We introduce the quantum indirect estimation theory, which provides a general framework to address the problem of which ensemble averages can be estimated by means of an available set of measuring apparatuses, e.g., estimating the ensemble average of an observable by measuring other observables. A main ingredient in this approach is that of informationally complete (infocomplete) measurements, which allow us to estimate the ensemble average of any arbitrary system operator, as for quantum tomography. This naturally leads to the more stringent concept of $AB$-informationally complete measurements, by which one can estimate jointly all the moments of two incompatible observables $A$ and $B$. After analyzing all general properties of such measurements, we address the problem of their optimality, and we completely solve the case of qubits, showing that a ${\sigma }_x{\sigma }_y$-infocomplete measurement is less noisy than any infocomplete one. We will also discuss the relation between the concept of $AB$ infocompleteness and the notion of joint measurement of observables $A$ and $B$.

In a recent paper, the generalization of the Jensen-Shannon divergence in the context of quantum theory has been studied [Majtey et al., Phys. Rev. A 72, 052310 (2005)]. This distance between quantum states has shown to verify several of the properties required for a good distinguishability measure. Here we investigate the metric character of this distance. More precisely we show, formally for pure states and by means of a numerical procedure for mixed states, that its square root verifies the triangle inequality.

We study the ground-state properties of a Bose-Einstein condensate with short-range repulsion and gravitylike $1/r$ interatomic attraction in two-dimensions (2D). Using the variational approach we obtain the ground-state energy and analyze the stability of the condensate for a range of interaction strengths in 2D. We also determine the collective excitations at zero temperature using the time-dependent variational method. We analyze the properties of the Thomas-Fermi-gravity and gravity regimes, and we examine the vortex states, finding the coherence length and monopole mode frequency for these regimes. Our results are compared and contrasted with those in 3D condensates.

We present a theory of spinor superfluidity in a two-species heteronuclear ultracold fermionic atomic gas consisting of arbitrary half-integer spin and spin one-half atoms. In particular, we focus on the magnetism of the superfluid phase and determine the possible phases in the absence of a magnetic field. Our work demonstrates similarities between heteronuclear fermionic superfluids and spinor Bose-Einstein condensates at the mean-field level. Possible experimental situations are discussed.

We apply wave-packet methods to study an ion-trap system imposing neither the rotating wave nor the Lamb-Dicke approximations. By this approach we show the existence of states with restricted phase-space evolution as a genuine consequence of quantum interference between wave-packet fractions. A particular instance of such a state oscillates between maximal entanglement and pure disentanglement between the constitute subsystems, where the characteristic crossover time is very rapid. Over longer time periods the dynamics of these states exhibits collapse-revival patterns with well-resolved fractional revivals in autocorrelation, inversion, and entanglement.

We propose a geometric phase gate of two ion qubits that are encoded in two levels linked by an optical dipole-forbidden transition. Compared to hyperfine geometric phase gates mediated by electric dipole transitions, the gate has many interesting properties, such as very low spontaneous emission rates, applicability to magnetic field insensitive states, and use of a co-propagating laser beam geometry. We estimate that current technology allows for infidelities of around ${10}^{-4}$.

Local or nonlocal character of quantum states can be quantified and is subject to various bounds that can be formulated as complementarity relations. Here, we investigate the local vs nonlocal character of pure three-qubit states by a four-way interferometer. The complete entanglement in the system can be measured as the entanglement of a specific qubit with the subsystem consisting of the other two qubits. The quantitative complementarity relations are verified experimentally in an NMR quantum information processor.

We analyze classically defined games for which a quantum team has an advantage over any classical team. The quantum team has a clear advantage in games in which the players of each team are separated in space and the quantum team can use unusually strong correlations of the Einstein-Podolsky-Rosen type. We present an example of a classically defined game played at one location for which quantum players have a real advantage.

Fine-structure intervals between $n=17$ Rydberg states of magnesium with $6\le L\ge 11$ were measured using the resonant excitation Stark ionization spectroscopy technique. Comparing the measured intervals with the long-range polarization model determines the dipole and quadrupole polarizabilities of ${\text{Mg}}^{+}$ to be ${\alpha }_1=35.00\left(5\right)a_0^3$ and ${\alpha }_2=222\left(54\right)a_0^5$, respectively.

