Criteria for generalized macroscopic and mesoscopic quantum coherence

We consider macroscopic, mesoscopic and "S-scopic" quantum superpositions of eigenstates of an observable, and develop some signatures for their existence. We define the extent, or size $S$ of a superposition, with respect to an observable \hat{x}, as being the range of outcomes of \hat{x} predicted by that superposition. Such superpositions are referred to as generalized $S$-scopic superpositions to distinguish them from the extreme superpositions that superpose only the two states that have a difference $S$ in their prediction for the observable. We also consider generalized $S$-scopic superpositions of coherent states. We explore the constraints that are placed on the statistics if we suppose a system to be described by mixtures of superpositions that are restricted in size. In this way we arrive at experimental criteria that are sufficient to deduce the existence of a generalized $S$-scopic superposition. The signatures developed are useful where one is able to demonstrate a degree of squeezing. We also discuss how the signatures enable a new type of Einstein-Podolsky-Rosen gedanken experiment.Comment: 15 pages, accepted for publication in Phys. Rev.

Experimental criteria for steering and the Einstein-Podolsky-Rosen paradox

We formally link the concept of steering (a concept created by Schrodinger but only recently formalised by Wiseman, Jones and Doherty [Phys. Rev. Lett. 98, 140402 (2007)] and the criteria for demonstrations of Einstein-Podolsky-Rosen (EPR) paradox introduced by Reid [Phys. Rev. A, 40, 913 (1989)]. We develop a general theory of experimental EPR-steering criteria, derive a number of criteria applicable to discrete as well as continuous-variables observables, and study their efficacy in detecting that form of nonlocality in some classes of quantum states. We show that previous versions of EPR-type criteria can be rederived within this formalism, thus unifying these efforts from a modern quantum-information perspective and clarifying their conceptual and formal origin. The theory follows in close analogy with criteria for other forms of quantum nonlocality (Bell-nonlocality, entanglement), and because it is a hybrid of those two, it may lead to insights into the relationship between the different forms of nonlocality and the criteria that are able to detect them.Comment: Changed title, updated references, minor corrections, added journal-ref and DO

Unified criteria for multipartite quantum nonlocality

Wiseman and co-workers (Phys. Rev. Lett. 98, 140402, 2007) proposed a distinction between the nonlocality classes of Bell's nonlocality, steering and entanglement based on whether or not an overseer trusts each party in a bipartite scenario where they are asked to demonstrate entanglement. Here we extend that concept to the multipartite case and derive inequalities that progressively test for those classes of nonlocality, with different thresholds for each level. This framework includes the three classes of nonlocality above in special cases and introduces a family of others.Comment: V2: corrected image display; V3: substantial changes including new proofs, arguments, and result

Symmetries of Differential Equations via Cartan's Method of Equivalence

We formulate a method of computing invariant 1-forms and structure equations of symmetry pseudo-groups of differential equations based on Cartan's method of equivalence and the moving coframe method introduced by Fels and Olver. Our apparoach does not require a preliminary computation of infinitesimal defining systems, their analysis and integration, and uses differentiation and linear algebra operations only. Examples of its applications are given.Comment: 15 pages, LaTeX 2.0

The not-so-massive black hole in the microquasar GRS1915+105

We present a new dynamical study of the black hole X-ray transient GRS1915+105 making use of near-infrared spectroscopy obtained with X-shooter at the VLT. We detect a large number of donor star absorption features across a wide range of wavelengths spanning the H and K bands. Our 24 epochs covering a baseline of over 1 year permit us to determine a new binary ephemeris including a refined orbital period of P=33.85 +/- 0.16 d. The donor star radial velocity curves deliver a significantly improved determination of the donor semi-amplitude which is both accurate (K_2=126 +/- 1 km/s) and robust against choice of donor star template and spectral features used. We furthermore constrain the donor star's rotational broadening to vsini=21 +/-4 km/s, delivering a binary mass ratio of q=0.042 +/- 0.024. If we combine these new constraints with distance and inclination estimates derived from modelling the radio emission, a black hole mass of M_BH=10.1 +/- 0.6 M_sun is inferred, paired with an evolved mass donor of M_2=0.47 +/- 0.27 M_sun. Our analysis suggests a more typical black hole mass for GRS1915+105 rather than the unusually high values derived in the pioneering dynamical study by Greiner et al. (2001). Our data demonstrate that high-resolution infrared spectroscopy of obscured accreting binaries can deliver dynamical mass determinations with a precision on par with optical studies

