A multi-photon Stokes-parameter invariant for entangled states

We consider the Minkowskian norm of the n-photon Stokes tensor, a scalar invariant under the group realized by the transformations of stochastic local quantum operations and classical communications (SLOCC). This invariant is offered as a candidate entanglement measure for n-qubit states and discussed in relation to measures of quantum state entanglement for certain important classes of two-qubit and three-qubit systems. This invariant can be directly estimated via a quantum network, obviating the need to perform laborious quantum state tomography. We also show that this invariant directly captures the extent of entanglement purification due to SLOCC filters.Comment: 9 pages, 0 figures, Accepted for publication in Physical Review

Feedback Control of an Exoskeleton for Paraplegics: Toward Robustly Stable Hands-free Dynamic Walking

This manuscript presents control of a high-DOF fully actuated lower-limb exoskeleton for paraplegic individuals. The key novelty is the ability for the user to walk without the use of crutches or other external means of stabilization. We harness the power of modern optimization techniques and supervised machine learning to develop a smooth feedback control policy that provides robust velocity regulation and perturbation rejection. Preliminary evaluation of the stability and robustness of the proposed approach is demonstrated through the Gazebo simulation environment. In addition, preliminary experimental results with (complete) paraplegic individuals are included for the previous version of the controller.Comment: Submitted to IEEE Control System Magazine. This version addresses reviewers' concerns about the robustness of the algorithm and the motivation for using such exoskeleton

Jones-matrix Formalism as a Representation of the Lorentz Group

It is shown that the two-by-two Jones-matrix formalism for polarization optics is a six-parameter two-by-two representation of the Lorentz group. The attenuation and phase-shift filters are represented respectively by the three-parameter rotation subgroup and the three-parameter Lorentz group for two spatial and one time dimensions. It is noted that the Lorentz group has another three-parameter subgroup which is like the two-dimensional Euclidean group. Possible optical filters having this Euclidean symmetry are discussed in detail. It is shown also that the Jones-matrix formalism can be extended to some of the non-orthogonal polarization coordinate systems within the framework of the Lorentz-group representation.Comment: RevTeX, 27 pages, no figures, to be published in J. Opt. Soc. Am.

Propagation of transverse intensity correlations of a two-photon state

The propagation of transverse spatial correlations of photon pairs through arbitrary first-order linear optical systems is studied experimentally and theoretically using the fractional Fourier transform. Highly-correlated photon pairs in an EPR-like state are produced by spontaneous parametric down-conversion and subject to optical fractional Fourier transform systems. It is shown that the joint detection probability can display either correlation, anti-correlation, or no correlation, depending on the sum of the orders $\alpha$ and $\beta$ of the transforms of the down-converted photons. We present analytical results for the propagation of the perfectly correlated EPR state, and numerical results for the propagation of the two-photon state produced from parametric down-conversion. We find good agreement between theory and experiment.Comment: 9 pages, 7 figures, to appear PR

Stokes Parameters as a Minkowskian Four-vector

It is noted that the Jones-matrix formalism for polarization optics is a six-parameter two-by-two representation of the Lorentz group. It is shown that the four independent Stokes parameters form a Minkowskian four-vector, just like the energy-momentum four-vector in special relativity. The optical filters are represented by four-by-four Lorentz-transformation matrices. This four-by-four formalism can deal with partial coherence described by the Stokes parameters. A four-by-four matrix formulation is given for decoherence effects on the Stokes parameters, and a possible experiment is proposed. It is shown also that this Lorentz-group formalism leads to optical filters with a symmetry property corresponding to that of two-dimensional Euclidean transformations.Comment: RevTeX, 22 pages, no figures, submitted to Phys. Rev.

X-ray Coherent diffraction interpreted through the fractional Fourier transform

Diffraction of coherent x-ray beams is treated through the Fractionnal Fourier transform. The transformation allow us to deal with coherent diffraction experiments from the Fresnel to the Fraunhofer regime. The analogy with the Huygens-Fresnel theory is first discussed and a generalized uncertainty principle is introduced.Comment: 7 pages, 8 figure

Identification and Dynamics of a Heparin-Binding Site in Hepatocyte Growth Factor †

Hepatocyte growth factor (HGF) is a heparin-binding, multipotent growth factor that transduces a wide range of biological signals, including mitogenesis, motogenesis, and morphogenesis. Heparin or closely related heparan sulfate has profound effects on HGF signaling. A heparin-binding site in the N-terminal (N) domain of HGF was proposed on the basis of the clustering of surface positive charges [Zhou, H., Mazzulla, M. J., Kaufman, J. D., Stahl, S. J., Wingfield, P. T., Rubin, J. S., Bottaro, D. P., and Byrd, R. A. (1998) Structure 6, 109-116]. In the present study, we confirmed this binding site in a heparin titration experiment monitored by nuclear magnetic resonance spectroscopy, and we estimated the apparent dissociation constant (K(d)) of the heparin-protein complex by NMR and fluorescence techniques. The primary heparin-binding site is composed of Lys60, Lys62, and Arg73, with additional contributions from the adjacent Arg76, Lys78, and N-terminal basic residues. The K(d) of binding is in the micromolar range. A heparin disaccharide analogue, sucrose octasulfate, binds with similar affinity to the N domain and to a naturally occurring HGF isoform, NK1, at nearly the same region as in heparin binding. (15)N relaxation data indicate structural flexibility on a microsecond-to-millisecond time scale around the primary binding site in the N domain. This flexibility appears to be dramatically reduced by ligand binding. On the basis of the NK1 crystal structure, we propose a model in which heparin binds to the two primary binding sites and the N-terminal regions of the N domains and stabilizes an NK1 dimer