A study of pre-validation

Given a predictor of outcome derived from a high-dimensional dataset, pre-validation is a useful technique for comparing it to competing predictors on the same dataset. For microarray data, it allows one to compare a newly derived predictor for disease outcome to standard clinical predictors on the same dataset. We study pre-validation analytically to determine if the inferences drawn from it are valid. We show that while pre-validation generally works well, the straightforward "one degree of freedom" analytical test from pre-validation can be biased and we propose a permutation test to remedy this problem. In simulation studies, we show that the permutation test has the nominal level and achieves roughly the same power as the analytical test.Comment: Published in at http://dx.doi.org/10.1214/07-AOAS152 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Pathwise coordinate optimization

We consider ``one-at-a-time'' coordinate-wise descent algorithms for a class of convex optimization problems. An algorithm of this kind has been proposed for the $L_1$-penalized regression (lasso) in the literature, but it seems to have been largely ignored. Indeed, it seems that coordinate-wise algorithms are not often used in convex optimization. We show that this algorithm is very competitive with the well-known LARS (or homotopy) procedure in large lasso problems, and that it can be applied to related methods such as the garotte and elastic net. It turns out that coordinate-wise descent does not work in the ``fused lasso,'' however, so we derive a generalized algorithm that yields the solution in much less time that a standard convex optimizer. Finally, we generalize the procedure to the two-dimensional fused lasso, and demonstrate its performance on some image smoothing problems.Comment: Published in at http://dx.doi.org/10.1214/07-AOAS131 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Fabrication of low-loss III-V Bragg-reflection waveguides for parametric down-conversion

Entangled photon pairs are an important resource for quantum cryptography schemes that go beyond point-to-point communication. Semiconductor Bragg-reflection waveguides are a promising photon-pair source due to mature fabrication, integrability, large transparency window in the telecom wavelength range, integration capabilities for electro-optical devices as well as a high second-order nonlinear coefficient. To increase performance we improved the fabrication of Bragg-reflection waveguides by employing fixed-beam-moving-stage optical lithography, low pressure and low chlorine concentration etching, and resist reflow. The reduction in sidewall roughness yields a low optical loss coefficient for telecom wavelength light of alpha_reflow = 0.08(6)mm^(-1). Owing to the decreased losses, we achieved a photon pair production rate of 8800(300)(mW*s*mm)^(-1) which is 15-fold higher than in previous samples

Time-bin entanglement at telecom wavelengths from a hybrid photonic integrated circuit

Mass-deployable implementations for quantum communication require compact, reliable, and low-cost hardware solutions for photon generation, control and analysis. We present a fiber-pigtailed hybrid photonic circuit comprising nonlinear waveguides for photon-pair generation and a polymer interposer reaching 68dB of pump suppression and photon separation with >25dB polarization extinction ratio. The optical stability of the hybrid assembly enhances the quality of the entanglement, and the efficient background suppression and photon routing further reduce accidental coincidences. We thus achieve a 96(-8,+3)% concurrence and a 96(-5,+2)% fidelity to a Bell state. The generated telecom-wavelength, time-bin entangled photon pairs are ideally suited for distributing Bell pairs over fiber networks with low dispersion

Extending Quantum Links: Modules for Fiber- and Memory-Based Quantum Repeaters

We analyze elementary building blocks for quantum repeaters based on fiber channels and memory stations. Implementations are considered for three different physical platforms, for which suitable components are available: quantum dots, trapped atoms and ions, and color centers in diamond. We evaluate and compare the performances of basic quantum repeater links for these platforms both for present-day, state-of-the-art experimental parameters as well as for parameters that could in principle be reached in the future. The ultimate goal is to experimentally explore regimes at intermediate distances, up to a few 100 km, in which the repeater-assisted secret key transmission rates exceed the maximal rate achievable via direct transmission. We consider two different protocols, one of which is better adapted to the higher source clock rate and lower memory coherence time of the quantum dot platform, while the other circumvents the need of writing photonic quantum states into the memories in a heralded, non-destructive fashion. The elementary building blocks and protocols can be connected in a modular form to construct a quantum repeater system that is potentially scalable to large distances.Comment: 48 pages in Word style, "White Paper" of Q.Link.X Consortiu

