The Measurement Calculus

Measurement-based quantum computation has emerged from the physics community as a new approach to quantum computation where the notion of measurement is the main driving force of computation. This is in contrast with the more traditional circuit model which is based on unitary operations. Among measurement-based quantum computation methods, the recently introduced one-way quantum computer stands out as fundamental. We develop a rigorous mathematical model underlying the one-way quantum computer and present a concrete syntax and operational semantics for programs, which we call patterns, and an algebra of these patterns derived from a denotational semantics. More importantly, we present a calculus for reasoning locally and compositionally about these patterns. We present a rewrite theory and prove a general standardization theorem which allows all patterns to be put in a semantically equivalent standard form. Standardization has far-reaching consequences: a new physical architecture based on performing all the entanglement in the beginning, parallelization by exposing the dependency structure of measurements and expressiveness theorems. Furthermore we formalize several other measurement-based models: Teleportation, Phase and Pauli models and present compositional embeddings of them into and from the one-way model. This allows us to transfer all the theory we develop for the one-way model to these models. This shows that the framework we have developed has a general impact on measurement-based computation and is not just particular to the one-way quantum computer.Comment: 46 pages, 2 figures, Replacement of quant-ph/0412135v1, the new version also include formalization of several other measurement-based models: Teleportation, Phase and Pauli models and present compositional embeddings of them into and from the one-way model. To appear in Journal of AC

Theory of Chiral Order in Random Copolymers

Recent experiments have found that polyisocyanates composed of a mixture of opposite enantiomers follow a chiral ``majority rule:'' the chiral order of the copolymer, measured by optical activity, is dominated by whichever enantiomer is in the majority. We explain this majority rule theoretically by mapping the random copolymer onto the random-field Ising model. Using this model, we predict the chiral order as a function of enantiomer concentration, in quantitative agreement with the experiments, and show how the sharpness of the majority-rule curve can be controlled.Comment: 13 pages, including 4 postscript figures, uses REVTeX 3.0 and epsf.st

Isotropic-Nematic Transition in Liquid-Crystalline Elastomers

In liquid-crystalline elastomers, the nematic order parameter and the induced strain vary smoothly across the isotropic-nematic transition, without the expected first-order discontinuity. To investigate this smooth variation, we measure the strain as a function of temperature over a range of applied stress, for elastomers crosslinked in the nematic and isotropic phases, and analyze the results using a variation on Landau theory. This analysis shows that the smooth variation arises from quenched disorder in the elastomer, combined with the effects of applied stress and internal stress.Comment: 4 pages, including 4 postscript figures, uses REVTeX

Order and Frustration in Chiral Liquid Crystals

This paper reviews the complex ordered structures induced by chirality in liquid crystals. In general, chirality favors a twist in the orientation of liquid-crystal molecules. In some cases, as in the cholesteric phase, this favored twist can be achieved without any defects. More often, the favored twist competes with applied electric or magnetic fields or with geometric constraints, leading to frustration. In response to this frustration, the system develops ordered structures with periodic arrays of defects. The simplest example of such a structure is the lattice of domains and domain walls in a cholesteric phase under a magnetic field. More complex examples include defect structures formed in two-dimensional films of chiral liquid crystals. The same considerations of chirality and defects apply to three-dimensional structures, such as the twist-grain-boundary and moire phases.Comment: 39 pages, RevTeX, 14 included eps figure

The Role of Bilayer Tilt Difference in Equilibrium Membrane Shapes

Lipid bilayer membranes below their main transition have two tilt order parameters, corresponding to the two monolayers. These two tilts may be strongly coupled to membrane shape but only weakly coupled to each other. We discuss some implications of this observation for rippled and saddle phases, bilayer tubules, and bicontinuous phases. Tilt difference introduces a length scale into the elastic theory of tilted fluid membranes. It can drive an instability of the flat phase; it also provides a simple mechanism for the spontaneous breaking of inversion symmetry seen in some recent experiments.Comment: Latex file; .ps available at http://dept.physics.upenn.edu/~nelson/saddle.p

