Non-Abelian generalization of off-diagonal geometric phases

If a quantum system evolves in a noncyclic fashion the corresponding geometric phase or holonomy may not be fully defined. Off-diagonal geometric phases have been developed to deal with such cases. Here, we generalize these phases to the non-Abelian case, by introducing off-diagonal holonomies that involve evolution of more than one subspace of the underlying Hilbert space. Physical realizations of the off-diagonal holonomies in adiabatic evolution and interferometry are put forward.Comment: Additional material, journal reference adde

The occurrence of hazel grouse in the boreal forest : effects of habitat composition at several spatial scales

This thesis presents data on factors determining the occurrence and dynamics of hazel grouse populations at several spatial scales in five landscapes with different management regimes. In a forested area with a low degree of habitat variation, the relationship between occurrence of hazel grouse and type of habitat was best explained at scales equal or larger than the home range, compared to smaller spatial scales. At this spatial scale the hazel grouse preferred spruce stands 20-69 years old and those older than 90 years, having 5-40% deciduous trees. More specifically the presence of hazel grouse in a habitat patch was positively influenced by a high amount of vertical ground cover, a rich field layer vegetation and the presence of alder. At the landscape scale the occurrence of hazel grouse in habitat patches in intensively managed landscapes was negatively affected by increasing distance between suitable habitats both in an agriculture-dominated landscape and in a forestdominated landscape. The threshold distances for hazel grouse movements were about 200 m in the agricultural landscape and about 10 times longer in the forested landscape, suggesting a strong effect of different types of matrix. The dynamics of hazel grouse occurrence in habitat patches in the intensively managed forested landscape, were determined by distance to nearest suitable habitat patch, amount of cover in the habitat patch and habitat patch size. In a fine-grained less intensively managed landscape, using a 21-year long data set, habitat size and isolation were also found to strongly affect the presence of hazel grouse. Hazel grouse occupancy increased considerably in habitat patches larger than 10 ha. However, the effect of isolation occurred at a smaller spatial scale and was not induced by distance, instead it occurred as an avoidance of open land surrounding the habitat patch. A high concordance, about 85%, between predicted and observed occurrence of hazel grouse was found when the models developed in the two differently managed forested areas were used on independent data from a third landscape. The results presented in this thesis suggest that the hazel grouse is a poor disperser, avoids open areas, and has very specific habitat requirements, many of which conflict with production of coniferous pulp and timber. Theoretical aspects of landscape ecology and specific guidelines, including applicable measurements and evaluations of forest descriptions for maintaining the species in managed boreal landscapes, are discussed

Operations and single particle interferometry

Interferometry of single particles with internal degrees of freedom is investigated. We discuss the interference patterns obtained when an internal state evolution device is inserted into one or both the paths of the interferometer. The interference pattern obtained is not uniquely determined by the completely positive maps (CPMs) that describe how the devices evolve the internal state of a particle. By using the concept of gluing of CPMs, we investigate the structure of all possible interference patterns obtainable for given trace preserving internal state CPMs. We discuss what can be inferred about the gluing, given a sufficiently rich set of interference experiments. It is shown that the standard interferometric setup is limited in its abilities to distinguish different gluings. A generalized interferometric setup is introduced with the capacity to distinguish all gluings. We also connect to another approach using the well known fact that channels can be realized using a joint unitary evolution of the system and an ancillary system. We deduce the set of all such unitary `representations' and relate the structure of this set to gluings and interference phenomena.Comment: Journal reference added. Material adde

Fidelity and coherence measures from interference

By utilizing single particle interferometry, the fidelity or coherence of a pair of quantum states is identified with their capacity for interference. We consider processes acting on the internal degree of freedom (e.g., spin or polarization) of the interfering particle, preparing it in states ρA or ρB in the respective path of the interferometer. The maximal visibility depends on the choice of interferometer, as well as the locality or nonlocality of the preparations, but otherwise depends only on the states ρA and ρB and not the individual preparation processes themselves. This allows us to define interferometric measures which probe locality and correlation properties of spatially or temporally separated processes, and can be used to differentiate between processes that cannot be distinguished by direct process tomography using only the internal state of the particle

