Multipartite maximally entangled states in symmetric scenarios

We consider the class of (N+1)-partite states suitable for protocols where there is a powerful party, the authority, and the other N parties play the same role, namely the state of their system live in the symmetric Hilbert space. We show that, within this scenario, there is a "maximally entangled state" that can be transform by a LOCC protocol into any other state. In addition, we show how to make the protocol efficiently including the construction of the state and discuss security issues for possible applications to cryptographic protocols. As an immediate consequence we recover a sequential protocol that implements the one to N symmetric cloning.Comment: 6 pages, 4 figure

Identifying residential sub-markets using intra-urban migrations: the case of study of Barcelona’s neighborhoods

The dynamic evolution of the real estate market, as well as the sophistications of the interactions of the actors involved in it have caused that, contrary to classical economic theory, the real estate market is increasingly being thought of as a set of submarkets. This is because, among other things, the modeling of a segmented housing market allows, on the one hand, to design housing policies that are better adapted to the needs of the population, but on the other hand, it allows the generation of both marketing and supply strategies Oriented to specific population sectors. Such strategies in theory should behave as options with relatively low uncertainty, thus representing an attractive offer to all market players. However, in praxis, the segmentation of the real estate market is usually modeled on the offer. It is therefore that this paper proposes a modeling from observed preferences3 seen through intraurban migrations. In particular, it is proposed to model the market through the interaction value of Coombes, scaling the results in order to visualize the resulting submarket structure from the construction of a PAM (Partitioning Algorithm Medoids).Peer ReviewedPostprint (published version

Euclidean distance between Haar orthogonal and gaussian matrices

In this work we study a version of the general question of how well a Haar distributed orthogonal matrix can be approximated by a random gaussian matrix. Here, we consider a gaussian random matrix $Y_n$ of order $n$ and apply to it the Gram-Schmidt orthonormalization procedure by columns to obtain a Haar distributed orthogonal matrix $U_n$. If $F_i^m$ denotes the vector formed by the first $m$-coordinates of the $i$th row of $Y_n-\sqrt{n}U_n$ and $\alpha=\frac{m}{n}$, our main result shows that the euclidean norm of $F_i^m$ converges exponentially fast to $\sqrt{ \left(2-\frac{4}{3} \frac{(1-(1 -\alpha)^{3/2})}{\alpha}\right)m}$, up to negligible terms. To show the extent of this result, we use it to study the convergence of the supremum norm $\epsilon_n(m)=\sup_{1\leq i \leq n, 1\leq j \leq m} |y_{i,j}- \sqrt{n}u_{i,j}|$ and we find a coupling that improves by a factor $\sqrt{2}$ the recently proved best known upper bound of $\epsilon_n(m)$. Applications of our results to Quantum Information Theory are also explained.Comment: v2: minor modifications to match journal version, 26 pages, 0 figures, J Theor Probab (2016

Undominated (and) perfect equilibria in Poisson games

In games with population uncertainty some perfect equilibria are in dominated strategies. We prove that every Poisson game has at least one perfect equilibrium in undominated strategies