Quantum measurements with prescribed symmetry

We introduce a method to determine whether a given generalised quantum measurement is isolated or it belongs to a family of measurements having the same prescribed symmetry. The technique proposed reduces to solving a linear system of equations in some relevant cases. As consequence, we provide a simple derivation of the maximal family of Symmetric Informationally Complete measurements (SIC)-POVM in dimension 3. Furthermore, we show that the following remarkable geometrical structures are isolated, so that free parameters cannot be introduced: (a) maximal sets of mutually unbiased bases in prime power dimensions from 4 to 16, (b) SIC-POVM in dimensions from 4 to 16 and (c) contextuality Kochen-Specker sets in dimension 3, 4 and 6, composed of 13, 18 and 21 vectors, respectively.Comment: 10 pages, 2 figure

Quantum mechanics in finite dimensional Hilbert space

The quantum mechanical formalism for position and momentum of a particle in a one dimensional cyclic lattice is constructively developed. Some mathematical features characteristic of the finite dimensional Hilbert space are compared with the infinite dimensional case. The construction of an unbiased basis for state determination is discussed.Comment: 14 pages, no figure

Vástago recubierto de hidroxiapatita: Revisión a 5 años

Se evalúan los resultados clínicos y radiológicos de 65 vástagos femorales recubiertos proximalmente de hidroxiapatita de más de 5 años y la existencia de una clara correlación de los cambios remodelativos con los patrones de estrés estudiados por elementos finitos. La edad media fue de 56 años y la patología preoperativa más frecuente fue la artrosis en 38 caos, seguida de la necrosis aséptica en 15. Se utilizó el protocolo de Johnston y col. y el baremo numérico de Merle D'Aubigné, pasando sobre 18 en la revisión. En el 98,4% no había dolor o era ligero y ocasional. Radiográficamente se vieron líneas radiolúcidas alrededor de la parte distal del vástago pulida y afilada en el 89,2%, no apareciendo en las zonas recubiertas de hidroxiapatita. Apareció hipertrofia cortical reactiva en el 13,8% y pequeñas imágenes de osteólisis a nivel proximal en el 10,8 %. Según los criterios de Neg. el 100% de los vástagos estaban osteointegrados.The clinical and radiological results of 65 proximally HA-coated femoral stems were assessed after a minimum follow-up period of five years. The relationship between remodelative changes and the stress patterns was clearly disclosed by finite element modelling. Mean age was 56 years. The most common etiology was osteoarthritis in 38 cases and vascular necrosis in 15. Radiographic and clinical assessment was done after Johnston and col's protocol and the numeric rating of Merle D'Aubigne respectively. The mean preoperative score was 8,5 points, becoming 17,4 points out of 18 at the 5 years review. Occasional or absent pain was fount in 98% of the cases. There were radiolucency lines surrounding the polished and sharp distal stem in 89%, but they were not present at the HA-coated zones. Reactive cortical hypertrophy was present in 14 % and proximal small osteolytics features in 11%. According Engh's criteria, the 100% of the stems were osteintegrated

Entanglement for all quantum states

It is shown that a state that is factorizable in the Hilbert space corresponding to some choice of degrees of freedom, becomes entangled for a different choice of degrees of freedom. Therefore, entanglement is not a special case but is ubiquitous in quantum systems. Simple examples are calculated and a general proof is provided. The physical relevance of the change of tensor product structure is mentioned.Comment: 9 page

Quantum diffusion on a cyclic one dimensional lattice

The quantum diffusion of a particle in an initially localized state on a cyclic lattice with N sites is studied. Diffusion and reconstruction time are calculated. Strong differences are found for even or odd number of sites and the limit N->infinit is studied. The predictions of the model could be tested with micro - and nanotechnology devices.Comment: 17 pages, 5 figure