The real rank two locus of an algebraic variety is the closure of the union of all secant lines spanned by real points. We seek a semi-algebraic description of this set. Its algebraic boundary consists of the tangential variety and the edge variety. Our study of Segre and Veronese varieties yields a characterization of tensors of real rank two.

In this paper, we construct a measure of entanglement by generalizing the quadric polynomial of the Segre variety for general multipartite states. We give explicit expressions for general pure three-partite and four-partite states. Moreover, we will discuss and compare this measure of entanglement with the generalized concurrence.

Worker-Patient Contacts and Personal Protective Equipment Adherence within Hospital Rooms Junyang Chen, BS; James F. Cremer, PhD; Alberto Maria Segre, PhD; Philip M. Polgreen, MD; University of Iowa, Iowa City, IA; Department of Computer Science, University of Iowa, Iowa City, IA; Division of Infectious Diseases, Department of Internal Medicine, University of Iowa Carver College of Medicine, Io...

Some recent results (and a conjecture) concerning the polynomial degree of the Grassmannian G1;n;2 of the lines of PG(n; 2) are shown to be equivalent to results (and a conjecture) concerning certain kinds of subgraphs of any (simple) graph = (V; E) which is of order jVj = n+ 1: It turns out that those graphs of size jEj = n = jVj 1 are of particular signi…cance. Somewhat similarly, results con...

We construct quantum gate entangler for general multipartite states based on topological unitary operators. We show that these operators can entangle quantum states if they satisfy the separability condition that is given by the complex multi-projective Segre variety. We also in detail discuss the construction of quantum gate entangler for higher dimensional bipartite and three-partite quantum ...

Inference in Bayesian statistics involves the evaluation of marginal likelihood integrals. We present algebraic algorithms for computing such integrals exactly for discrete data of small sample size. The underlying statistical models are mixtures of independent distributions, or, in geometric language, secant varieties of Segre-Veronese varieties.