There is entanglement in the primes

Large series of prime numbers can be superposed on a single quantum register and then analyzed in full parallelism. The construction of this Prime state is efficient, as it hinges on the use of a quantum version of any efficient primality test. We show that the Prime state turns out to be very entangled as shown by the scaling properties of purity, Renyi entropy and von Neumann entropy. An analytical approximation to these measures of entanglement can be obtained from the detailed analysis of the entanglement spectrum of the Prime state, which in turn produces new insights in the Hardy-Littlewood conjecture for the pairwise distribution of primes. The extension of these ideas to a Twin Prime state shows that this new state is even more entangled than the Prime state, obeying majorization relations. We further discuss the construction of quantum states that encompass relevant series of numbers and opens the possibility of applying quantum computation to Arithmetics in novel ways.Comment: 30 pages, 11 Figs. Addition of two references and correction of typo

Aplicaciones empresariales de data mining

El Data Mining, o extracción de información útil y no evidente de grandes bases de datos, es una tecnología con un gran potencial para ayudar a las empresas a focalizar sus esfuerzos alrededor de la información importante contenida en sus "data warehouses". En este artículo analizaremos las ideas básicas que sustentan el Data Mining y, más concretamente, la utilización de redes neuronales como herramienta estadística avanzada. Presentaremos también dos ejemplos reales de la aplicación de estas técnicas: predicciones bursátiles y predicción de propagación de fuego en cables eléctricos

Uncovering the attitudes towards science, scientific contents and scientists of mass media communication professionals

We present an exploratory descriptive study designed to assess attitudes towards science, science based media contents and scientists of media communication professionals. The research explores the attitudes of a group of senior audiovisual communication students before and after taking a course on production of radio programs based on scientific contents. Our main results indicate that these students show strong attitudes against scientific communication and lack of interest to work on scientific contents which would not favor the inclusion of these contents in their future work as media communication professionals.Presentamos un estudio descriptivo exploratorio diseñado para avanzar en la identificación de las actitudes de los profesionales de los medios de comunicación audiovisuales hacia la ciencia, los contenidos mediáticos inspirados en ciencia y los científicos mismos. La investigación explora las actitudes de un grupo de estudiantes avanzados de Comunicación audiovisual antes y después de que fuesen sometidos a un curso de producción de programas radiofónicos basados únicamente en ciencia. Nuestros principales resultados indican que estos estudiantes, próximos a trabajar en los medios de comunicación, muestran fuertes actitudes en contra de la comunicación científica, además de ausencia de interés por trabajar con contenidos audiovisuales inspirados en ciencia. Dichas actitudes no favorecerían la inclusión de estos contenidos en su trabajo como profesionales de los medios de comunicación

Experimental test of Mermin inequalities on a five-qubit quantum computer

Violation of Mermin inequalities is tested on the five-qubit IBM quantum computer. For three, four, and five parties, quantum states that violate the corresponding Mermin inequalities are constructed using quantum circuits on superconducting qubits. Measurements on different bases are included as additional final gates in the circuits. The experimental results obtained using the quantum computer show violation of all Mermin inequalities, with a clear degradation of the results in the five-qubit case. Though this quantum computer is not competitive to test Mermin inequalities as compared to other techniques when applied to a few qubits, it does offer the opportunity to explore multipartite entanglement for four and five qubits beyond the reach of other alternative technologies

Quantum nonlocality in two three-level systems

Recently a new Bell inequality has been introduced by Collins et al. [Phys. Rev. Lett. 88, 040404 (2002)], which is strongly resistant to noise for maximally entangled states of two d-dimensional quantum systems. We prove that a larger violation, or equivalently a stronger resistance to noise, is found for a nonmaximally entangled state. It is shown that the resistance to noise is not a good measure of nonlocality and we introduce some other possible measures. The nonmaximally entangled state turns out to be more robust also for these alternative measures. From these results it follows that two von Neumann measurements per party may be not optimal for detecting nonlocality. For d=3,4, we point out some connections between this inequality and distillability. Indeed, we demonstrate that any state violating it, with the optimal von Neumann settings, is distillable

Absolute Maximal Entanglement and Quantum Secret Sharing

We study the existence of absolutely maximally entangled (AME) states in quantum mechanics and its applications to quantum information. AME states are characterized by being maximally entangled for all bipartitions of the system and exhibit genuine multipartite entanglement. With such states, we present a novel parallel teleportation protocol which teleports multiple quantum states between groups of senders and receivers. The notable features of this protocol are that (i) the partition into senders and receivers can be chosen after the state has been distributed, and (ii) one group has to perform joint quantum operations while the parties of the other group only have to act locally on their system. We also prove the equivalence between pure state quantum secret sharing schemes and AME states with an even number of parties. This equivalence implies the existence of AME states for an arbitrary number of parties based on known results about the existence of quantum secret sharing schemes.Comment: 5 pages, 2 figure