Related papers: Semidefinite programming lower bounds on the squas…
Disjointly constrained multilinear programming concerns the problem of maximizing a multilinear function on the product of finitely many disjoint polyhedra. While maximizing a linear function on a polytope (linear programming) is known to…
We define quasiconvex programming, a form of generalized linear programming in which one seeks the point minimizing the pointwise maximum of a collection of quasiconvex functions. We survey algorithms for solving quasiconvex programs either…
We present an extension of known semidefinite and linear programming upper bounds for spherical codes. We apply the main result for the distance distribution of a spherical code and show that this method can work effectively In particular,…
The quantum internet aims to interconnect distant devices and enable large-scale computation through distributed quantum algorithms. One of the key obstacles is communication latency during computation. Even separations of a few hundred…
Positive semidefinite rank (PSD-rank) is a relatively new quantity with applications to combinatorial optimization and communication complexity. We first study several basic properties of PSD-rank, and then develop new techniques for…
Semiconstrained systems were recently suggested as a generalization of constrained systems, commonly used in communication and data-storage applications that require certain offending subsequences be avoided. In an attempt to apply…
We work out the general theory of one-parameter families of partial entanglement properties and the resulting entanglement depth-like quantities. Special cases of these are the depth of partitionability, the depth of producibility (or…
We apply the semidefinite programming method to derive bounds for projective codes over a finite field.
Squashed entanglement is a measure for the entanglement of bipartite quantum states. In this paper we present a lower bound for squashed entanglement in terms of a distance to the set of separable states. This implies that squashed…
Given labeled points in a high-dimensional vector space, we seek a low-dimensional subspace such that projecting onto this subspace maintains some prescribed distance between points of differing labels. Intended applications include…
In this paper we study bipartite quantum correlations using techniques from tracial noncommutative polynomial optimization. We construct a hierarchy of semidefinite programming lower bounds on the minimal entanglement dimension of a…
Shifted combinatorial optimization is a new nonlinear optimization framework, which is a broad extension of standard combinatorial optimization, involving the choice of several feasible solutions at a time. It captures well studied and…
Quantum entanglement is a useful resource for implementing communication tasks. However, for the resource to be useful in practice, it needs to be accessible by parties with bounded computational resources. Computational entanglement…
We introduce an intuitive measure of genuine multipartite entanglement which is based on the well-known concurrence. We show how lower bounds on this measure can be derived that also meet important characteristics of an entanglement…
New measures of multipartite entanglement are constructed based on two definitions of multipartite information and different methods of optimizing over extensions of the states. One is a generalization of the squashed entanglement where one…
The min-knapsack problem with compactness constraints extends the classical knapsack problem, in the case of ordered items, by introducing a restriction ensuring that they cannot be too far apart. This problem has applications in…
We apply the semidefinite programming approach developed in arxiv:math.MG/0608426 to obtain new upper bounds for codes in spherical caps. We compute new upper bounds for the one-sided kissing number in several dimensions where we in…
Semidefinite programs (SDPs) are standard convex problems that are frequently found in control and optimization applications. Interior-point methods can solve SDPs in polynomial time up to arbitrary accuracy, but scale poorly as the size of…
In structured output learning, obtaining labelled data for real-world applications is usually costly, while unlabelled examples are available in abundance. Semi-supervised structured classification has been developed to handle large amounts…
Squashed entanglement [Christandl and Winter, J. Math. Phys. 45(3):829-840 (2004)] is a monogamous entanglement measure, which implies that highly extendible states have small value of the squashed entanglement. Here, invoking a recent…