Related papers: Certificates of convexity for basic semi-algebraic…
Certifying that quantum devices behave as intended is crucial for quantum information science. Here, methods are developed for certification of both state preparation devices and measurement devices based on prepare-and-measure experiments…
Convex sets of completely positive maps and positive semidefinite kernels are considered in the most general context of modules over $C^*$-algebras and a complete charaterization of their extreme points is obtained. As a byproduct, we…
In local certification, vertices of a $n$-vertex graph perform a local verification to check if a given property is satisfied by the graph. This verification is performed thanks to certificates, which are pieces of information that are…
We investigate the regularity of the marginals onto hyperplanes for sets of finite perimeter. We prove, in particular, that if a set of finite perimeter has log-concave marginals onto a.e. hyperplane then the set is convex.
We give two sufficient conditions for the lattice Co(R^n,X) of relatively convex sets of n-dimensional real space R^n to be join-semidistributive, where X is a finite union of segments. We also prove that every finite lower bounded lattice…
In this paper, we present a computational approach to certify almost sure reachability for discrete-time polynomial stochastic systems by turning drift--variant criteria into sum-of-squares (SOS) programs solved with standard semidefinite…
In this paper, we study the employment of $\Sigma_1$-sentences with certificates, i.e., $\Sigma_1$-sentences where a number of principles is added to ensure that the witness is sufficiently number-like. We develop certificates in some…
We introduce several classes of set-valued maps with generalized convexity. We obtain minimax theorems for set-valued maps which satisfy the introduced properties and are not continuous, by using a fixed point theorem for weakly naturally…
The completely bounded trace and spectral norms in finite dimensions are shown to be expressible by semidefinite programs. This provides an efficient method by which these norms may be both calculated and verified, and gives alternate…
Symmetry and dominance breaking can be crucial for solving hard combinatorial search and optimisation problems, but the correctness of these techniques sometimes relies on subtle arguments. For this reason, it is desirable to produce…
We prove that for two-component maps in dimension two, rank-one convexity is equivalent to quasiconvexity. The essential tool for the proof is a fixed-point argument for a suitable set-valued map going from one component to the other that…
A simple geometric condition is sufficient for analytic hypoellipticity of sums of squares of two vector fields in ${\mathbb R}^2$. This condition is proved to be necessary for generic vector fields and for various special cases, and to be…
In this letter we consider the problem of certification of quantum measurements with an arbitrary number of outcomes. We propose a simple scheme for certifying any set of $d$-outcome projective measurements which do not share any common…
A set is called semidefinite representable or semidefinite programming (SDP) representable if it can be represented as the projection of a higher dimensional set which is represented by some Linear Matrix Inequality (LMI). This paper…
Randomness is fundamental for secure communication and information processing. While continuous-variable optical systems offer an attractive platform for this task, certifying genuine quantum randomness in such setups remains challenging.…
We show that after mapping each element of a set of second class constraints to the surface of the other ones, half of them form a subset of abelian first class constraints. The explicit form of the map is obtained considering the most…
We prove that each semialgebraic subset of $\R^n$ of positive codimension can be locally approximated of any order by means of an algebraic set of the same dimension. As a consequence of previous results, algebraic approximation preserving…
Polyhedral convex set optimization problems are the simplest optimization problems with set-valued objective function. Their role in set optimization is comparable to the role of linear programs in scalar optimization. Vector linear…
We establish necessary and sufficient conditions on simultaneous symplectic spectral decomposition of a family of $2n \times 2n$ real positive semidefinite matrices with symplectic kernels. We also provide a precise algebraic condition on a…
The recently introduced notions of ranking functions and closure certificates utilize well-foundedness arguments to facilitate the verification of dynamical systems against $\omega$-regular properties. A ranking function and a closure…