Impact of the energetic landscape on polariton condensates’ propagation along a coupler

Funding: This work has been partly supported by the Spanish MINECO Grant No. MAT2017-83722-R. E.R. acknowledges financial support from the FPI Scholarship No. BES-2015-074708. The Würzburg and Jena group acknowledge financial support within the DFG project PE 523/18-1,KL3124/2-1and SCHN1376 3-1. The Würzburg group is grateful for support from the state of Bavaria and within the Würzburg-Dresden Cluster of Excellence ct.qmat. A.Y.and I.A.S. thank the Russian Science Foundation for financial support, Project No. 18-72-10110.Polariton condensates' propagation is strongly dependent on the particular energy landscape the particles are moving upon, in which the geometry of the pathway laid for their movement plays a crucial role. Bends in the circuit's trajectories affect the condensates' speed and oblique geometries introduce an additional discretization of the polaritons' momenta due to the mixing of short and long axis wavevectors on the propagating eigenvalues. In this work, the nature of the propagation of condensates along the arms of a polariton coupler is studied by a combination of time‐resolved micro‐tomography measurements and a theoretical model based on a mean field approximation where condensed polaritons are described by an equation for the slow varying amplitude of the polariton field coupled to an equation for the density of incoherent excitons.Publisher PDFPeer reviewe

Platform for electrically pumped polariton simulators and topological lasers

We acknowledge support by the ImPACT Program, Japan Science and Technology Agency, the State of Bavaria and by the German Research Foundation (DFG) within project SCHN1376/2-1, SCHN1376/3-1 and KL3124/2-1. S.K. acknowledges the European Commission for the H2020 Marie Sklodowska-Curie Actions (MSCA) fellowship (Topopolis). R.T. is supported by the DFG through SFB 1170 (project B04) and by the European Research Council through ERC-StGTOPOLECTRICS- Thomale-336012. S.H. acknowledges support within the EPSRC Hybrid Polaritonics Grant (EP/M025330/1).Two-dimensional electronic materials such as graphene and transition metal dichalgenides feature unique electrical and optical properties due to the conspirative effect of band structure, orbital coupling, and crystal symmetry. Synthetic matter, as accomplished by artificial lattice arrangements of cold atoms, molecules, electron patterning, and optical cavities, has emerged to provide manifold intriguing frameworks to likewise realize such scenarios. Exciton-polaritons have recently been added to the list of promising candidates for the emulation of system Hamiltonians on a semiconductor platform, offering versatile tools to engineer the potential landscape and to access the non-linear electro-optical regime. In this work, we introduce an electronically driven square and honeycomb lattice of exciton-polaritons, paving the way towards real world devices based on polariton lattices for on-chip applications. Our platform exhibits laser-like emission from high-symmetry points under direct current injection, hinting at the prospect of electrically driven polariton lasers with possibly topologically non-trivial properties.PostprintPeer reviewe

Time-bin entangled photon pairs from Bragg-reflection waveguides

This work was supported by the Austrian Science Fund (FWF) through the project nos. I 2065 and J 4125, the DFG project no. SCHN1376/2-1, the ERC project EnSeNa (257531), the State of Bavaria and China Scholarship Council (201503170272).Semiconductor Bragg-reflection waveguides are well-established sources of correlated photon pairs as well as promising candidates for building up integrated quantum optics devices. Here, we use such a source with optimized non-linearity for preparing time-bin entangled photons in the telecommunication wavelength range. By taking advantage of pulsed state preparation and efficient free-running single-photon detection, we drive our source at low pump powers, which results in a strong photon-pair correlation. The tomographic reconstruction of the state’s density matrix reveals that our source exhibits a high degree of entanglement. We extract a concurrence of 88.9(1.8)% and a fidelity of 94.2(9)% with respect to a Bell state.Publisher PDFPeer reviewe