State Transfer and Spin Measurement

We present a Hamiltonian that can be used for amplifying the signal from a quantum state, enabling the measurement of a macroscopic observable to determine the state of a single spin. We prove a general mapping between this Hamiltonian and an exchange Hamiltonian for arbitrary coupling strengths and local magnetic fields. This facilitates the use of existing schemes for perfect state transfer to give perfect amplification. We further prove a link between the evolution of this fixed Hamiltonian and classical Cellular Automata, thereby unifying previous approaches to this amplification task. Finally, we show how to use the new Hamiltonian for perfect state transfer in the, to date, unique scenario where total spin is not conserved during the evolution, and demonstrate that this yields a significantly different response in the presence of decoherence.Comment: 4 pages, 2 figure

A Witness of Multipartite Entanglement Strata

We describe an entanglement witness for $N$-qubit mixed states based on the properties of $N$-point correlation functions. Depending on the degree of violation, this witness can guarantee that no more than $M$ qubits are separable from the rest of the state for any $M\leq N$, or that there is some genuine $M$-party or greater multipartite entanglement present. We illustrate the use our criterion by investigating the existence of entanglement in thermal stabilizer states, where we demonstrate that the witness is capable of witnessing bound-entangled states. Intriguingly, this entanglement can be shown to persist in the thermodynamic limit at arbitrary temperature.Comment: 7 pages, 1 figur

Continuity of symplectically adjoint maps and the algebraic structure of Hadamard vacuum representations for quantum fields on curved spacetime

We derive for a pair of operators on a symplectic space which are adjoints of each other with respect to the symplectic form (that is, they are sympletically adjoint) that, if they are bounded for some scalar product on the symplectic space dominating the symplectic form, then they are bounded with respect to a one-parametric family of scalar products canonically associated with the initially given one, among them being its ``purification''. As a typical example we consider a scalar field on a globally hyperbolic spacetime governed by the Klein-Gordon equation; the classical system is described by a symplectic space and the temporal evolution by symplectomorphisms (which are symplectically adjoint to their inverses). A natural scalar product is that inducing the classical energy norm, and an application of the above result yields that its ``purification'' induces on the one-particle space of the quantized system a topology which coincides with that given by the two-point functions of quasifree Hadamard states. These findings will be shown to lead to new results concerning the structure of the local (von Neumann) observable-algebras in representations of quasifree Hadamard states of the Klein-Gordon field in an arbitrary globally hyperbolic spacetime, such as local definiteness, local primarity and Haag-duality (and also split- and type III_1-properties). A brief review of this circle of notions, as well as of properties of Hadamard states, forms part of the article.Comment: 42 pages, LaTeX. The Def. 3.3 was incomplete and this has been corrected. Several misprints have been removed. All results and proofs remain unchange

Natural three-qubit interactions in one-way quantum computing

We address the effects of natural three-qubit interactions on the computational power of one-way quantum computation (\QC). A benefit of using more sophisticated entanglement structures is the ability to construct compact and economic simulations of quantum algorithms with limited resources. We show that the features of our study are embodied by suitably prepared optical lattices, where effective three-spin interactions have been theoretically demonstrated. We use this to provide a compact construction for the Toffoli gate. Information flow and two-qubit interactions are also outlined, together with a brief analysis of relevant sources of imperfection.Comment: 4 pages, 3 figures, RevTeX

Using ForeCAT Deflections and Rotations to Constrain the Early Evolution of CMEs

To accurately predict the space weather effects of coronal mass ejection (CME) impacts at Earth one must know if and when a CME will impact Earth, and the CME parameters upon impact. Kay et al. (2015b) presents Forecasting a CME's Altered Trajectory (ForeCAT), a model for CME deflections based on the magnetic forces from the background solar magnetic field. Knowing the deflection and rotation of a CME enables prediction of Earth impacts, and the CME orientation upon impact. We first reconstruct the positions of the 2008 April 10 and the 2012 July 12 CMEs from the observations. The first of these CMEs exhibits significant deflection and rotation (34 degrees deflection and 58 degrees rotation), while the second shows almost no deflection or rotation (<3 degrees each). Using ForeCAT, we explore a range of initial parameters, such as the CME location and size, and find parameters that can successfully reproduce the behavior for each CME. Additionally, since the deflection depends strongly on the behavior of a CME in the low corona (Kay et al. (2015a, 2015b)), we are able to constrain the expansion and propagation of these CMEs in the low corona.Comment: accepted in Ap

