. In the limit of a weak probe excitation and a large number of excited states, I show that the free-induction decay signal that would naturally follow the excitation pulse is strongly suppressed, and the envelope of the probe pulse suffers a distortion in its temporal profile as the pulse propagates into the medium. This distortion is characterized by a stronger absorption of the leading edge of the pulse than that of its trailing edge. The temporal phase of the pulse, however, remains constant throughout propagation.

It is shown that dynamical entanglement between two qubits depends on the symmetry of the quantum model. On the other hand, the latter is reflected in the qualitative properties of the dynamics of a classical approximation of the quantum system. For generic separable pure initial states, the dynamical entanglement is larger if the system is less symmetric and its classical approximation is chaotic. The influence of different types of Markov environments on the established relation between the dynamical entanglement, symmetry and the classical dynamics is also studied.

We consider the role of the reconstruction of the initial state in the deviation from exponential decay at short and long times. The long-time decay can be attributed to a wave that was, in a classical-like, probabilistic sense, fully outside the initial state or the inner region at intermediate times, i.e., to a completely reconstructed state, whereas the decay during the exponential regime is due instead to a nonreconstructed wave. At short times, quantum interference between reconstructed and nonreconstructed paths is responsible for the deviation from the exponential decay. We may thus conclude that state reconstruction is a “consistent history” for long-time deviations but not for short ones.

We prove that for a programmable measurement device that approximates every POVM with an error $⩽\delta$, the dimension of the program space has to grow at least polynomially with $\frac{1}{\delta }$. In the case of qubits we can improve the general result by showing a linear growth. This proves the optimality of the programmable measurement devices recently designed in G. M. D’Ariano and P. Perinotti, Phys. Rev. Lett. 94, 090401 (2005).

We investigate the performance of a continuous-variable quantum key distribution scheme in a practical setting. More specifically, we take a nonideal error reconciliation procedure into account. The quantum channel connecting the two honest parties is assumed to be lossy but noiseless. Secret key rates are given for the case that the measurement outcomes are postselected or a reverse reconciliation scheme is applied. The reverse reconciliation scheme loses its initial advantage in the practical setting. If one combines postselection with reverse reconciliation, however, much of this advantage can be recovered.

The construction of two-qubit gates appropriate for universal quantum computation is of enormous importance to quantum-information processing. Building such gates is dependent on accurate knowledge of the interaction dynamics between two-qubit systems. This paper will present a systematic method for reconstructing the full two-qubit interaction Hamiltonian through experimental measures of concurrence. This not only gives a convenient method for constructing two qubit quantum gates, but can also be used to experimentally determine various Hamiltonian parameters in physical systems. We show explicitly how this method can be employed to determine the first- and second-order spin-orbit corrections to the exchange coupling in quantum dots.