Adaptive Measurements in the Optical Quantum Information Laboratory

Adaptive techniques make practical many quantum measurements that would otherwise be beyond current laboratory capabilities. For example: they allow discrimination of nonorthogonal states with a probability of error equal to the Helstrom bound; they allow measurement of the phase of a quantum oscillator with accuracy approaching (or in some cases attaining) the Heisenberg limit; and they allow estimation of phase in interferometry with a variance scaling at the Heisenberg limit, using only single qubit measurement and control. Each of these examples has close links with quantum information, in particular experimental optical quantum information: the first is a basic quantum communication protocol; the second has potential application in linear optical quantum computing; the third uses an adaptive protocol inspired by the quantum phase estimation algorithm. We discuss each of these examples, and their implementation in the laboratory, but concentrate upon the last, which was published most recently [Higgins {\em et al.}, Nature vol. 450, p. 393, 2007].Comment: 12 pages, invited paper to be published in IEEE Journal of Selected Topics in Quantum Electronics: Quantum Communications and Information Scienc

XY checkerboard antiferromagnet in external field

Ordering by thermal fluctuations is studied for the classical XY antiferromagnet on a checkerboard lattice in zero and finite magnetic fields by means of analytical and Monte Carlo methods. The model exhibits a variety of novel broken symmetries including states with nematic ordering in zero field and with triatic order parameter at high fields.Comment: 6 page

Stick-slip instability for viscous fingering in a gel

The growth dynamics of an air finger injected in a visco-elastic gel (a PVA/borax aqueous solution) is studied in a linear Hele-Shaw cell. Besides the standard Saffmann-Taylor instability, we observe - with increasing finger velocities - the existence of two new regimes: (a) a stick-slip regime for which the finger tip velocity oscillates between 2 different values, producing local pinching of the finger at regular intervals, (b) a ``tadpole'' regime where a fracture-type propagation is observed. A scaling argument is proposed to interpret the dependence of the stick-slip frequency with the measured rheological properties of the gel.Comment: 7 pages, 4 figures. Submitted to Europhysics Letter

Phase Separation in Binary Fluid Mixtures with Continuously Ramped Temperature

We consider the demixing of a binary fluid mixture, under gravity, which is steadily driven into a two phase region by slowly ramping the temperature. We assume, as a first approximation, that the system remains spatially isothermal, and examine the interplay of two competing nonlinearities. One of these arises because the supersaturation is greatest far from the meniscus, creating inversion of the density which can lead to fluid motion; although isothermal, this is somewhat like the Benard problem (a single-phase fluid heated from below). The other is the intrinsic diffusive instability which results either in nucleation or in spinodal decomposition at large supersaturations. Experimental results on a simple binary mixture show interesting oscillations in heat capacity and optical properties for a wide range of ramp parameters. We argue that these oscillations arise under conditions where both nonlinearities are important

PERFORMANCE OF THE EXACT AND CHI-SQUARE TESTS ON SPARSE CONTINGENCY TABLES

A cross-sectional observational study design was used to determine the prevalence of Escherichia coli 0157:H7 in wild deer feces. Samples were voluntarily submitted at a number of different locations. In order to determine if the proportions of E. coli 0157: H7 positive samples submitted were equal for each of the 26 locations, a 26 by 2 contingency table was analyzed. There were only four E. coli 0157:H7 positive samples, which resulted in a sparse table. It is possible to obtain statistically significant results in sparse tables using Fisher\u27s exact test, whereas the chi-square test is generally unreliable in such situations. Thus, Fisher\u27s exact test should be considered when small expected cell counts bring into question the validity of the chi-square test. However, the statistical conclusions based on either the exact test or an asymptotic chi-square test are shown to vary drastically by slight alterations in the distribution of non-empty cells. Therefore, a different statistical conclusion very easily could have been reached if a volunteer had submitted a sample at a different location. In addition, we show that the computational times for exact tests in SAS® can be an applicational limitation

Infinite partition monoids

Let $\mathcal P_X$ and $\mathcal S_X$ be the partition monoid and symmetric group on an infinite set $X$. We show that $\mathcal P_X$ may be generated by $\mathcal S_X$ together with two (but no fewer) additional partitions, and we classify the pairs $\alpha,\beta\in\mathcal P_X$ for which $\mathcal P_X$ is generated by $\mathcal S_X\cup\{\alpha,\beta\}$. We also show that $\mathcal P_X$ may be generated by the set $\mathcal E_X$ of all idempotent partitions together with two (but no fewer) additional partitions. In fact, $\mathcal P_X$ is generated by $\mathcal E_X\cup\{\alpha,\beta\}$ if and only if it is generated by $\mathcal E_X\cup\mathcal S_X\cup\{\alpha,\beta\}$. We also classify the pairs $\alpha,\beta\in\mathcal P_X$ for which $\mathcal P_X$ is generated by $\mathcal E_X\cup\{\alpha,\beta\}$. Among other results, we show that any countable subset of $\mathcal P_X$ is contained in a $4$-generated subsemigroup of $\mathcal P_X$, and that the length function on $\mathcal P_X$ is bounded with respect to any generating set

Role of oxygen in the electron-doped superconducting cuprates

We report on resistivity and Hall measurements in thin films of the electron-doped superconducting cuprate Pr$_{2-x}$Ce$_{x}$CuO$_{4\pm\delta}$. Comparisons between x = 0.17 samples subjected to either ion-irradiation or oxygenation demonstrate that changing the oxygen content has two separable effects: 1) a doping effect similar to that of cerium, and 2) a disorder effect. These results are consistent with prior speculations that apical oxygen removal is necessary to achieve superconductivity in this compound.Comment: 5 pages, 5 figure

Entanglement-enhanced measurement of a completely unknown phase

The high-precision interferometric measurement of an unknown phase is the basis for metrology in many areas of science and technology. Quantum entanglement provides an increase in sensitivity, but present techniques have only surpassed the limits of classical interferometry for the measurement of small variations about a known phase. Here we introduce a technique that combines entangled states with an adaptive algorithm to precisely estimate a completely unspecified phase, obtaining more information per photon that is possible classically. We use the technique to make the first ab initio entanglement-enhanced optical phase measurement. This approach will enable rapid, precise determination of unknown phase shifts using interferometry.Comment: 6 pages, 4 figure

The distribution of extremal points of Gaussian scalar fields

We consider the signed density of the extremal points of (two-dimensional) scalar fields with a Gaussian distribution. We assign a positive unit charge to the maxima and minima of the function and a negative one to its saddles. At first, we compute the average density for a field in half-space with Dirichlet boundary conditions. Then we calculate the charge-charge correlation function (without boundary). We apply the general results to random waves and random surfaces. Furthermore, we find a generating functional for the two-point function. Its Legendre transform is the integral over the scalar curvature of a 4-dimensional Riemannian manifold.Comment: 22 pages, 8 figures, corrected published versio