Environment and classical channels in categorical quantum mechanics

We present a both simple and comprehensive graphical calculus for quantum computing. In particular, we axiomatize the notion of an environment, which together with the earlier introduced axiomatic notion of classical structure enables us to define classical channels, quantum measurements and classical control. If we moreover adjoin the earlier introduced axiomatic notion of complementarity, we obtain sufficient structural power for constructive representation and correctness derivation of typical quantum informatic protocols.Comment: 26 pages, many pics; this third version has substantially more explanations than previous ones; Journal reference is of short 14 page version; Proceedings of the 19th EACSL Annual Conference on Computer Science Logic (CSL), Lecture Notes in Computer Science 6247, Springer-Verlag (2010

Evolution of a global string network in a matter dominated universe

We evolve the network of global strings in the matter-dominated universe by means of numerical simulations. The existence of the scaling solution is confirmed as in the radiation-dominated universe but the scaling parameter $\xi$ takes a slightly smaller value, $\xi \simeq 0.6 \pm 0.1$, which is defined as $\xi = \rho_{s} t^{2} / \mu$ with $\rho_{s}$ the energy density of global strings and $\mu$ the string tension per unit length. The change of $\xi$ from the radiation to the matter-dominated universe is consistent with that obtained by Albrecht and Turok by use of the one-scale model. We also study the loop distribution function and find that it can be well fitted with that predicted by the one-scale model, where the number density $n_{l}(t)$ of the loop with the length $l$ is given by $n_{l}(t) = \nu/[t^2 (l + \kappa t)^2]$ with $\nu \sim 0.040$ and $\kappa \sim 0.48$. Thus, the evolution of the global string network in the matter-dominated universe can be well described by the one-scale model as in the radiation-dominated universe.Comment: 10 pages, 5 figure

A Comprehensive Archival Search for Counterparts to Ultra-Compact High Velocity Clouds: Five Local Volume Dwarf Galaxies

We report five Local Volume dwarf galaxies (two of which are presented here for the first time) uncovered during a comprehensive archival search for optical counterparts to ultra-compact high velocity clouds (UCHVCs). The UCHVC population of HI clouds are thought to be candidate gas-rich, low mass halos at the edge of the Local Group and beyond, but no comprehensive search for stellar counterparts to these systems has been presented. Careful visual inspection of all publicly available optical and ultraviolet imaging at the position of the UCHVCs revealed six blue, diffuse counterparts with a morphology consistent with a faint dwarf galaxy beyond the Local Group. Optical spectroscopy of all six candidate dwarf counterparts show that five have an H$\alpha$-derived velocity consistent with the coincident HI cloud, confirming their association, the sixth diffuse counterpart is likely a background object. The size and luminosity of the UCHVC dwarfs is consistent with other known Local Volume dwarf irregular galaxies. The gas fraction ($M_{HI}/M_{star}$) of the five dwarfs are generally consistent with that of dwarf irregular galaxies in the Local Volume, although ALFALFA-Dw1 (associated with ALFALFA UCHVC HVC274.68+74.70$-$123) has a very high $M_{HI}/M_{star}$$\sim$40. Despite the heterogenous nature of our search, we demonstrate that the current dwarf companions to UCHVCs are at the edge of detectability due to their low surface brightness, and that deeper searches are likely to find more stellar systems. If more sensitive searches do not reveal further stellar counterparts to UCHVCs, then the dearth of such systems around the Local Group may be in conflict with $\Lambda$CDM simulations.Comment: 18 pages, 4 tables, 4 figures, ApJ Accepte

Using of small-scale quantum computers in cryptography with many-qubit entangled states

We propose a new cryptographic protocol. It is suggested to encode information in ordinary binary form into many-qubit entangled states with the help of a quantum computer. A state of qubits (realized, e.g., with photons) is transmitted through a quantum channel to the addressee, who applies a quantum computer tuned to realize the inverse unitary transformation decoding of the message. Different ways of eavesdropping are considered, and an estimate of the time needed for determining the secret unitary transformation is given. It is shown that using even small quantum computers can serve as a basis for very efficient cryptographic protocols. For a suggested cryptographic protocol, the time scale on which communication can be considered secure is exponential in the number of qubits in the entangled states and in the number of gates used to construct the quantum network

Scaling Property of the global string in the radiation dominated universe

We investigate the evolution of the global string network in the radiation dominated universe by use of numerical simulations in 3+1 dimensions. We find that the global string network settles down to the scaling regime where the energy density of global strings, $\rho_{s}$, is given by $\rho_{s} = \xi \mu / t^2$ with $\mu$ the string tension per unit length and the scaling parameter, $\xi \sim (0.9-1.3)$, irrespective of the cosmic time. We also find that the loop distribution function can be fitted with that predicted by the so-called one scale model. Concretely, the number density, $n_{l}(t)$, of the loop with the length, $l$, is given by $n_{l}(t) = \nu/[t^{3/2} (l + \kappa t)^{5/2}]$ where $\nu \sim 0.0865$ and $\kappa$ is related with the Nambu-Goldstone(NG) boson radiation power from global strings, $P$, as $P = \kappa \mu$ with $\kappa \sim 0.535$. Therefore, the loop production function also scales and the typical scale of produced loops is nearly the horizon distance. Thus, the evolution of the global string network in the radiation dominated universe can be well described by the one scale model in contrast with that of the local string network.Comment: 18 pages, 9 figures, to appear in Phys. Rev.

