Estimating entanglement monotones with a generalization of the Wootters formula

Entanglement monotones, such as the concurrence, are useful tools to characterize quantum correlations in various physical systems. The computation of the concurrence involves, however, difficult optimizations and only for the simplest case of two qubits a closed formula was found by Wootters [Phys. Rev. Lett. 80, 2245 (1998)]. We show how this approach can be generalized, resulting in lower bounds on the concurrence for higher dimensional systems as well as for multipartite systems. We demonstrate that for certain families of states our results constitute the strongest bipartite entanglement criterion so far; moreover, they allow to recognize novel families of multiparticle bound entangled states.Comment: 8 pages, one figure, v2: small change

Low-Light Enhancement in the Frequency Domain

Decreased visibility, intensive noise, and biased color are the common problems existing in low-light images. These visual disturbances further reduce the performance of high-level vision tasks, such as object detection, and tracking. To address this issue, some image enhancement methods have been proposed to increase the image contrast. However, most of them are implemented only in the spatial domain, which can be severely influenced by noise signals while enhancing. Hence, in this work, we propose a novel residual recurrent multi-wavelet convolutional neural network R2-MWCNN learned in the frequency domain that can simultaneously increase the image contrast and reduce noise signals well. This end-to-end trainable network utilizes a multi-level discrete wavelet transform to divide input feature maps into distinct frequencies, resulting in a better denoise impact. A channel-wise loss function is proposed to correct the color distortion for more realistic results. Extensive experiments demonstrate that our proposed R2-MWCNN outperforms the state-of-the-art methods quantitively and qualitatively.Comment: 8 page

Improved lower bounds on genuine-multipartite-entanglement concurrence

Genuine-multipartite-entanglement (GME) concurrence is a measure of genuine multipartite entanglement that generalizes the well-known notion of concurrence. We define an observable for GME concurrence. The observable permits us to avoid full state tomography and leads to different analytic lower bounds. By means of explicit examples we show that entanglement criteria based on the bounds have a better performance with respect to the known methods.Comment: 17 pages, 1 EPS figure; v3 is in one column to improve readability of equation