Decoherence of Anyonic Charge in Interferometry Measurements

We examine interferometric measurements of the topological charge of (non-Abelian) anyons. The target's topological charge is measured from its effect on the interference of probe particles sent through the interferometer. We find that superpositions of distinct anyonic charges a and a' in the target decohere (exponentially in the number of probes particles used) when the probes have nontrivial monodromy with the charges that may be fused with a to give a'.Comment: 5 pages, 1 figure; v2: reference added, example added, clarifying changes made to conform to the version published in PR

Topological Degeneracy and Vortex Manipulation in Kitaev's Honeycomb Model

The classification of loop symmetries in Kitaev's honeycomb lattice model provides a natural framework to study the Abelian topological degeneracy. We derive a perturbative low-energy effective Hamiltonian that is valid to all orders of the expansion and for all possible toroidal configurations. Using this form we demonstrate at what order the system's topological degeneracy is lifted by finite size effects and note that in the thermodynamic limit it is robust to all orders. Further, we demonstrate that the loop symmetries themselves correspond to the creation, propagation, and annihilation of fermions. We note that these fermions, made from pairs of vortices, can be moved with no additional energy cost

The modular S-matrix as order parameter for topological phase transitions

We study topological phase transitions in discrete gauge theories in two spatial dimensions induced by the formation of a Bose condensate. We analyse a general class of euclidean lattice actions for these theories which contain one coupling constant for each conjugacy class of the gauge group. To probe the phase structure we use a complete set of open and closed anyonic string operators. The open strings allow one to determine the particle content of the condensate, whereas the closed strings enable us to determine the matrix elements of the modular $S$-matrix, also in the broken phase. From the measured broken $S$-matrix we may read off the sectors that split or get identified in the broken phase, as well as the sectors that are confined. In this sense the modular $S$-matrix can be employed as a matrix valued non-local order parameter from which the low-energy effective theories that occur in different regions of parameter space can be fully determined. To verify our predictions we studied a non-abelian anyon model based on the quaternion group $H=\bar{D_2}$ of order eight by Monte Carlo simulation. We probe part of the phase diagram for the pure gauge theory and find a variety of phases with magnetic condensates leading to various forms of (partial) confinement in complete agreement with the algebraic breaking analysis. Also the order of various transitions is established.Comment: 37 page

Topological Qubit Design and Leakage

We examine how best to design qubits for use in topological quantum computation. These qubits are topological Hilbert spaces associated with small groups of anyons. Op- erations are performed on these by exchanging the anyons. One might argue that, in order to have as many simple single qubit operations as possible, the number of anyons per group should be maximized. However, we show that there is a maximal number of particles per qubit, namely 4, and more generally a maximal number of particles for qudits of dimension d. We also look at the possibility of having topological qubits for which one can perform two-qubit gates without leakage into non-computational states. It turns out that the requirement that all two-qubit gates are leakage free is very restrictive and this property can only be realized for two-qubit systems related to Ising-like anyon models, which do not allow for universal quantum computation by braiding. Our results follow directly from the representation theory of braid groups which means they are valid for all anyon models. We also make some remarks on generalizations to other exchange groups.Comment: 13 pages, 3 figure

Tamoxifen may prevent both ER+ and ER- breast cancers and select for ER- carcinogenesis: an alternative hypothesis

Introduction: Breast Cancer Prevention Trial (BCPT) and Multiple Outcomes of Raloxifene (MORE) data have been interpreted to indicate that tamoxifen reduces the risk of ER+ but not ER- breast carcinogenesis. We explored whether these data also support an alternative hypothesis, that tamoxifen influences the natural history of both ER+ and ER- cancers, that it may be equally effective in abrogating or delaying ER- and ER+ carcinogenesis, and place selection pressure, in some cases, for the outgrowth of ER- cancers. Methods: BCPT and MORE data were used to investigate whether: first, tamoxifen could reduce equally the emergence of ER- and ER+ tumors; and second, tamoxifen could select a fraction of emerging ER+ cancers and promote their transformation to ER- cancers. Assuming that some proportion, Z, of ER+ tumors becomes ER- after tamoxifen exposure and that the risk reduction for both ER- and ER+ tumors is equal, we solved for both the transformation rate and the risk reduction rate. Results: If tamoxifen equally reduces the incidence of ER+ and ER- tumors by 60%, the BCPT results are achieved with a transformation of approximately Z = 20% of ER+ to ER- tumors. Validation with MORE data using an equal risk reduction of 60% associated with tamoxifen produces an almost identical transformation rate Z of 23%. Conclusion: Data support an alternative hypothesis that tamoxifen may promote ER- carcinogenesis from a precursor lesion that would otherwise have developed as ER+ without tamoxifen selection

