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

Classical Structures Based on Unitaries

Starting from the observation that distinct notions of copying have arisen in different categorical fields (logic and computation, contrasted with quantum mechanics) this paper addresses the question of when, or whether, they may coincide. Provided all definitions are strict in the categorical sense, we show that this can never be the case. However, allowing for the defining axioms to be taken up to canonical isomorphism, a close connection between the classical structures of categorical quantum mechanics, and the categorical property of self-similarity familiar from logical and computational models becomes apparent. The required canonical isomorphisms are non-trivial, and mix both typed (multi-object) and untyped (single-object) tensors and structural isomorphisms; we give coherence results that justify this approach. We then give a class of examples where distinct self-similar structures at an object determine distinct matrix representations of arrows, in the same way as classical structures determine matrix representations in Hilbert space. We also give analogues of familiar notions from linear algebra in this setting such as changes of basis, and diagonalisation.Comment: 24 pages,7 diagram

Central Proper-Motion Kinematics of NGC 6752

We present proper motions derived from WFPC2 imaging for stars in the core of the peculiar globular cluster NGC 6752. The central velocity dispersion in both components of the proper motion is 12 km/s. We discuss the implications of this result as well as the intrinsic difficulties in making such measurements. We also give an alternative correction for the 34-row problem in the WFPC2 CCDs.Comment: 25 pages, 7 figures, 1 table included. Accepted for publication in A

Searching for visual companions of close Cepheids. VLT/NACO lucky imaging of Y~Oph, FF~Aql, X~Sgr, W~Sgr and η\eta~Aql

Aims: High-resolution imaging in several photometric bands can provide color and astrometric information of the wide-orbit component of Cepheid stars. Such measurements are needed to understand the age and evolution of pulsating stars. In addition, binary Cepheids have the potential to provide direct and model-independent distances and masses. Methods: We used the NAOS-CONICA adaptive optics instrument (NACO) in the near-infrared to perform a deep search for wide components around the classical Cepheids, Y~Oph, FF~Aql, X~Sgr, W~Sgr, and $\eta$~Aql, within a field of view (FoV) of $1.7"\times 1.7"$ ($3.4"\times 3.4"$ for $\eta$~Aql). Results: We were able to reach contrast $\Delta H = 5$-8\,mag and $\Delta K_\mathrm{s} = 4$-7\,mag in the radius range $r > 0.2"$, which enabled us to constrain the presence of wide companions. For Y~Oph, FF~Aql, X~Sgr, W~Sgr, and $\eta$~Aql at $r > 0.2"$, we ruled out the presence of companions with a spectral type that is earlier than a B7V, A9V, A9V, A1V, and G5V star, respectively. For $0.1"< r < 0.2"$, no companions earlier than O9V, B3V, B4V, B2V, and B2V star, respectively, are detected. A component is detected close to $\eta$~Aql at projected separation $\rho = 654.7 \pm 0.9$\,mas and a position angle $PA = 92.8 \pm 0.1^\circ$. We estimated its dereddened apparent magnitude to be $m_H^0 = 9.34 \pm 0.04$ and derived a spectral type that ranges between an F1V and F6V star. Additional photometric and astrometric measurements are necessary to better constrain this star and check its physical association to the $\eta$~Aql system.Comment: Accepted for publication in Astronomy and Astrophysic

Discrepancies in Determinations of the Ginzburg-Landau Parameter

Long-standing discrepancies within determinations of the Ginzburg-Landau parameter $\kappa$ from supercritical field measurements on superconducting microspheres are reexamined. The discrepancy in tin is shown to result from differing methods of analyses, whereas the discrepancy in indium is a consequence of significantly differing experimental results. The reanalyses however confirms the lower $\kappa$ determinations to within experimental uncertainties.Comment: submitted to Phys. Rev.

Polarization state of the optical near-field

The polarization state of the optical electromagnetic field lying several nanometers above complex dielectric structures reveals the intricate light-matter interaction that occurs in this near-field zone. This information can only be extracted from an analysis of the polarization state of the detected light in the near-field. These polarization states can be calculated by different numerical methods well-suited to near--field optics. In this paper, we apply two different techniques (Localized Green Function Method and Differential Theory of Gratings) to separate each polarisation component associated with both electric and magnetic optical near-fields produced by nanometer sized objects. The analysis is carried out in two stages: in the first stage, we use a simple dipolar model to achieve insight into the physical origin of the near-field polarization state. In the second stage, we calculate accurate numerical field maps, simulating experimental near-field light detection, to supplement the data produced by analytical models. We conclude this study by demonstrating the role played by the near-field polarization in the formation of the local density of states.Comment: 9 pages, 11 figures, accepted for publication in Phys. Rev.

Factorization of Numbers with the temporal Talbot effect: Optical implementation by a sequence of shaped ultrashort pulses

We report on the successful operation of an analogue computer designed to factor numbers. Our device relies solely on the interference of classical light and brings together the field of ultrashort laser pulses with number theory. Indeed, the frequency component of the electric field corresponding to a sequence of appropriately shaped femtosecond pulses is determined by a Gauss sum which allows us to find the factors of a number

Real-time information processing of environmental sensor network data using Bayesian Gaussian processes

In this article, we consider the problem faced by a sensor network operator who must infer, in real time, the value of some environmental parameter that is being monitored at discrete points in space and time by a sensor network. We describe a powerful and generic approach built upon an efficient multi-output Gaussian process that facilitates this information acquisition and processing. Our algorithm allows effective inference even with minimal domain knowledge, and we further introduce a formulation of Bayesian Monte Carlo to permit the principled management of the hyperparameters introduced by our flexible models. We demonstrate how our methods can be applied in cases where the data is delayed, intermittently missing, censored, and/or correlated. We validate our approach using data collected from three networks of weather sensors and show that it yields better inference performance than both conventional independent Gaussian processes and the Kalman filter. Finally, we show that our formalism efficiently reuses previous computations by following an online update procedure as new data sequentially arrives, and that this results in a four-fold increase in computational speed in the largest cases considered