Optimal state for keeping reference frames aligned and the Platonic solids

The optimal N qubit states featuring highest sensitivity to small misalignment of cartesian reference frames are found using the Quantum Cramer-Rao bound. It is shown that the optimal states are supported on the symmetric subspace and hence are mathematically equivalent to a single spin J=N/2. Majorana representation of spin states is used to reveal a beautiful connection between the states optimal for aligning reference frames and the platonic solids

Quantum phase estimation with lossy interferometers

We give a detailed discussion of optimal quantum states for optical two-mode interferometry in the presence of photon losses. We derive analytical formulae for the precision of phase estimation obtainable using quantum states of light with a definite photon number and prove that maximization of the precision is a convex optimization problem. The corresponding optimal precision, i.e. the lowest possible uncertainty, is shown to beat the standard quantum limit thus outperforming classical interferometry. Furthermore, we discuss more general inputs: states with indefinite photon number and states with photons distributed between distinguishable time bins. We prove that neither of these is helpful in improving phase estimation precision.Comment: 12 pages, 5 figure

Characterisation of the Gradient Coatings TiN/(Ti,Al,Si)N/TiN Type Deposited on Sintered Tool Materials

The paper presents results of the structural examinations, tests of mechanical and working properties ofthin wear resistant gradient coatings of the TiN/(Ti,Al,Si)N/TiN type, deposited in the CAE process ontothe substrate from the cermets and cemented carbides. Structural examinations are presented of theapplied coatings and their substrate made on the SEM, TEM and on the LM.Evaluation of the adhesion of the deposited coatings onto the cemented carbides and cermets was madeusing the scratch test. Cutting properties of the investigated materials were determined basing on thetechnological continuous cutting tests of the C45E steel. Substrate hardness tests and microhardness testsof the deposited coatings were made on the ultra-micro-hardness tester at 70 mN load. Surface roughnesstests were also made before depositing the coatings and after completing the PVD process

Quantum-enhanced gyroscopy with rotating anisotropic Bose–Einstein condensates

High-precision gyroscopes are a key component of inertial navigation systems. By considering matter wave gyroscopes that make use of entanglement it should be possible to gain some advantages in terms of sensitivity, size, and resources used over unentangled optical systems. In this paper we consider the details of such a quantum-enhanced atom interferometry scheme based on atoms trapped in a carefully-chosen rotating trap. We consider all the steps: entanglement generation, phase imprinting, and read-out of the signal and show that quantum enhancement should be possible in principle. While the improvement in performance over equivalent unentangled schemes is small, our feasibility study opens the door to further developments and improvements

Optimal Quantum Phase Estimation

By using a systematic optimization approach we determine quantum states of light with definite photon number leading to the best possible precision in optical two mode interferometry. Our treatment takes into account the experimentally relevant situation of photon losses. Our results thus reveal the benchmark for precision in optical interferometry. Although this boundary is generally worse than the Heisenberg limit, we show that the obtained precision beats the standard quantum limit thus leading to a significant improvement compared to classical interferometers. We furthermore discuss alternative states and strategies to the optimized states which are easier to generate at the cost of only slightly lower precision.Comment: 4 pages, 4 figures. Replaced with final versio

Entanglement production in Quantized Chaotic Systems

Quantum chaos is a subject whose major goal is to identify and to investigate different quantum signatures of classical chaos. Here we study entanglement production in coupled chaotic systems as a possible quantum indicator of classical chaos. We use coupled kicked tops as a model for our extensive numerical studies. We find that, in general, presence of chaos in the system produces more entanglement. However, coupling strength between two subsystems is also very important parameter for the entanglement production. Here we show how chaos can lead to large entanglement which is universal and describable by random matrix theory (RMT). We also explain entanglement production in coupled strongly chaotic systems by deriving a formula based on RMT. This formula is valid for arbitrary coupling strengths, as well as for sufficiently long time. Here we investigate also the effect of chaos on the entanglement production for the mixed initial state. We find that many properties of the mixed state entanglement production are qualitatively similar to the pure state entanglement production. We however still lack an analytical understanding of the mixed state entanglement production in chaotic systems.Comment: 16 pages, 5 figures. To appear in Pramana:Journal of Physic

Great Canadian Lagerstätten 3. Late Ordovician Konservat-Lagerstätten in Manitoba

Konservat-Lagerstätten, deposits in which soft-bodied or lightly sclerotized fossils are preserved, are very rare in Ordovician strata. Three significant sites are known from Upper Ordovician rocks in Manitoba: at Cat Head – McBeth Point, William Lake, and Airport Cove. These sites are in two distinct sedimentary basins: the former two are in the Williston Basin, while the latter is in the Hudson Bay Basin. All three sites contain marine fossils, but each has a different assemblage that contributes a distinct piece of the diversity picture. Important groups represented at one or more of the sites include seaweeds (algae), sponges, cnidarian medusae (jellyfish), conulariids, trilobites, eurypterids, xiphosurids (horseshoe crabs), and pycnogonids (‘sea spiders’). The different biotas reflect depositional conditions at each site. Many of the fossils are unknown elsewhere in the Ordovician at the family level or higher. The province of Manitoba therefore makes a significant contribution to knowledge of Late Ordovician biodiversity.SOMMAIRELes lagerstätten de conservation, ces sédiments contenant des fossiles d’organismes à corps mou ou légèrement sclérotisés particulièrement bien conservés, sont très rares dans les strates ordoviciennes.  Trois sites d’importance sont connus dans des roches de l'Ordovicien supérieur à Cat Head, Manitoba, soit McBeth Point, William Lake et  Airport Cove.  Ces sites sont situés dans deux bassins sédimentaires distincts : les deux premiers sont situés dans le bassin de Williston, tandis que le second est situé dans le bassin de la baie d'Hudson.  Les trois sites contiennent des fossiles marins, mais chacun présente un assemblage différent, chacun montrant une composante distincte de la diversité biologique d’alors.  Les groupes les plus importants représentés, dans un ou plusieurs de ces sites, sont les algues, les éponges, les cnidarian medusae (méduses), les conularides, les trilobites, les euryptérides, xiphosurides (limules) et pycnogonides.  Les différents biotopes reflètent les conditions de dépôt de chaque site.  Nombre de ces fossiles sont inconnus ailleurs dans l'Ordovicien, au niveau de la famille ou du taxon supérieur de la classification.  Ainsi, la province du Manitoba offre-t-elle une contribution importante à la connaissance de la biodiversité de l'Ordovicien supérieur