Evolutionary optimization of classifiers and features for single-trial EEG Discrimination

which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Background: State-of-the-art signal processing methods are known to detect information in single-trial event-related EEG data, a crucial aspect in development of real-time applications such as brain computer interfaces. This paper investigates one such novel approach, evaluating how individual classifier and feature subset tailoring affects classification of single-trial EEG finger movements. The discrete wavelet transform was used to extract signal features that were classified using linear regression and non-linear neural network models, which were trained and architecturally optimized with evolutionary algorithms. The input feature subsets were also allowed to evolve, thus performing feature selection in a wrapper fashion. Filter approaches were implemented as well by limiting the degree of optimization. Results: Using only 10 features and 100 patterns, the non-linear wrapper approach achieved the highest validation classification accuracy (subject mean 75%), closely followed by the linear wrapper method (73.5%). The optimal features differed much between subjects, yet some physiologically plausible patterns were observed

Min- and Max-Entropy in Infinite Dimensions

We consider an extension of the conditional min- and max-entropies to infinite-dimensional separable Hilbert spaces. We show that these satisfy characterizing properties known from the finite-dimensional case, and retain information-theoretic operational interpretations, e.g., the min-entropy as maximum achievable quantum correlation, and the max-entropy as decoupling accuracy. We furthermore generalize the smoothed versions of these entropies and prove an infinite-dimensional quantum asymptotic equipartition property. To facilitate these generalizations we show that the min- and max-entropy can be expressed in terms of convergent sequences of finite-dimensional min- and max-entropies, which provides a convenient technique to extend proofs from the finite to the infinite-dimensional settin

Comparison Between Visual and Tactile Signal Detection Tasks Applied to the Safety Assessment of In-Vehicle Information Systems

The Peripheral Detection Task (PDT) is a widely applied method for safety assessment of in-vehicle information systems (IVIS). In this study, the PDT was compared to a Tactile Detection Task (TDT) where the visual stimulus used for the PDT was replaced by tactile vibrators, placed on the wrists. The sensitivity of the two methods to different cognitive and visual secondary tasks was investigated in different real-world driving conditions. The results showed that both methods were sensitive to visual and cognitive secondary task load in a range of different driving environments.The sensitivity was generally stronger for the TDT than the PDT. It was concluded that the TDT could be a viable alternative to the PDT for IVIS assessment

Weak cloning of an unknown quantum state

The impossibility to clone an unknown quantum state is a powerful principle to understand the nature of quantum mechanics, especially within the context of quantum computing and quantum information. This principle has been generalized to quantitative statements as to what extent imperfect cloning is possible. We delineate an aspect of the border between the possible and the impossible concerning quantum cloning, by putting forward an entanglement-assisted scheme for simulating perfect cloning in the context of weak measurements. This phenomenon we call weak cloning of an unknown quantum state.Comment: Minor corrections, journal reference adde

Noncyclic geometric changes of quantum states

Non-Abelian quantum holonomies, i.e., unitary state changes solely induced by geometric properties of a quantum system, have been much under focus in the physics community as generalizations of the Abelian Berry phase. Apart from being a general phenomenon displayed in various subfields of quantum physics, the use of holonomies has lately been suggested as a robust technique to obtain quantum gates; the building blocks of quantum computers. Non-Abelian holonomies are usually associated with cyclic changes of quantum systems, but here we consider a generalization to noncyclic evolutions. We argue that this open-path holonomy can be used to construct quantum gates. We also show that a structure of partially defined holonomies emerges from the open-path holonomy. This structure has no counterpart in the Abelian setting. We illustrate the general ideas using an example that may be accessible to tests in various physical systems.Comment: Extended version, new title, journal reference adde

Adiabatic geometric phases in hydrogenlike atoms

We examine the effect of spin-orbit coupling on geometric phases in hydrogenlike atoms exposed to a slowly varying magnetic field. The marginal geometric phases associated with the orbital angular momentum and the intrinsic spin fulfill a sum rule that explicitly relates them to the corresponding geometric phase of the whole system. The marginal geometric phases in the Zeeman and Paschen-Back limit are analyzed. We point out the existence of nodal points in the marginal phases that may be detected by topological means.Comment: Clarifying material added, one figure removed, journal reference adde