Coherent Time Evolution and Boundary Conditions of Two-Photon Quantum Walks

Multi-photon quantum walks in integrated optics are an attractive controlled quantum system, that can mimic less readily accessible quantum systems and exhibit behavior that cannot in general be accurately replicated by classical light without an exponential overhead in resources. The ability to observe time evolution of such systems is important for characterising multi-particle quantum dynamics---notably this includes the effects of boundary conditions for walks in spaces of finite size. Here we demonstrate the coherent evolution of quantum walks of two indistinguishable photons using planar arrays of 21 evanescently coupled waveguides fabricated in silicon oxynitride technology. We compare three time evolutions, that follow closely a model assuming unitary evolution, corresponding to three different lengths of the array---in each case we observe quantum interference features that violate classical predictions. The longest array includes reflecting boundary conditions.Comment: 7 pages,7 figure

Quantum walks of correlated photon pairs in two-dimensional waveguide arrays

We demonstrate quantum walks of correlated photons in a 2D network of directly laser written waveguides coupled in a 'swiss cross' arrangement. The correlated detection events show high-visibility quantum interference and unique composite behaviour: strong correlation and independence of the quantum walkers, between and within the planes of the cross. Violations of a classically defined inequality, for photons injected in the same plane and in orthogonal planes, reveal non-classical behaviour in a non-planar structure.Comment: 5 pages, 5 figure

MHC-correlated preferences in diestrous female horses (Equus caballus).

Genes of the major histocompatibility complex (MHC) have been shown to influence communication in many vertebrates, possibly with context-specific MHC-correlated reactions. Here we test for MHC-linked female preferences in the polygynous horse (Equus caballus) by repeatedly exposing 19 mares to a group of seven sexually experienced stallions. Each mare was tested four times during two consecutive reproductive cycles, twice during estrus and twice during diestrus. Male plasma testosterone concentrations were determined from weekly blood samples, and equine leukocyte antigen (ELA) class I and II alleles were determined serologically at the end of the experiments. Perception of male attractiveness was strongly dependent on estrous cycle: mean preference scores did not correlate for mares in diestrus and estrus and varied more during estrus than during diestrus. We found elevated female interests for MHC-dissimilar stallions, but only during diestrus, not during estrus. Female preferences were not significantly predicted by mean male testosterone plasma concentrations. However, testosterone concentrations changed during the 11 weeks of the experiment. By the end of the experiment, average testosterone concentration was significantly correlated to the average number of MHC alleles the stallions shared with the mares. We conclude that the MHC affects female preferences for stallions, but non-MHC linked male characteristics can overshadow effects of the MHC during estrus

Algebraic geometric comparison of probability distributions

We propose a novel algebraic framework for treating probability distributions represented by their cumulants such as the mean and covariance matrix. As an example, we consider the unsupervised learning problem of finding the subspace on which several probability distributions agree. Instead of minimizing an objective function involving the estimated cumulants, we show that by treating the cumulants as elements of the polynomial ring we can directly solve the problem, at a lower computational cost and with higher accuracy. Moreover, the algebraic viewpoint on probability distributions allows us to invoke the theory of Algebraic Geometry, which we demonstrate in a compact proof for an identifiability criterion

Algebraic Geometric Comparison of Probability Distributions

We propose a novel algebraic framework for treating probability distributions represented by their cumulants such as the mean and covariance matrix. As an example, we consider the unsupervised learning problem of finding the subspace on which several probability distributions agree. Instead of minimizing an objective function involving the estimated cumulants, we show that by treating the cumulants as elements of the polynomial ring we can directly solve the problem, at a lower computational cost and with higher accuracy. Moreover, the algebraic viewpoint on probability distributions allows us to invoke the theory of Algebraic Geometry, which we demonstrate in a compact proof for an identifiability criterion

The nonrelativistic limit of the Majorana equation and its simulation in trapped ions

We analyze the Majorana equation in the limit where the particle is at rest. We show that several counterintuitive features, absent in the rest limit of the Dirac equation, do appear. Among them, Dirac-like positive energy solutions that turn into negative energy ones by free evolution, or nonstandard oscillations and interference between real and imaginary spinor components for complex solutions. We also study the ultrarelativistic limit, showing that the Majorana and Dirac equations mutually converge. Furthermore, we propose a physical implementation in trapped ions.Comment: 7 pages, 1 figure. Proceedings of 18th Central European Workshop on Quantum Optics (CEWQO 2011), Madrid, Spai