Picturing classical and quantum Bayesian inference

We introduce a graphical framework for Bayesian inference that is sufficiently general to accommodate not just the standard case but also recent proposals for a theory of quantum Bayesian inference wherein one considers density operators rather than probability distributions as representative of degrees of belief. The diagrammatic framework is stated in the graphical language of symmetric monoidal categories and of compact structures and Frobenius structures therein, in which Bayesian inversion boils down to transposition with respect to an appropriate compact structure. We characterize classical Bayesian inference in terms of a graphical property and demonstrate that our approach eliminates some purely conventional elements that appear in common representations thereof, such as whether degrees of belief are represented by probabilities or entropic quantities. We also introduce a quantum-like calculus wherein the Frobenius structure is noncommutative and show that it can accommodate Leifer's calculus of `conditional density operators'. The notion of conditional independence is also generalized to our graphical setting and we make some preliminary connections to the theory of Bayesian networks. Finally, we demonstrate how to construct a graphical Bayesian calculus within any dagger compact category.Comment: 38 pages, lots of picture

Anomalous Elasticity of Polymer Cholesterics

We show that polymer cholesterics have much longer pitches than comparable short molecule cholesterics, due to their anomalous elasticity. The pitch $P$ of a chiral mixture with concentration $c$ near the racemic (non-chiral) concentration $c^*$ diverges like $\vert c-c^*\vert^{-\nu}$ with $\nu=1.43 \pm 0.04$ (for short molecule cholesterics $\nu=1$). The short molecule law is recovered for polymers of finite molecular length $\ell$ once the pitch is longer than a length that diverges like $\ell^\gamma$ with $\gamma=0.67 \pm 0.01$. Our predictions could be tested by measurements of the pitch in DNA.Comment: 12 pages, Plain TeX, (1 postscript figure, compressed, uuencoded and appended to paper), minor corrections, IASSNS-HEP-94/4

Non-therapeutic administration of a model antimicrobial growth promoter modulates intestinal immune responses

<p>Abstract</p> <p>Background</p> <p>The development of efficacious alternatives to antimicrobial growth promoters (AGP) in livestock production is an urgent issue, but is hampered by a lack of knowledge regarding the mode of action of AGP. The belief that AGP modulate the intestinal microbiota has become prominent in the literature; however, there is a lack of experimental evidence to support this hypothesis. Using a chlortetracycline-murine-<it>Citrobacter rodentium </it>model, the ability of AGP to modulate the intestinal immune system in mammals was investigated.</p> <p>Results</p> <p><it>C. rodentium </it>was transformed with the tetracycline resistance gene, <it>tet</it>O, and continuous oral administration of a non-therapeutic dose of chlortetracycline to mice did not affect densities of <it>C. rodentium </it>CFU in feces throughout the experiment or associated with mucosal surfaces in the colon (i.e. at peak and late infection). However, chlortetracycline regulated transcription levels of Th1 and Th17 inflammatory cytokines in a temporal manner in <it>C. rodentium</it>-inoculated mice, and ameliorated weight loss associated with infection. In mice inoculated with <it>C. rodentium</it>, those that received chlortetracycline had less pathologic changes in the distal colon than mice not administered CTC (i.e. relative to untreated mice). Furthermore, chlortetracycline administration at a non-therapeutic dose did not impart either prominent or consistent effects on the colonic microbiota.</p> <p>Conclusion</p> <p>Data support the hypothesis that AGP function by modulating the intestinal immune system in mammals. This finding may facilitate the development of biorationale-based and efficacious alternatives to AGP.</p

Raman spectroscopy investigation of the H content of heated hard amorphous carbon layers

We revisit here how Raman spectroscopy can be used to estimate the H content in hard hydrogenated amorphous carbon layers. The H content was varied from 2 at.% to 30 at.%, using heat treatments of a a-C:H, from room temperature to 1300 K and was determined independently using ion beam analysis. We examine the correlation of various Raman parameters and the consistency of their thermal evolution with thermo-desorption results. We identify a weak band at 860 cm-1 attributed to H bonded to C(sp2). We show that the HD/HG parameter (Height ratio between the D and G bands) is quasi-linear in the full range of H content and can thus be used to estimate the H content. Conversely, we show that the m/HG parameter (ratio between the photoluminescence background, m, and the height of the G band), often used to estimate the H content, should be used with care, first because it is sensitive to various photoluminescence quenching processes and second because it is not sensitive to H bonded to C(sp2)