Global consensus Monte Carlo

To conduct Bayesian inference with large data sets, it is often convenient or necessary to distribute the data across multiple machines. We consider a likelihood function expressed as a product of terms, each associated with a subset of the data. Inspired by global variable consensus optimisation, we introduce an instrumental hierarchical model associating auxiliary statistical parameters with each term, which are conditionally independent given the top-level parameters. One of these top-level parameters controls the unconditional strength of association between the auxiliary parameters. This model leads to a distributed MCMC algorithm on an extended state space yielding approximations of posterior expectations. A trade-off between computational tractability and fidelity to the original model can be controlled by changing the association strength in the instrumental model. We further propose the use of a SMC sampler with a sequence of association strengths, allowing both the automatic determination of appropriate strengths and for a bias correction technique to be applied. In contrast to similar distributed Monte Carlo algorithms, this approach requires few distributional assumptions. The performance of the algorithms is illustrated with a number of simulated examples

Entanglement of Pure Two-Mode Gaussian States

The entanglement of general pure Gaussian two-mode states is examined in terms of the coefficients of the quadrature components of the wavefunction. The entanglement criterion and the entanglement of formation are directly evaluated as a function of these coefficients, without the need for deriving local unitary transformations. These reproduce the results of other methods for the special case of symmetric pure states which employ a relation between squeezed states and Einstein-Podolsky-Rosen correlations. The modification of the quadrature coefficients and the corresponding entanglement due to application of various optical elements is also derived.Comment: 12 page

Global consensus Monte Carlo

To conduct Bayesian inference with large data sets, it is often convenient or necessary to distribute the data across multiple machines. We consider a likelihood function expressed as a product of terms, each associated with a subset of the data. Inspired by global variable consensus optimisation, we introduce an instrumental hierarchical model associating auxiliary statistical parameters with each term, which are conditionally independent given the top-level parameters. One of these top-level parameters controls the unconditional strength of association between the auxiliary parameters. This model leads to a distributed MCMC algorithm on an extended state space yielding approximations of posterior expectations. A trade-off between computational tractability and fidelity to the original model can be controlled by changing the association strength in the instrumental model. We further propose the use of a SMC sampler with a sequence of association strengths, allowing both the automatic determination of appropriate strengths and for a bias correction technique to be applied. In contrast to similar distributed Monte Carlo algorithms, this approach requires few distributional assumptions. The performance of the algorithms is illustrated with a number of simulated examples

Entanglement of a Double Dot with a Quantum Point Contact

Entanglement between particle and detector is known to be inherent in the measurement process. Gurvitz recently analyzed the coupling of an electron in a double dot (DD) to a quantum point contact (QPC) detector. In this paper we examine the dynamics of entanglement that result between the DD and QPC. The rate of entanglement is optimized as a function of coupling when the electron is initially in one of the dots. It decreases asymptotically towards zero with increased coupling. The opposite behavior is observed when the DD is initially in a superposition: the rate of entanglement increases unboundedly as the coupling is increased. The possibility that there are conditions for which measurement occurs versus entanglement is considered

Prospective memory functioning among ecstasy/polydrug users: evidence from the Cambridge Prospective Memory Test (CAMPROMPT)

Rationale: Prospective memory (PM) deficits in recreational drug users have been documented in recent years. However, the assessment of PM has largely been restricted to self-reported measures that fail to capture the distinction between event-based and time-based PM. The aim of the present study is to address this limitation. Objectives: Extending our previous research, we augmented the range laboratory measures of PM by employing the CAMPROMPT test battery to investigate the impact of illicit drug use on prospective remembering in a sample of cannabis only, ecstasy/polydrug and non-users of illicit drugs, separating event and time-based PM performance. We also administered measures of executive function and retrospective memory in order to establish whether ecstasy/polydrug deficits in PM were mediated by group differences in these processes. Results: Ecstasy/polydrug users performed significantly worse on both event and time-based prospective memory tasks in comparison to both cannabis only and non-user groups. Furthermore, it was found that across the whole sample, better retrospective memory and executive functioning was associated with superior PM performance. Nevertheless, this association did not mediate the drug-related effects that were observed. Consistent with our previous study, recreational use of cocaine was linked to PM deficits. Conclusions: PM deficits have again been found among ecstasy/polydrug users, which appear to be unrelated to group differences in executive function and retrospective memory. However, the possibility that these are attributable to cocaine use cannot be excluded

Structure of the Phase in Pure Two-Mode Gaussian States

The two-mode relative phase associated with Gaussian states plays an important role in quantum information processes in optical, atomic and electronic systems. In this work, the origin and structure of the two-mode relative phase in pure Gaussian states is studied in terms of its dependences on the quadratures of the modes. This is done by constructing local canonical transformations to an associated two-mode squeezed state. The results are illustrated by studying the time dependence of the phase under a nonlocal unitary model evolution containing correlations between the modes. In a more general context, this approach may allow the two-mode phase to be studied in situations sensitive to different physical parameters within experimental configurations relevant to quantum information processing tasks

Gate voltage dependent Rashba spin splitting in hole transverse magnetic focussing

Magnetic focussing of charge carriers in two-dimensional systems provides a solid state version of a mass spectrometer. In the presence of a spin-orbit interaction, the first focussing peak splits into two spin dependent peaks, allowing focussing to be used to measure spin polarisation and the strength of the spin-orbit interaction. In hole systems, the k^3 dependence of the Rashba spin-orbit term allows the spatial separation of spins to be changed in-situ using a voltage applied to an overall top gate. Here we demonstrate that this can be used to control the splitting of the magnetic focussing peaks. Additionally, we compare the focussing peak splitting to that predicted by Shubnikov-de Haas oscillations and k.p bandstructure calculations. We find that the focussing peak splitting is consistently larger than expected, suggesting further work is needed on understanding spin dependent magnetic focussing

Surface shape resonances in lamellar metallic gratings

The specular reflectivity of lamellar gratings of gold with grooves 0.5 microns wide separated by a distance of 3.5 microns was measured on the 2000 cm$^{-1}$ - 7000 cm$^{-1}$ spectral range for p-polarized light. For the first time, experimental evidence of the excitation of electromagnetic surface shape resonances for optical frequencies is given. In these resonances the electric field is highly localized inside the grooves and is almost zero in all other regions. For grooves of depth equal to 0.6 microns, we have analyzed one of these modes whose wavelength (3.3 microns) is much greater than the lateral dimension of the grooves.Comment: 4 pages (LaTex), 5 postscript figures, to be published in Physical Review Letter

Spin polarisation and spin dependent scattering of holes in transverse magnetic focussing

In 2D systems with a spin-orbit interaction, magnetic focussing can be used to create a spatial separation of particles with different spin. Here we measure hole magnetic focussing for two different magnitudes of the Rashba spin-orbit interaction. We find that when the Rashba spin-orbit magnitude is large there is significant attenuation of one of the focussing peaks, which is conventionally associated with a change in the spin polarisation. We instead show that in hole systems with a $k^3$ spin-orbit interaction, this peak suppression is due to a change in the scattering of one spin state, not a change in spin polarisation. We also show that the change in scattering length extracted from magnetic focussing is consistent with results obtained from measurements of Shubnikov-de Haas oscillations. This result suggests that scattering must be considered when relating focussing peak amplitude to spin polarisation in hole system