Correspondence between continuous-variable and discrete quantum systems of arbitrary dimensions

We establish a mapping between a continuous-variable (CV) quantum system and a discrete quantum system of arbitrary dimension. This opens up the general possibility to perform any quantum information task with a CV system as if it were a discrete system. The Einstein-Podolsky-Rosen state is mapped onto the maximally entangled state in any finite-dimensional Hilbert space and thus can be considered as a universal resource of entanglement. An explicit example of the map and a proposal for its experimental realization are discussed.

Boson pairs in a one-dimensional split trap

We describe the properties of a pair of ultracold bosonic atoms in a one-dimensional harmonic trapping potential with a tunable zero-ranged barrier at the trap center. The full characterization of the ground state is done by calculating the reduced single-particle density, the momentum distribution, and the two-particle entanglement. We derive several analytical expressions in the limit of infinite repulsion (Tonks-Girardeau limit) and extend the treatment to finite interparticle interactions by numerical solution. As pair interactions in double wells form a fundamental building block for many-body systems in periodic potentials, our results have implications for a wide range of problems.

Low-energy excitations of a boson pair in a double-well trap

The states of a boson pair in a one-dimensional double-well potential are investigated. Properties of the ground and lowest excited states of this system are studied, including the two-particle wave function, momentum pair distribution, and entanglement. The effects of varying both the barrier height and the effective interaction strength are investigated.

Bioinformatics inspired algorithm for stereo correspondence

In this paper, we exploit the analogy between protein sequence alignment and image pair correspondence to design a bioinformatics-inspired framework for stereo matching based on dynamic programming. This approach also led to the creation of a meaningfulness graph, which helps to predict matching validity according to image overlap and pixel similarity. Finally, we propose an automatic procedure to estimate automatically all matching parameters. This work is evaluated qualitatively and quantitatively using a standard benchmarking dataset and by conducting stereo matching experiments between images captured at different resolutions. Results confirm the validity of the computer vision/bioinformatics analogy to develop a versatile and accurate low complexity stereo matching algorithm.

Reply (Correspondence)

We appreciate the interest of Galvis and associates in our work.1 It has been suggested that undercorrection of children's refractive error might retard myopia progression. Previous studies,2,3 limited by size, have generally not been consistent with this. We performed a post hoc analysis on data from our large trial of spectacle provision in China and found no evidence of worsening visual acuity (VA) among children randomized to receive glasses compared to controls. In fact, the final uncorrected VA of Treatment Group children was significantly better than that of controls.