We employed the Schwinger multichannel method to compute elastic cross sections for low-energy electron collisions with propane $\left({\text{C}}_3{\text{H}}_8\right)$. The calculations are carried out within the static-exchange and static-exchange plus polarization approximations and covered the energy range from 0 to 15 eV. The computed differential cross sections show good agreement with the experiment, and the computed integral cross sections present the same shape as the measured total cross sections. We found a broad structure in the integral cross section around 8.5 eV and also a Ramsauer-Townsend minimum around 0.1 eV. These results are in agreement with the experimental observations.

The isotopically mixed hydrogen molecular ion ${\text{HD}}^{+}$ was investigated in intense pulsed laser fields with high, i.e., vibrational resolution of the fragments. An ion beam of ${\text{HD}}^{+}$ with a translational energy of 11.1 keV was exposed to femtosecond laser pulses (100 fs) of intensities in the range from ${10}^{13}–{10}^{15}\text{W}/{\text{cm}}^2$. Fragments from the two dissociation channels ${\text{HD}}^{+}\to \text{H}+{\text{D}}^{+}$, and ${\text{HD}}^{+}\to \text{D}+{\text{H}}^{+}$, as well as the Coulomb explosion channel, ${\text{HD}}^{+}\to {\text{H}}^{+}+{\text{D}}^{+}+e^{-}$, were projected onto a two-dimensional multichannel plate detector to measure their velocity distributions. The fragments from the three channels were spatially clearly distinguished because of the different velocities of H $\left({\text{H}}^{+}\right)$ and D $\left({\text{D}}^{+}\right)$ fragments. Fragments from most of the populated vibrational states of ${\text{HD}}^{+}$ can be discerned as well-resolved peaks in the speed and angular distributions. The typical light induced potential (LIP) effects such as bond softening and level shifting already observed in the studies of ${\text{H}}_2^{+}$ and ${\text{D}}_2^{+}$ are here also observed. In addition to these one-photon peaks, also peaks due to three- (net two-) and finally also to direct two-photon absorption, typical of the asymmetric ${\text{HD}}^{+}$, were found in the vibrationally resolved fragment spectra of the dissociation channels. Besides the fragments from one-photon bond softening, also fragments formed by two- and three-photon processes were found to have narrow angular distributions, in contrast to the approximately ${\text{cos}}^2$ distribution of fragments from vibrational levels above the LIP crossing being fragmented by classical dissociation. The relative probability of the two dissociation channels was investigated, addressing the question of the higher electron affinity to the proton or the deuteron during the dissociation, but could not be decided because of too low accuracy here. The Coulomb explosion channel was also clearly discerned by its fragment velocities as well as the narrow angular distributions of ${\text{H}}^{+}$ and ${\text{D}}^{+}$ fragments, which is quite analogous to those found in the cases of ${\text{H}}_2^{+}$ and ${\text{D}}_2^{+}$.

We investigate Bose-Einstein condensation for interacting bosons at zero and nonzero temperature. Functional renormalization provides us with a consistent method to compute the effect of fluctuations beyond the Bogoliubov approximation. For three-dimensional dilute gases, we find an upper bound on the scattering length $a$ which is of the order of the microphysical scale—typically the range of the van der Waals interaction. In contrast to fermions near the unitary bound, no strong interactions occur for bosons with approximately pointlike interactions, thus explaining the high quantitative reliability of perturbation theory for most quantities. For zero temperature we compute the quantum phase diagram for bosonic quasiparticles with a general dispersion relation, corresponding to an inverse microphysical propagator with terms linear and quadratic in the frequency. We compute the temperature dependence of the condensate and particle density $n$, and find for the critical temperature $T_c$ a deviation from the free theory, $\Delta T_c/T_c=2.1a{n}^{1/3}$. For the sound velocity at zero temperature we find very good agreement with the Bogoliubov result, such that it may be used to determine the particle density accurately.

The effect of spontaneously generated coherence (SGC) on spontaneous emission and dynamical evolution of a microwave-driven four-level atomic system is studied. Interesting phenomena due to SGC, such as spectral-line narrowing, spectra-line enhancement, spectral-line suppression, and fluorescence quenching, are shown in the spontaneous emission spectra, which can be effectively modulated by amplitude and phase of the microwave field. Due to SGC, the total populations are partly, even completely, trapped in upper levels in steady state, the decay time of which is sensitive to the phase of the microwave field. In the dressed state picture, multiple SGC arise during the process of three close-lying states decaying to the same state. The corresponding experiment to observe the expected phenomena related to SGC can be more conveniently realized in atoms, since no rigorous conditions are required and the amplitude and phase of the microwave field can be conveniently controlled.