A Description of Kitaev's Honeycomb Model with Toric-Code Stabilizers

We present a solution of Kitaev's spin model on the honeycomb lattice and of related topologically ordered spin models. We employ a Jordan-Wigner type fermionization and find that the Hamiltonian takes a BCS type form, allowing the system to be solved by Bogoliubov transformation. Our fermionization does not employ non-physical auxiliary degrees of freedom and the eigenstates we obtain are completely explicit in terms of the spin variables. The ground-state is obtained as a BCS condensate of fermion pairs over a vacuum state which corresponds to the toric code state with the same vorticity. We show in detail how to calculate all eigenstates and eigenvalues of the model on the torus. In particular, we find that the topological degeneracy on the torus descends directly from that of the toric code, which now supplies four vacua for the fermions, one for each choice of periodic vs. anti-periodic boundary conditions. The reduction of the degeneracy in the non-Abelian phase of the model is seen to be due to the vanishing of one of the corresponding candidate BCS ground-states in that phase. This occurs in particular in the fully periodic vortex-free sector. The true ground-state in this sector is exhibited and shown to be gapped away from the three partially anti-periodic ground-states whenever the non-Abelian phase is gapped.Comment: 10 pages, 4 figure

Clebsch-Gordan and 6j-coefficients for rank two quantum groups

We calculate (q-deformed) Clebsch-Gordan and 6j-coefficients for rank two quantum groups. We explain in detail how such calculations are done, which should allow the reader to perform similar calculations in other cases. Moreover, we tabulate the q-Clebsch-Gordan and 6j-coefficients explicitly, as well as some other topological data associated with theories corresponding to rank-two quantum groups. Finally, we collect some useful properties of the fusion rules of particular conformal field theories.Comment: 43 pages. v2: minor changes and added references. For mathematica notebooks containing the various q-CG and 6j symbols, see http://arxiv.org/src/1004.5456/an

A theory of topological edges and domain walls

We investigate domain walls between topologically ordered phases in two spatial dimensions and present a simple but general framework from which their degrees of freedom can be understood. The approach we present exploits the results on topological symmetry breaking that we have introduced and presented elsewhere. After summarizing the method, we work out predictions for the spectrum of edge excitations and for the transport through edges in some representative examples. These include domain walls between the Abelian and non-Abelian topological phases of Kitaev's honeycomb lattice model in a magnetic field, as well as recently proposed domain walls between spin polarized and unpolarized non-Abelian fractional quantum Hall states at different filling fractions.Comment: 4 pages, 1 figure, late

Comparison of Accu Chek Inform II point-of-care test blood glucose meter with Hexokinase Plasma method for a diabetes mellitus population during surgery under general anesthesia

Purpose Blood glucose (BG) concentrations of patients with diabetes mellitus (DM) are monitored during surgery to prevent hypo- and hyperglycemia. Access to point-of-care test (POCT) glucose meters at an operating room will usually provide monitoring at shorter intervals and may improve glycemic control. However, these meters are not validated for patients under general anesthesia. Methods This cross-sectional study included 75 arterial BG measurements from 75 patients (71 with DM, mostly insulin dependent) who underwent elective non-cardiac surgery under general anesthesia. Arterial blood samples were taken at least 60 minutes after induction. One drop of blood was used for Accu Chek Inform II (ACI II) POCT BG meter and the residual blood was sent to the clinical laboratory for a Hexokinase Plasma reference method. A Bland-Altman plot was used to visualize the differences between both methods, and correlation was assessed using the intra-class correlation coefficient (ICC). Results The results showed an estimated mean difference of 0.8 mmol/L between ACI II and the reference method, with limits of agreement equal to -0.6 and 2.2 mmol/L. In general, the reference method produced higher values than ACI II. ICC was 0.955 (95% CI 0.634-0.986), P &lt; 0.001, and concordance correlation coefficient (CCC) was 0.955 (95% CI 0.933-0.970). Conclusion Arterial BG measurements during surgery in patients with DM under general anesthesia using POCT BG meter are in general lower than laboratory measurements, but the ICC and CCC show a clinically acceptable correlation. We conclude that POCT measurements conducted on arterial specimens using the ACI II provide sufficiently accurate results for glucose measurement during surgery under general anesthesia.</p