Quantum Stabilizer Codes and Classical Linear Codes

We show that within any quantum stabilizer code there lurks a classical binary linear code with similar error-correcting capabilities, thereby demonstrating new connections between quantum codes and classical codes. Using this result -- which applies to degenerate as well as nondegenerate codes -- previously established necessary conditions for classical linear codes can be easily translated into necessary conditions for quantum stabilizer codes. Examples of specific consequences are: for a quantum channel subject to a delta-fraction of errors, the best asymptotic capacity attainable by any stabilizer code cannot exceed H(1/2 + sqrt(2*delta*(1-2*delta))); and, for the depolarizing channel with fidelity parameter delta, the best asymptotic capacity attainable by any stabilizer code cannot exceed 1-H(delta).Comment: 17 pages, ReVTeX, with two figure

Gaseous fission product release during storage at various temperatures for HTGR-type fuels

Measurements were made of gaseous fission product releases from an HTGR-type fuel body under conditions simulating storage at temperatures up to 300/sup 0/C. The fuel was a recycle test element containing BISO-BISO coated fuel particles which had been irradiated for 701 effective full-power days in the Peach Bottom HTGR. Storage test temperatures were ambient (about 30/sup 0/C), 100, 150, 200, and 300/sup 0/C. The initial release rates of /sup 85/Kr varied after each change in temperature. A fairly stable release rate was reached that increased from approximately 60 ..mu..Ci/day at ambient temperature to approximately 1000 ..mu..Ci/day after 30 days at 200/sup 0/C and slowly decreased to about 200 ..mu..Ci/day after 554 days at 200/sup 0/C. In the experiment at 300/sup 0/C, a final release rate of 4000 ..mu..Ci/day was attained after 66 days. The releases of /sup 85/Kr were followed for about two and one-half years. The stabilized release rates for /sup 3/H were approximately 0.02 ..mu..Ci/day at ambient temperature, approximately 0.750 ..mu..Ci/day at 200/sup 0/C after 30 days, and 0.460 ..mu..Ci/day after 554 days. The final release rate at 300/sup 0/C was about 30 ..mu..Ci/day after 66 days.Over the lifetime of the experiment, approximately 22% of the initial /sup 85/Kr inventory was evolved and swept out, and approximately 4% of the initial /sup 3/H inventory was evolved and swept out. The activation energies calculated for the Kr and /sup 3/H evolution were approximately 7.8 kcal/mole and approximately 12.4 kcal/mole, respectively

Statistical mechanics of typical set decoding

The performance of ``typical set (pairs) decoding'' for ensembles of Gallager's linear code is investigated using statistical physics. In this decoding, error happens when the information transmission is corrupted by an untypical noise or two or more typical sequences satisfy the parity check equation provided by the received codeword for which a typical noise is added. We show that the average error rate for the latter case over a given code ensemble can be tightly evaluated using the replica method, including the sensitivity to the message length. Our approach generally improves the existing analysis known in information theory community, which was reintroduced by MacKay (1999) and believed as most accurate to date.Comment: 7 page

Thorex solvent extraction studies with irradiated HTGR fuel: series I

A series of solvent extraction experiments to test the first-cycle fuel reprocessing flowsheet, proposed by the General Atomic Company for the Hot Engineering Test Facility, was completed. Using irradiated fuel, the experiments were designed to test the extraction, partition, partition-scrub, and strip operations. Each experiment utilized crosscurrent batch extractions and consecutive stages. Each stage was tested in duplicate. Experimental procedures were developed with synthetic feeds and then were used in a hot cell with radioactive solutions of dissolved irradiated fuel. The analytical measurements for thorium and acid compared favorably with the values predicted by the computer program for solvent extraction processes having interacting solutes (SEPHIS-MOD4). The SEPHIS-MOD4 program was valuable in interpreting this first set of experiments with irradiated fuels. Significant problems were experienced in the analysis for uranium in irradiated solutions. These problems emphasize the need for continued development of new or improved procedures for analyzing highly radioactive materials

The importance of OH radical–neutral low temperature tunnelling reactions in interstellar clouds using a new model

Recent laboratory experiments using a pulsed Laval nozzle apparatus have shown that reactions between a neutral molecule and the radical OH can occur efficiently at low temperatures despite activation energy barriers if there is a hydrogen-bonded complex in the entrance channel which allows the system to tunnel efficiently under the barrier. Since OH is a major radical in the interstellar medium, this class of reactions may well be important in the chemistry that occurs in the gas phase of interstellar clouds. Using a new gas-grain chemical network with both gas-phase reactions and reactions on the surfaces of dust particles, we studied the role of OH–neutral reactions in dense interstellar clouds at 10, 50, and 100 K. We determined that at least one of these reactions can be significant, especially at the lowest temperatures studied, where the rate constants are large. It was found in particular that the reaction between CH3OH and OH provides an effective and unambiguous gas-phase route to the production of the gaseous methoxy radical (CH3O), which has been recently detected in cold, dense interstsellar clouds. The role of other reactions in this class is explored

