Related papers: Effective methods for constructing extreme quantum…
Maximum entropy methods, rooted in the inverse Ising/Potts problem from statistical physics, are widely used to model pairwise interactions in complex systems across disciplines such as bioinformatics and neuroscience. While successful,…
We present a technique for reducing the computational requirements by several orders of magnitude in the evaluation of semidefinite relaxations for bounding the set of quantum correlations arising from finite-dimensional Hilbert spaces. The…
In many practical settings control decisions must be made under partial/imperfect information about the evolution of a relevant state variable. Partially Observable Markov Decision Processes (POMDPs) is a relatively well-developed framework…
We provide a definition of POVM in terms of abstract tensor structure only. It is justified in two distinct manners. i. At this abstract level we are still able to prove Naimark's theorem, hence establishing a bijective correspondence…
Quantum tomography is a process of quantum state reconstruction using data from multiple measurements. An essential goal for a quantum tomography algorithm is to find measurements that will maximize the useful information about an unknown…
Quantum measurement not only can destroy coherence but also can create it. Here, we estimate the maximum amount of coherence, one can create under a complete non-selective measurement process. For our analysis, we consider projective as…
We construct extremal metrics on the total space of certain destabilising test configurations for strictly semistable K\"ahler manifolds. This produces infinitely many new examples of manifolds admitting extremal K\"ahler metrics. It also…
S. Gudder and, later, S. Pulmanova and E. Vincekova, have studied in two recent papers a certain ordering of bounded self-adjoint operators on a Hilbert space. We present some further results on this ordering and show that some structure…
We examine a sequence of examples of pairs of moduli spaces of sheaves on $\mathbb P^2$ where Le Potier's strange duality is expected to hold. One of the moduli spaces in these pairs is the Hilbert scheme of two points. We compute the…
Instance ranking problems intend to recover the true ordering of the instances in a data set with a variety of applications in for example scientific, social and financial contexts. Robust statistics studies the behaviour of estimators in…
By ``position operators,'' I mean here a POVM (positive-operator-valued measure) on a suitable configuration space acting on a suitable Hilbert space that serves as defining the position observable of a quantum theory, and by ``positron…
Comparing probability distributions is a core challenge across the natural, social, and computational sciences. Existing methods, such as Maximum Mean Discrepancy (MMD), struggle in high-dimensional and non-compact domains. Here we…
We introduce a novel method for bounding high-order multi-dimensional polynomials in finite element approximations. The method involves precomputing optimal piecewise-linear bounding boxes for polynomial basis functions, which can then be…
In this paper we consider the problem of constructing measurements optimized to distinguish between a collection of possibly non-orthogonal quantum states. We consider a collection of pure states and seek a positive operator-valued measure…
We describe a framework for bounding extreme values of quantities on global attractors of differential dynamical systems. A global attractor is the minimal set that attracts all bounded sets; it contains all forward-time limit points. Our…
We consider the set of the power non-negative polynomials of several variables and its subset that consists of polynomials which can be represented as a sum of squares. It is shown in the classic work by D.Hilbert that it is a proper…
An unavoidable task in quantum information processing is how to obtain data about the state of an individual system by suitable measurements. Informationally complete measurements are relevant in quantum state tomography, quantum…
The estimation of conditional quantiles at extreme tails is of great interest in numerous applications. Various methods that integrate regression analysis with an extrapolation strategy derived from extreme value theory have been proposed…
We give a characterization for the extreme points of the convex set of correlation matrices with a countable index set. A Hermitian matrix is called a correlation matrix if it is positive semidefinite with unit diagonal entries. Using the…
We consider the concept of rank as a measure of the vertical levels and positions of elements of partially ordered sets (posets). We are motivated by the need for algorithmic measures on large, real-world hierarchically-structured data…