Relation between classical communication capacity and entanglement capability for two-qubit unitary operations

Two-qubit operations may be characterized by their capacities for communication, both with and without free entanglement, and their capacity for creating entanglement. We establish a set of inequalities that give an ordering to the capacities of two-qubit unitary operations. Specifically, we show that the capacities for entanglement creation and bidirectional communication without entanglement assistance are at least as great as half the bidirectional communication capacity with entanglement assistance. In addition, we show that the bidirectional communication that can be performed using an ensemble may be increased via a two-qubit unitary operation by twice the operation's capacity for entanglement.Comment: 12 pages, published version plus minor correction

Implementation of multipartite unitary operations with limited resources

A general method for implementing weakly entangling multipartite unitary operations using a small amount of entanglement and classical communication is presented. For the simple Hamiltonian \sigma_z\otimes\sigma_z this method requires less entanglement than previously known methods. In addition, compression of multiple operations is applied to reduce the average communication required.Comment: 7 pages, 4 figures, comments welcom

Anomalies and entanglement renormalization

We study 't Hooft anomalies of discrete groups in the framework of (1+1)-dimensional multiscale entanglement renormalization ansatz states on the lattice. Using matrix product operators, general topological restrictions on conformal data are derived. An ansatz class allowing for optimization of MERA with an anomalous symmetry is introduced. We utilize this class to numerically study a family of Hamiltonians with a symmetric critical line. Conformal data is obtained for all irreducible projective representations of each anomalous symmetry twist, corresponding to definite topological sectors. It is numerically demonstrated that this line is a protected gapless phase. Finally, we implement a duality transformation between a pair of critical lines using our subclass of MERA.Comment: 12+18 pages, 6+5 figures, 0+2 tables, v2 published versio

Convergence Analysis for a Finite Element Approximation of a Steady Model for Electrorheological Fluids

In this paper we study the finite element approximation of systems of $p(\cdot)$-Stokes type, where $p(\cdot)$ is a (non constant) given function of the space variables. We derive --in some cases optimal-- error estimates for finite element approximation of the velocity and of the pressure, in a suitable functional setting

Is Betelgeuse the Outcome of a Past Merger?

We explore the possibility that the star alpha Orionis (Betelgeuse) is the outcome of a merger that occurred in a low mass ratio (q = M2/M1 = 0.07 - 0.25) binary system some time in the past hundreds of thousands of years. To that goal, we present a simple analytical model to approximate the perturbed internal structure of a post-merger object following the coalescence of a secondary in the mass range 1-4 Msun into the envelope of a 15-17 Msun primary. We then compute the long-term evolution of post-merger objects for a grid of initial conditions and make predictions about their surface properties for evolutionary stages that are consistent with the observed location of Betelgeuse in the Hertzsprung-Russell diagram. We find that if a merger occurred after the end of the primary's main-sequence phase, while it was expanding toward becoming a red supergiant star and typically with radius ~200 - 300 Rsun, then it's envelope is spun-up to values which remain in a range consistent with the Betelgeuse observations for thousands of years of evolution. We argue that the best scenario that can explain both the fast rotation of Betelgeuse and its observed large space velocity is one where a binary was dynamically ejected by its parent cluster a few million years ago and then subsequently merged. An alternative scenario in which the progenitor of Betelgeuse was spun up by accretion in a binary and released by the supernova explosion of the companion requires a finely tuned set of conditions but cannot be ruled out.Comment: 20 pages, 8 figures, accepted for publication in the Astrophysical Journa