On the Computation of Power in Volume Integral Equation Formulations

We present simple and stable formulas for computing power (including absorbed/radiated, scattered and extinction power) in current-based volume integral equation formulations. The proposed formulas are given in terms of vector-matrix-vector products of quantities found solely in the associated linear system. In addition to their efficiency, the derived expressions can guarantee the positivity of the computed power. We also discuss the application of Poynting's theorem for the case of sources immersed in dissipative materials. The formulas are validated against results obtained both with analytical and numerical methods for scattering and radiation benchmark cases

Bell inequalities for continuous-variable correlations

We derive a new class of correlation Bell-type inequalities. The inequalities are valid for any number of outcomes of two observables per each of n parties, including continuous and unbounded observables. We show that there are no first-moment correlation Bell inequalities for that scenario, but such inequalities can be found if one considers at least second moments. The derivation stems from a simple variance inequality by setting local commutators to zero. We show that above a constant detector efficiency threshold, the continuous variable Bell violation can survive even in the macroscopic limit of large n. This method can be used to derive other well-known Bell inequalities, shedding new light on the importance of non-commutativity for violations of local realism.Comment: 4 pages, 1 figure. v2: New results on detector efficiencies and macroscopic limit, new co-author, changed title and abstract, changed figure, added journal reference and DO

Brown dwarfs in the Hyades and beyond?

We have used both the Low-Resolution Imaging Spectrograph and the HIRES echelle spectrograph on the Keck telescopes to obtain spectra of twelve candidate members of the Hyades cluster identified by Leggett and Hawkins (1988, 1989). All of the objects are chromospherically-active, late-type M-dwarfs, with H$\alpha$ equivalent widths varying from 1 to 30\AA. Based on our measured radial velocities, the level of stellar activity and other spectroscopic features, only one of the twelve stars has properties consistent with cluster membership. We consider how this result affects estimates of the luminosity and mass function of the Hyades cluster. Five of the eleven field stars have weak K I 7665/7699\AA and CaH absorption as compared with M-dwarf standards of the same spectral type, suggesting a lower surface gravity. Two of these sources, LH0416+14 and LH0419+15, exhibit significant lithium 6708 \AA absorption. Based partly on parallax measurements by the US Naval Observatory (Harris et al, 1998), we identify all five as likely to be young, pre-main sequence objects in or near the Taurus-Auriga association at distances of between 150 and 250 parsecs. A comparison with theoretical models of pre-main sequence stars indicates masses of less than 0.05 M$_\odot$.Comment: to appear in AJ, January 1999; 34 pages, (Latex format), including 10 embedded postscript figures and two table

Isolation and characterisation of 17 microsatellite loci for the red-billed chough (Pyrrhocorax pyrrhocorax)

Peer reviewedPostprin

Violations of Bell Inequalities for Measurements with Macroscopic Uncertainties: What does it Mean to Violate Macroscopic Local Realism?

We suggest to test the premise of ``macroscopic local realism'' which is sufficient to derive Bell inequalities when measurements of photon number are only accurate to an uncertainty of order $n$ photons, where $n$ is macroscopic. Macroscopic local realism is only sufficient to imply, in the context of the original Einstein-Podolsky-Rosen argument, fuzzy ``elements of reality'' which have a macroscopic indeterminacy. We show therefore how the violation of local realism in the presence of macroscopic uncertainties implies the failure of ``macroscopic local realism''. Quantum states violating this macroscopic local realism are presented.Comment: 28 pages, 5 figures- new version is unchanged but tightened-20 pages, 5 figure