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

Two Qubits in the Dirac Representation

A general two qubit system expressed in terms of the complete set of unit and fifteen traceless, Hermitian Dirac matrices, is shown to exhibit novel features of this system. The well-known physical interpretations associated with the relativistic Dirac equation involving the symmetry operations of time-reversal T, charge conjugation C, parity P, and their products are reinterpreted here by examining their action on the basic Bell states. The transformation properties of the Bell basis states under these symmetry operations also reveal that C is the only operator that does not mix the Bell states whereas all others do. In a similar fashion, expressing the various logic gates introduced in the subject of quantum computers in terms of the Dirac matrices shows for example, that the NOT gate is related to the product of time-reversal and parity operators.Comment: 11 page

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

Categorizing click trains to increase taxonomic precision in echolocation click loggers

L.R. and K.J.P. were supported by Marine Scotland Science and the Marine Alliance for Science and Technology for Scotland (MASTS) pooling initiative and their support is gratefully acknowledged. MASTS is funded by the Scottish Funding Council (grant reference HR09011) and contributing institutions.Passive acoustic monitoring is an efficient way to study acoustically active animals but species identification remains a major challenge. C-PODs are popular logging devices that automatically detect odontocete echolocation clicks. However, the accompanying analysis software does not distinguish between delphinid species. Click train features logged by C-PODs were compared to frequency spectra from adjacently deployed continuous recorders. A generalized additive model was then used to categorize C-POD click trains into three groups: broadband click trains, produced by bottlenose dolphin (Tursiops truncatus) or common dolphin (Delphinus delphis), frequency-banded click trains, produced by Risso's (Grampus griseus) or white beaked dolphins (Lagenorhynchus albirostris), and unknown click trains. Incorrect categorization rates for broadband and frequency banded clicks were 0.02 (SD 0.01), but only 30% of the click trains met the categorization threshold. To increase the proportion of categorized click trains, model predictions were pooled within acoustic encounters and a likelihood ratio threshold was used to categorize encounters. This increased the proportion of the click trains meeting either the broadband or frequency banded categorization threshold to 98%. Predicted species distribution at the 30 study sites matched well to visual sighting records from the region.PostprintPeer reviewe

Edge state transmission, duality relation and its implication to measurements

The duality in the Chalker-Coddington network model is examined. We are able to write down a duality relation for the edge state transmission coefficient, but only for a specific symmetric Hall geometry. Looking for broader implication of the duality, we calculate the transmission coefficient $T$ in terms of the conductivity $\sigma_{xx}$ and $\sigma_{xy}$ in the diffusive limit. The edge state scattering problem is reduced to solving the diffusion equation with two boundary conditions $(\partial_y-(\sigma_{xy})/(\sigma_{xx})\partial_x)\phi=0$ and $[\partial_x+(\sigma_{xy}-\sigma_{xy}^{lead})/(\sigma_{xx}) \partial_y]\phi=0$. We find that the resistances in the geometry considered are not necessarily measures of the resistivity and $\rho_{xx}=L/W R/T h/e^2$ ($R=1-T$) holds only when $\rho_{xy}$ is quantized. We conclude that duality alone is not sufficient to explain the experimental findings of Shahar et al and that Landauer-Buttiker argument does not render the additional condition, contrary to previous expectation.Comment: 16 pages, 3 figures, to appear in Phys. Rev.

