Solutions of the Yang-Baxter equation: descendants of the six-vertex model from the Drinfeld doubles of dihedral group algebras

The representation theory of the Drinfeld doubles of dihedral groups is used to solve the Yang-Baxter equation. Use of the 2-dimensional representations recovers the six-vertex model solution. Solutions in arbitrary dimensions, which are viewed as descendants of the six-vertex model case, are then obtained using tensor product graph methods which were originally formulated for quantum algebras. Connections with the Fateev-Zamolodchikov model are discussed.Comment: 34 pages, 2 figure

Grothendieck's constant and local models for noisy entangled quantum states

We relate the nonlocal properties of noisy entangled states to Grothendieck's constant, a mathematical constant appearing in Banach space theory. For two-qubit Werner states \rho^W_p=p \proj{\psi^-}+(1-p){\one}/{4}, we show that there is a local model for projective measurements if and only if $p \le 1/K_G(3)$, where $K_G(3)$ is Grothendieck's constant of order 3. Known bounds on $K_G(3)$ prove the existence of this model at least for $p \lesssim 0.66$, quite close to the current region of Bell violation, $p \sim 0.71$. We generalize this result to arbitrary quantum states.Comment: 6 pages, 1 figur

More efficient Bell inequalities for Werner states

In this paper we study the nonlocal properties of two-qubit Werner states parameterized by the visibility parameter 0<p<1. New family of Bell inequalities are constructed which prove the two-qubit Werner states to be nonlocal for the parameter range 0.7056<p<1. This is slightly wider than the range 0.7071<p<1, corresponding to the violation of the Clauser-Horne-Shimony-Holt (CHSH) inequality. This answers a question posed by Gisin in the positive, i.e., there exist Bell inequalities which are more efficient than the CHSH inequality in the sense that they are violated by a wider range of two-qubit Werner states.Comment: 7 pages, 1 figur

The great ideas of biology: Exploration through experimentation in an undergraduate lab course

We developed an introductory laboratory course to provide a visceral experience that aims at getting students truly excited about scientific study of the living world. Our vehicle to do that was to focus on what Paul Nurse dubbed “the great ideas of biology” rather than an approach to biology that celebrates specific factual knowledge. To that end, we developed eight diverse experimental modules, each of which highlights a key biological concept and gives an opportunity to use theory to generate testable hypotheses, to perform high quality measurements to test those hypotheses (some of which are clearly wrong), and to perform sophisticated computational data analysis. Some modules incorporate modern microscopy and computational techniques in classic experiments, such as bacterial growth and the Luria‐Delbrück experiment, while others address current research questions using methods like optogenetics and single molecule measurements. We have offered the course eight times, and in the most recent edition of the course, we conducted pre/post‐course interviews and attitude surveys. The students, both bio and non‐bio majors alike, reported being captivated by seeing life occur across the broad range of experiments and model organisms. We observed demonstrable development of their curiosity and enthusiasm for biology. Additionally, we found that prior to the course, students had only vague notions about what it means to make quantitative biological measurements and interpret them. They completed the course with a clearer understanding of scientific inquiry in biology and the skills and confidence to actually perform and interpret measurements in living systems