Using foreCAT deflections and rotations to constrain the early evolution of CMEs

To accurately predict the space weather effects of the impacts of coronal mass ejection (CME) at Earth one must know if and when a CME will impact Earth and the CME parameters upon impact. In 2015 Kay et al. presented Forecasting a CME's Altered Trajectory (ForeCAT), a model for CME deflections based on the magnetic forces from the background solar magnetic field. Knowing the deflection and rotation of a CME enables prediction of Earth impacts and the orientation of the CME upon impact. We first reconstruct the positions of the 2010 April 8 and the 2012 July 12 CMEs from the observations. The first of these CMEs exhibits significant deflection and rotation (34° deflection and 58° rotation), while the second shows almost no deflection or rotation (<3° each). Using ForeCAT, we explore a range of initial parameters, such as the CME's location and size, and find parameters that can successfully reproduce the behavior for each CME. Additionally, since the deflection depends strongly on the behavior of a CME in the low corona, we are able to constrain the expansion and propagation of these CMEs in the low corona.C.K.'s research was supported by an appointment to the NASA Postdoctoral Program at NASA GSFC, administered by the Universities Space Research Association under contract with NASA. A.V. acknowledges support from JHU/APL. R.C.C. acknowledges the support of NASA contract S-136361-Y to NRL. The SECCHI data are produced by an international consortium of the NRL, LMSAL, and NASA GSFC (USA), RAL and Univ. of Birmingham (UK), MPS (Germany), CSL (Belgium), IOTA and IAS (France). (JHU/APL; S-136361-Y - NASA)Published versio

A comprehensive survey of hearing questionnaires: how many are there, what do they measure, and how have they been validated?

The self-report questionnaire is a popular tool for measuring outcomes in trials of interventions for hearing impairment. Many have been designed over the last fifty years, and there is no single standard questionnaire that is widely accepted and used. We felt it would be a valuable resource to have a comprehensive collection of all adult hearing-loss questionnaires (excluding those wholly devoted to tinnitus, children, or cochlear implants) and to survey their degree of validation. We collated copies of every published hearing difficulty questionnaire that we could find. The search was primarily done by iterative reference searching. Questionnaire topics were obtained by mapping the text of each questionnaire onto a set of categories; reports of validation methods were taken from the primary paper(s) on each questionnaire. In total we found 139 hearing-specific questionnaires (though many others were found that were primarily about something else). Though not formally systematic, we believe that we have included every questionnaire that is important, most of those of some notice, and a fair fraction of those obscure. We classified 111 as “primary” and the remaining 28 as “contractions”, being shortened versions of a primary without any new questions. In total, there were 3618 items across all the primary questionnaires. The median number of items per questionnaire was 20; the maximum was 158. Across all items, about one third were concerned with the person’s own hearing, another third with the repercussions of it, and about a quarter with hearing aids. There was a wide range in validation methods, from only using items chosen statistically from wider pools and with formal validation against independent measures of clinical outcomes, to just reporting a correlation with an audiogram measure of hearing loss. The “state of play” of the field of hearing questionnaires will be discussed

Quantum Communication in Spin Systems With Long-Range Interactions

We calculate the fidelity of transmission of a single qubit between distant sites on semi-infinite and finite chains of spins coupled via the magnetic dipole interaction. We show that such systems often perform better than their Heisenberg nearest-neighbour coupled counterparts, and that fidelities closely approaching unity can be attained between the ends of finite chains without any special engineering of the system, although state transfer becomes slow in long chains. We discuss possible optimization methods, and find that, for any length, the best compromise between the quality and the speed of the communication is obtained in a nearly uniform chain of 4 spins.Comment: 15 pages, 8 eps figures, updated references, corrected text and corrected figs. 1, 4 and

Adaptive time-stepping for incompressible flow. Part II: Navier-Stokes equations

We outline a new class of robust and efficient methods for solving the Navier- Stokes equations. We describe a general solution strategy that has two basic building blocks: an implicit time integrator using a stabilized trapezoid rule with an explicit Adams-Bashforth method for error control, and a robust Krylov subspace solver for the spatially discretized system. We present numerical experiments illustrating the potential of our approach. © 2010 Society for Industrial and Applied Mathematics

Perfect State Transfer: Beyond Nearest-Neighbor Couplings

In this paper we build on the ideas presented in previous works for perfectly transferring a quantum state between opposite ends of a spin chain using a fixed Hamiltonian. While all previous studies have concentrated on nearest-neighbor couplings, we demonstrate how to incorporate additional terms in the Hamiltonian by solving an Inverse Eigenvalue Problem. We also explore issues relating to the choice of the eigenvalue spectrum of the Hamiltonian, such as the tolerance to errors and the rate of information transfer.Comment: 8 pages, 2 figures. Reorganised, more detailed derivations provided and section on rate of information transfer adde