In situ micro gas tungsten constricted arc welding of ultra-thin walled 2.275 mm outer diameter grade 2 commercially pure titanium tubing

Ultra-thin walled cooling tubes for heat exchangers and condenser units have applications in multiple high-value manufacturing industries. Grade 2 commercially pure titanium (CP-2 Ti) requires far less mass to achieve the same mass flow handling abilities as stainless steel tubing yet it is more challenging to join, particularly at wall thicknesses less than 500 μm (termed ultra-thin walled tube). This paper presents a single-pass joinery method that produces reliable welds on 2.275 mm outer diameter (OD), 160 ± 10 μm wall thickness tubing with a service life of 20 of more years. This is achieved through an automated orbital gas tungsten constricted arc welding (GTCAW) process incorporating enveloping low-mass sleeves used in tandem with a buttressing internal gas pressure to support the molten metal and maintain consistent internal diameter inside the tube. The industrial applicability is demonstrated through the production of a 1:1 scale mock-up of a fixed geometry CO2 cooling circuit for a next-generation particle detector. The tensile strengths of the joints, 403.8 ± 4.2 MPa, exceed the tensile strength of the parent CP-2 Ti

Commensurability oscillations in the rf conductivity of unidirectional lateral superlattices: measurement of anisotropic conductivity by coplanar waveguide

We have measured the rf magnetoconductivity of unidirectional lateral superlattices (ULSLs) by detecting the attenuation of microwave through a coplanar waveguide placed on the surface. ULSL samples with the principal axis of the modulation perpendicular (S_perp) and parallel (S_||) to the microwave electric field are examined. For low microwave power, we observe expected anisotropic behavior of the commensurability oscillations (CO), with CO in samples S_perp and S_|| dominated by the diffusion and the collisional contributions, respectively. Amplitude modulation of the Shubnikov-de Haas oscillations is observed to be more prominent in sample S_||. The difference between the two samples is washed out with the increase of the microwave power, letting the diffusion contribution govern the CO in both samples. The failure of the intended directional selectivity in the conductivity measured with high microwave power is interpreted in terms of large-angle electron-phonon scattering.Comment: 8 pages, 5 figure

Computational and Mathematical Modelling of the EGF Receptor System

This chapter gives an overview of computational and mathematical modelling of the EGF receptor system. It begins with a survey of motivations for producing such models, then describes the main approaches that are taken to carrying out such modelling, viz. differential equations and individual-based modelling. Finally, a number of projects that applying modelling and simulation techniques to various aspects of the EGF receptor system are described

Individual, unit and vocal clan level identity cues in sperm whale codas

Fieldwork was supported by Discovery and Equipment grants to H.W. from the Natural Sciences and Engineering Research Council of Canada (NSERC) and the Whale and Dolphin Conservation Society. S.G. and L.R. were supported by the Marine Alliance for Science and Technology for Scotland (MASTs) pooling initiative and their support is gratefully acknowledged. MASTs is funded by the Scottish Funding Council (grant reference HR09011) and contributing institutions. S.G. was also supported by an NSERC Postgraduate Scholarship (PGS-M), an NSERC Canadian Graduate Scholarship (CGS-D), the Izaak Killam Memorial Scholarship, the Patrick F. Lett Fund, the Dalhousie’s Presidents Award, and an FNU fellowship for the Danish Council for Independent Research from the Ministry of Higher Education and Science supplemented by a Sapere Aude Research Talent Award.The ‘social complexity hypothesis’ suggests that complex social structure is a driver of diversity in animal communication systems. Sperm whales have a hierarchically structured society in which the largest affiliative structures, the vocal clans, are marked on ocean-basin scales by culturally transmitted dialects of acoustic signals known as ‘codas’. We examined variation in coda repertoires among both individual whales and social units—the basic element of sperm whale society—using data from nine Caribbean social units across six years. Codas were assigned to individuals using photo-identification and acoustic size measurement, and we calculated similarity between repertoires using both continuous and categorical methods. We identified 21 coda types. Two of those (‘1+1+3’ and ‘5R1’) made up 65% of the codas recorded, were shared across all units and have dominated repertoires in this population for at least 30 years. Individuals appear to differ in the way they produce ‘5R1’ but not ‘1+1+3’ coda. Units use distinct 4-click coda types which contribute to making unit repertoires distinctive. Our results support the social complexity hypothesis in a marine species as different patterns of variation between coda types suggest divergent functions, perhaps representing selection for identity signals at several levels of social structure.Publisher PDFPeer reviewe