NaIrO3 - A pentavalent post-perovskite

Sodium iridium(V) oxide, NaIrO3, was synthesized by a high pressure solid state method and recovered to ambient conditions. It is found to be isostructural with CaIrO3, the much-studied structural analogue of the high-pressure post-perovskite phase of MgSiO3. Among the oxide post-perovskites, NaIrO3 is the first example with a pentavalent cation. The structure consists of layers of corner- and edge-sharing IrO6 octahedra separated by layers of NaO8 bicapped trigonal prisms. NaIrO3 shows no magnetic ordering and resistivity measurements show non-metallic behavior. The crystal structure, electrical and magnetic properties are discussed and compared to known post-perovskites and pentavalent perovskite metal oxides.Comment: 22 pages, 5 figures. Submitted to Journal of Solid State Chemistr

The Kagome-staircase lattice: Magnetic ordering in Ni3V2O8 and Co3V2O8

Ni3V2O8 and Co3V2O8 have spin-1 and spin-3/2 magnetic lattices that are a new anisotropic variant of the Kagome net, wherein edge-sharing MO6 octahedra form the rises and rungs of a "Kagome staircase". The anisotropy largely relieves the geometric frustration, but results in rich magnetic behavior. Characterization of the magnetization of polycrystalline samples reveals that the compounds are ferrimagnetic in character. Heat capacity measurements show the presence of four magnetic phase transitions below 9 K for Ni3V2O8 and two below 11 K for Co3V2O8. Comparison to the low temperature heat capacity of isostructural nonmagnetic Zn3V2O8 provides an estimate of the magnetic entropy involved with the phase transitions. The results suggest that Co3V2O8 may display magnetic transitions below 2 K.Comment: 9 pages, 5 figure

Spreading lengths of Hermite polynomials

The Renyi, Shannon and Fisher spreading lengths of the classical or hypergeometric orthogonal polynomials, which are quantifiers of their distribution all over the orthogonality interval, are defined and investigated. These information-theoretic measures of the associated Rakhmanov probability density, which are direct measures of the polynomial spreading in the sense of having the same units as the variable, share interesting properties: invariance under translations and reflections, linear scaling and vanishing in the limit that the variable tends towards a given definite value. The expressions of the Renyi and Fisher lengths for the Hermite polynomials are computed in terms of the polynomial degree. The combinatorial multivariable Bell polynomials, which are shown to characterize the finite power of an arbitrary polynomial, play a relevant role for the computation of these information-theoretic lengths. Indeed these polynomials allow us to design an error-free computing approach for the entropic moments (weighted L^q-norms) of Hermite polynomials and subsequently for the Renyi and Tsallis entropies, as well as for the Renyi spreading lengths. Sharp bounds for the Shannon length of these polynomials are also given by means of an information-theoretic-based optimization procedure. Moreover, it is computationally proved the existence of a linear correlation between the Shannon length (as well as the second-order Renyi length) and the standard deviation. Finally, the application to the most popular quantum-mechanical prototype system, the harmonic oscillator, is discussed and some relevant asymptotical open issues related to the entropic moments mentioned previously are posed.Comment: 16 pages, 4 figures. Journal of Computational and Applied Mathematics (2009), doi:10.1016/j.cam.2009.09.04

Stuffed Rare Earth Pyrochlore Solid Solutions

Synthesis and crystal structures are described for the compounds Ln2(Ti2-xLnx)O7-x/2, where Ln = Tb, Dy, Ho, Er, Tm, Yb, Lu, and x ranges from 0 to 0.67. Rietveld refinements on X-ray powder diffraction data indicate that in Tb and Dy titanate pyrochlores, extra Ln3+ cations mix mainly on the Ti4+ site with little disorder on the original Ln3+ site. For the smaller rare earths (Ho-Lu), stuffing additional lanthanide ions results in a pyrochlore to defect fluorite transition, where the Ln3+ and Ti4+ ions become completely randomized at the maximum (x=0.67). In all of these Ln-Ti-O pyrochlores, the addition of magnetic Ln3+ in place of nonmagnetic Ti4+ adds edge sharing tetrahedral spin interactions to a normally corner sharing tetrahedral network of spins. The increase in spin connectivity in this family of solid solutions represents a new avenue for investigating geometrical magnetic frustration in the rare earth titanate pyrochlores.Comment: 25 pages, 7 figures, submitted to J. Solid State Che

Exchange coupling in CaMnO3_3 and LaMnO3_3: configuration interaction and the coupling mechanism

The equilibrium structure and exchange constants of CaMnO$_3$ and LaMnO$_3$ have been investigated using total energy unrestricted Hartree-Fock (UHF) and localised orbital configuration interaction (CI) calculations on the bulk compounds and Mn$_2$O$_{11}^{14-}$ and Mn$_2$O$_{11}^{16-}$ clusters. The predicted structure and exchange constants for CaMnO$_3$ are in reasonable agreement with estimates based on its N\'eel temperature. A series of calculations on LaMnO$_3$ in the cubic perovskite structure shows that a Hamiltonian with independent orbital ordering and exchange terms accounts for the total energies of cubic LaMnO$_3$ with various spin and orbital orderings. Computed exchange constants depend on orbital ordering. UHF calculations tend to underestimate exchange constants in LaMnO$_3$, but have the correct sign when compared with values obtained by neutron scattering; exchange constants obtained from CI calculations are in good agreement with neutron scattering data provided the Madelung potential of the cluster is appropriate. Cluster CI calculations reveal a strong dependence of exchange constants on Mn d e$_g$ orbital populations in both compounds. CI wave functions are analysed in order to determine which exchange processes are important in exchange coupling in CaMnO$_3$ and LaMnO$_3$.Comment: 25 pages and 9 postscript figure