Non-adaptive Measurement-based Quantum Computation and Multi-party Bell Inequalities

Quantum correlations exhibit behaviour that cannot be resolved with a local hidden variable picture of the world. In quantum information, they are also used as resources for information processing tasks, such as Measurement-based Quantum Computation (MQC). In MQC, universal quantum computation can be achieved via adaptive measurements on a suitable entangled resource state. In this paper, we look at a version of MQC in which we remove the adaptivity of measurements and aim to understand what computational abilities still remain in the resource. We show that there are explicit connections between this model of computation and the question of non-classicality in quantum correlations. We demonstrate this by focussing on deterministic computation of Boolean functions, in which natural generalisations of the Greenberger-Horne-Zeilinger (GHZ) paradox emerge; we then explore probabilistic computation, via which multipartite Bell Inequalities can be defined. We use this correspondence to define families of multi-party Bell inequalities, which we show to have a number of interesting contrasting properties.Comment: 13 pages, 4 figures, final version accepted for publicatio

Constructions of diagonal quartic and sextic surfaces with infinitely many rational points

In this note we construct several infinite families of diagonal quartic surfaces \begin{equation*} ax^4+by^4+cz^4+dw^4=0, \end{equation*} where $a,b,c,d\in\Z\setminus\{0\}$ with infinitely many rational points and satisfying the condition $abcd\neq \square$. In particular, we present an infinite family of diagonal quartic surfaces defined over \Q with Picard number equal to one and possessing infinitely many rational points. Further, we present some sextic surfaces of type $ax^6+by^6+cz^6+dw^i=0$, $i=2$, $3$, or $6$, with infinitely many rational points.Comment: revised version will appear in International Journal of Number Theor

Outcome Independence of Entanglement in One-Way Computation

We show that the various intermediate states appearing in the process of one-way computation at a given step of measurement are all equivalent modulo local unitary transformations. This implies, in particular, that all those intermediate states share the same entanglement irrespective of the measurement outcomes, indicating that the process of one-way computation is essentially unique with respect to local quantum operations.Comment: 6 pages, 4 figure

Surface-acoustic-wave-driven luminescence from a lateral p-n junction

The authors report surface-acoustic-wave-driven luminescence from a lateral p-n junction formed by molecular beam epitaxy regrowth of a modulation doped GaAs/AlGaAs quantum well on a patterned GaAs substrate. Surface-acoustic-wave-driven transport is demonstrated by peaks in the electrical current and light emission from the GaAs quantum well at the resonant frequency of the transducer. This type of junction offers high carrier mobility and scalability. The demonstration of surface-acoustic-wave luminescence is a significant step towards single-photon applications in quantum computation and quantum cryptography.Comment: 4 pages, 3 figure

A practical scheme for quantum computation with any two-qubit entangling gate

Which gates are universal for quantum computation? Although it is well known that certain gates on two-level quantum systems (qubits), such as the controlled-not (CNOT), are universal when assisted by arbitrary one-qubit gates, it has only recently become clear precisely what class of two-qubit gates is universal in this sense. Here we present an elementary proof that any entangling two-qubit gate is universal for quantum computation, when assisted by one-qubit gates. A proof of this important result for systems of arbitrary finite dimension has been provided by J. L. and R. Brylinski [arXiv:quant-ph/0108062, 2001]; however, their proof relies upon a long argument using advanced mathematics. In contrast, our proof provides a simple constructive procedure which is close to optimal and experimentally practical [C. M. Dawson and A. Gilchrist, online implementation of the procedure described herein (2002), http://www.physics.uq.edu.au/gqc/].Comment: 3 pages, online implementation of procedure described can be found at http://www.physics.uq.edu.au/gqc

Large Deviation Bounds for k-designs

We present a technique for derandomising large deviation bounds of functions on the unitary group. We replace the Haar distribution with a pseudo-random distribution, a k-design. k-designs have the first k moments equal to those of the Haar distribution. The advantage of this is that (approximate) k-designs can be implemented efficiently, whereas Haar random unitaries cannot. We find large deviation bounds for unitaries chosen from a k-design and then illustrate this general technique with three applications. We first show that the von Neumann entropy of a pseudo-random state is almost maximal. Then we show that, if the dynamics of the universe produces a k-design, then suitably sized subsystems will be in the canonical state, as predicted by statistical mechanics. Finally we show that pseudo-random states are useless for measurement based quantum computation.Comment: 20 page

The Dynamic Oval Pupil

The dynamic oval pupil is defined and its distinction from corectopia, as well as their different clinical significance is proposed. A literature search for instances presenting this condition yielded only 20 such cases with enough clinical data. A review of these cases allows us to draw some tentative conclusions regarding the most likely anatomical location for its causative lesion and the pathophysiological mechanism responsible for its occurrence

Whole body and splanchnic amino acid metabolism in sheep during an acute endotoxin challenge

Acknowledgements The expertise of A. Graham Calder and Susan Anderson for the various stable isotope analyses is gratefully recognised. Ngaire Dennison is also thanked for her surgical expertise with the trans-splanchnic tissue catheter preparations. This study was supported by funds provided to the Rowett Institute of Nutrition and Health, University of Aberdeen and Biomathematics and Statistics Scotland by the Rural and Environment Science and Analytical Services Division of the Scottish Government. S. O. H. was a recipient of a FoRST (NZ) award to study abroad.Peer reviewedPostprin

Evidence That Pupil Size and Reactivity Are Determined More by Your Parents Than by Your Environment

Purpose: A classic twin study to evaluate the relative contributions of genetic and environmental factors to resting pupil size and reactivity. Methods: Pupillometry was performed on 326 female twins (mean age 64 years) from the TwinsUK Adult Twin Registry, assessing resting pupil diameter in darkness and increasing levels of ambient light, alongside dynamic pupillary characteristics. Maximum-likelihood structural equation models estimated the proportion of trait variance attributable to genetic factors. Results: Mean (SD) pupil diameter in darkness was 5.29 mm (0.81), decreasing to 3.24 mm (0.57) in bright light. Pupil light reaction (PLR) had a mean (SD) amplitude of 1.38 mm (0.27) and latency of 250.34 milliseconds (28.58). Pupil size and PLR were not associated with iris colour, intraocular pressure or refractive error, but were associated with age (diameter beta = -0.02, p = 0.016, constriction amplitude beta = -0.01, p < 0.001, velocity beta = 0.03, p < 0.001, and latency beta = 0.98, p < 0.001). In darkness the resting pupil size showed a MZ intraclass correlation coefficient of 0.85, almost double that of DZ (0.44), suggesting strong additive genetic effects, with the most parsimonious model estimating a heritability of 86% [95% confidence interval (CI) 79-90%] with 14% (95% CI 10-21%) explained by unique environmental factors. PLR amplitude, latency and constriction velocity had estimated heritabilities of 69% (95% CI 54-79%), 40% (95% CI 21-56%), and 64% (95% CI 48-75%), respectively. Conclusion: Genetic effects are key determinants of resting pupil size and reactivity. Future studies to identify these genetic factors could improve our understanding of variation in pupil size and pupillary reactions in health and disease