Gravitational Lensing Signature of Long Cosmic Strings

The gravitational lensing by long, wiggly cosmic strings is shown to produce a large number of lensed images of a background source. In addition to pairs of images on either side of the string, a number of small images outline the string due to small-scale structure on the string. This image pattern could provide a highly distinctive signature of cosmic strings. Since the optical depth for multiple imaging of distant quasar sources by long strings may be comparable to that by galaxies, these image patterns should be clearly observable in the next generation of redshift surveys such as the Sloan Digital Sky Survey.Comment: 4 pages, revtex with 3 postscript figures include

The Satellite Luminosity Function of M101 into the Ultra-Faint Dwarf Galaxy Regime

We have obtained deep Hubble Space Telescope (HST) imaging of four faint and ultra-faint dwarf galaxy candidates in the vicinity of M101 - Dw21, Dw22, Dw23 and Dw35, originally discovered by Bennet et al. (2017). Previous distance estimates using the surface brightness fluctuation technique have suggested that these four dwarf candidates are the only remaining viable M101 satellites identified in ground based imaging out to the virial radius of M101 (D~250 kpc). Advanced Camera for Surveys imaging of all four dwarf candidates shows no associated resolved stellar populations, indicating that they are thus background galaxies. We confirm this by generating simulated HST color magnitude diagrams of similar brightness dwarfs at the distance of M101. Our targets would have displayed clear, resolved red giant branches with dozens of stars if they had been associated with M101. With this information, we construct a satellite luminosity function for M101, which is 90% complete to M_V=-7.7 mag and 50% complete to M_V=-7.4 mag, that extends into the ultra-faint dwarf galaxy regime. The M101 system is remarkably poor in satellites in comparison to the Milky Way and M31, with only eight satellites down to an absolute magnitude of M_V=-7.7 mag, compared to the 14 and 26 seen in the Milky Way and M31, respectively. Further observations of Milky Way analogs are needed to understand the halo-to-halo scatter in their faint satellite systems, and connect them with expectations from cosmological simulations.Comment: 9 Pages, 3 Figures, 1 Table, Accepted by ApJ

Observing Long Cosmic Strings Through Gravitational Lensing

We consider the gravitational lensing produced by long cosmic strings formed in a GUT scale phase transition. We derive a formula for the deflection of photons which pass near the strings that reduces to an integral over the light cone projection of the string configuration plus constant terms which are not important for lensing. Our strings are produced by performing numerical simulations of cosmic string networks in flat, Minkowski space ignoring the effects of cosmological expansion. These strings have more small scale structure than those from an expanding universe simulation - fractal dimension 1.3 for Minkowski versus 1.1 for expanding - but share the same qualitative features. Lensing simulations show that for both point-like and extended objects, strings produce patterns unlike more traditional lenses, and, in particluar, the kinks in strings tend to generate demagnified images which reside close to the string. Thus lensing acts as a probe of the small scale structure of a string. Estimates of lensing probablity suggest that for string energy densities consistant with string seeded structure formation, on the order of tens of string lenses should be observed in the Sloan Digital Sky Survey quasar catalog. We propose a search strategy in which string lenses would be identified in the SDSS quasar survey, and the string nature of the lens can be confirmed by the observation of nearby high redshift galaxies which are also be lensed by the string.Comment: 24 pages revtex with 12 postscript firgure

Entanglement of electrons in interacting molecules

Quantum entanglement is a concept commonly used with reference to the existence of certain correlations in quantum systems that have no classical interpretation. It is a useful resource to enhance the mutual information of memory channels or to accelerate some quantum processes as, for example, the factorization in Shor's Algorithm. Moreover, entanglement is a physical observable directly measured by the von Neumann entropy of the system. We have used this concept in order to give a physical meaning to the electron correlation energy in systems of interacting electrons. The electronic correlation is not directly observable, since it is defined as the difference between the exact ground state energy of the many--electrons Schroedinger equation and the Hartree--Fock energy. We have calculated the correlation energy and compared with the entanglement, as functions of the nucleus--nucleus separation using, for the hydrogen molecule, the Configuration Interaction method. Then, in the same spirit, we have analyzed a dimer of ethylene, which represents the simplest organic conjugate system, changing the relative orientation and distance of the molecules, in order to obtain the configuration corresponding to maximum entanglement.Comment: 15 pages, 7 figures, standard late