Related papers: Total correlations as fully additive entanglement …
We establish sufficient conditions for finite convergence of the alternating projections method for two non-intersecting and potentially nonconvex sets. Our results are based on a generalization of the concept of intrinsic transversality,…
We give a condition for absolute continuity of self-similar measures in arbitrary dimensions. This allows us to construct the first explicit absolutely continuous examples of inhomogeneous self-similar measures in dimension one and two. In…
Discovering a correlation from one variable to another variable is of fundamental scientific and practical interest. While existing correlation measures are suitable for discovering average correlation, they fail to discover hidden or…
In this paper we extend the notion of a Lorentz cone. We call a closed convex set isotone projection set with respect to a pointed closed convex cone if the projection onto the set is isotone (i.e., monotone) with respect to the order…
Based on the idea of measuring the factorizability of a given density matrix, we propose a pairwise analysis strategy for quantifying and understanding multipartite entanglement. The methodology proves very effective as it immediately…
Methods are developed for checking and completing systems of bivariate and multivariate Kendall's tau concordance measures in applications where only partial information about dependencies between variables is available. The concept of a…
We analyse a new notion of total anisotropic higher-order variation which, differently from the Total Generalized Variation by Bredies et al., quantifies for possibly non-symmetric tensor fields their variations at arbitrary order weighted…
We investigate the properties of three entanglement measures that quantify the statistical distinguishability of a given state with the closest disentangled state that has the same reductions as the primary state. In particular, we…
Finding a point in the intersection of a collection of closed convex sets, that is the convex feasibility problem, represents the main modeling strategy for many computational problems. In this paper we analyze new stochastic reformulations…
Based on the residual entanglement [9] (Phys. Rev. A \textbf{71}, 044301 (2005)), we present the global entanglement for a multipartite quantum state. The measure is shown to be also obtained by the bipartite partitions of the multipartite…
We investigate the possibility of replacing the topology of convergence in probability with convergence in $L^1$. A characterization of continuous linear functionals on the space of measurable functions is also obtained.
For any matroid $M$, we compute the Tutte polynomial $T_M(x,y)$ using the mixed intersection numbers of certain classes in the combinatorial Chow ring $A^\bullet(M)$ arising from hypersimplices. Using the mixed Hodge-Riemann relations, we…
In this paper we provide a sufficient condition for a Furstenberg measure generated by a finitely supported measure to be absolutely continuous. Using this, we give a very broad class of examples of absolutely continuous Furstenberg…
Although many different entanglement measures have been proposed so far, much less is known in the multipartite case, which leads to the previous monogamy relations in literatures are not complete. We establish here a strict framework for…
A principal curve serves as a powerful tool for uncovering underlying structures of data through 1-dimensional smooth and continuous representations. On the basis of optimal transport theories, this paper introduces a novel principal curve…
We propose a new approach to the problem of defining the degree of entanglement between two particles in a pure state with Hilbert spaces of arbitrary finite dimensions. The central idea is that entanglement gives rise to correlations…
We expose a theoretical hedging optimization framework with variational preferences under convex risk measures. We explore a general dual representation for the composition between risk measures and utilities. We study the properties of the…
We propose and examine several candidates for universal multipartite entanglement measures. The most promising candidate for applications needing entanglement in the full Hilbert space is the ent-concurrence, which detects all entanglement…
The pair correlations of the Thue--Morse sequence and system are revisited, with focus on asymptotic results on various means. First, it is shown that all higher-order correlations of the Thue--Morse sequence with general real weights are…
We continue the development of transfer operator techniques for expanding maps on a lattice coupled by general interaction functions. We obtain a spectral gap for an appropriately defined transfer operator, and, as corollaries, the…