Twin entangled beams produced by single-pass parametric down-conversion (PDC) offer the opportunity to detect weak amount of absorption with an improved sensitivity with respect to standard techniques which make use of classical light sources. We propose a differential measurement scheme which exploits the spatial quantum correlation of type-II PDC to image a weak amplitude object with a sensitivity beyond the standard quantum limit imposed by shot noise. By applying a quantitative numerical model to a specific PDC system (a type-II beta-barium borate crystal), we are able to identify conditions in parameter space suitable for a substantial enhancement of the imaging sensitivity, and we investigate the robustness of this enhancement against experimental imperfections.

The concept of time delayed creation of entanglement by the dissipative process of spontaneous emission is investigated. A threshold effect for the creation of entanglement is found where the initially unentangled qubits can be entangled after a finite time despite the fact that the coherence between the qubits exists for all times. This delayed creation of entanglement, which we call sudden birth of entanglement, is opposite to the currently extensively discussed sudden death of entanglement and is characteristic for transient dynamics of one-photon entangled states of the system. We determine the threshold time for the creation of entanglement and find it is related to time at which the antisymmetric state remains the only excited state being populated. It is shown that the threshold time can be controlled by the distance between the qubits and the direction of initial excitation relative to the interatomic axis. This effect suggests an alternative for the study of entanglement and provides an interesting resource for creation on demand of entanglement between two qubits.

We present measurements of total cross sections for 1 to 30 eV positrons scattered by uracil molecules. The measurements are done using a beam transmission technique on a setup adjusted to accommodate the nature of uracil and we discuss possibilities of future experiments studying positron interactions with more complicated targets. These and future investigations of positron interactions with biomolecules have potential relevance to various biomedical applications.

The best qubit one-way quantum-key-distribution (QKD) protocol can tolerate up to 14.6% in the error rate. It has been shown how this rate can be increased by using larger quantum systems. The polarization state of a biphoton can encode a three-level quantum system—a qutrit. The realization of a QKD system with biphotons encounters several problems in generating, manipulating, and detecting such photon states. We define those limitations and find within them a few protocols that perform almost as well as the ideal qutrit protocol. One advantage is that these protocols can be implemented with minor modifications into existing single photon systems. The security of one protocol is proved for the most general coherent attacks and the largest acceptable error rate for this protocol is found to be around 17.7%. For comparison, the security of the best possible qutrit protocol of four mutually unbiased bases was also rigorously analyzed against general attacks, with a proven bound on the acceptable error rate of 21.1%.

Entangling two systems at distant locations using a separable mediating ancilla is a counterintuitive phenomenon proposed for qubits by T. Cubitt et al. [Phys. Rev. Lett. 91, 037902 (2003)]. We show that such entanglement distribution is possible with Gaussian states, using a certain three-mode fully separable mixed Gaussian state and linear optics elements readily available in experiments. Two modes of the state become entangled by sequentially mixing them on two beam splitters, while the third one remains separable in all stages of the protocol.

We investigate dynamics of semiquantal spin systems in which quantum bits are attached to classically and possibly stochastically moving classical particles. The interaction between the quantum bits takes place when the respective classical particles get close to each other in space. We find that with Heisenberg $XX$ couplings quantum homogenization takes place after a long enough time, regardless of the details of the underlying classical dynamics. This is accompanied by the development of a stationary bipartite entanglement. If the information on the details of the motion of a stochastic classical system is disregarded, the stationary state of the whole quantum subsystem is found to be a complete mixture in the studied cases, though the transients depend on the properties of the classical motion.

Matrix product states can be defined as the family of quantum states that can be sequentially generated in a one-dimensional system [Schön et al., Phys. Rev. Lett. 95, 110503 (2005)]. We introduce a family of states that extends this definition to two dimensions. Like in matrix product states, expectation values of few body observables can be efficiently evaluated and, for the case of translationally invariant systems, the correlation functions decay exponentially with the distance. We show that such states are a subclass of projected entangled pair states and investigate their suitability for approximating the ground states of local Hamiltonians.