相关论文: Lars Brink and SIC_POVMs

We propose the Sobolev Independence Criterion (SIC), an interpretable dependency measure between a high dimensional random variable X and a response variable Y . SIC decomposes to the sum of feature importance scores and hence can be used…

In this PhD thesis, we give a new geometric approach to higher Teichm\"uller theory. In particular we construct a geometric structure on surfaces, generalizing the complex structure, and we explore its link to Hitchin components. The…

We present a multiresolution approach to the theory of quantum information. It arose from an effort to develop a systematic mathematical approach to the analysis of an infinite array of qubits, i.e., a structure that may be interpreted as a…

Although symmetric informationally complete positive operator valued measures (SIC POVMs, or SICs for short) have been constructed in every dimension up to 67, a general existence proof remains elusive. The purpose of this paper is to show…

We present a practical implementation of the perturbation theory derived by Lynden-Bell (2015) for describing, to arbitrary precision, the orbit of a particle in an arbitrary spherically-symmetric potential. Our implementation corrects…

Bohr's dictum "Physical phenomena are observed relative to different experimental setups" is applied to a set of binary elements that represent the smallest units of information. A description relative to "macroscopic" setups of such…

The $S$-matrix Ansatz for the construction of a quantum theory of black holes is further exploited. We first note that treating the metric tensor $g_{\m\n}$ as an operator rather than a background allows us to use a setting where…

Theories involving localized collapse allow the possibility that classical information could be obtained about quantum states without using POVMS and without allowing superluminal signalling. We can model this by extending quantum theory to…

Semidefinite programs (SDPs) are a class of optimisation problems that find application in numerous areas of physics, engineering and mathematics. Semidefinite programming is particularly suited to problems in quantum physics and quantum…

We introduce the key ideas and mathematical tools central to modern discussions of collapse. We assume knowledge of basic quantum mechanics -- the Schr\"{o}dinger evolution of states in Hilbert space, the Born probability rule, the Dirac…

For their ability to capture non-linearities in the data and to scale to large training sets, local Support Vector Machines (SVMs) have received a special attention during the past decade. In this paper, we introduce a new local SVM method,…

Bound states in the continuum (BICs) realized in two-dimensional (2D) photonic crystal slabs (PhCSs) have attracted considerable attentions, owing to the advantages in the fabrications and on-chip applications. The polarization vortex…

We apply the generalised concept of witness operators to arbitrary convex sets, and review the criteria for the optimisation of these general witnesses. We then define an embedding of state vectors and operators into a higher-dimensional…

Why does quantum theory need the complex numbers? With a view toward answering this question, this paper argues that the usual Hilbert-space formalism is a special case of the general method of Markovian embeddings. This paper then…

Support vector machine (SVM) is a particularly powerful and flexible supervised learning model that analyzes data for both classification and regression, whose usual algorithm complexity scales polynomially with the dimension of data space…

Consider a photon that has just emerged from a linear polarizing filter. If the photon is then subjected to an orthogonal polarization measurement-e.g., horizontal vs vertical-the photon's preparation cannot be fully expressed in the…

The rather unintuitive nature of quantum theory has led numerous people to develop sets of (physically motivated) principles that can be used to derive quantum mechanics from the ground up, in order to better understand where the structure…

In this work, we study the minimal normal measurement models of quantum instruments. We show that usually the apparatus' Hilbert space in such a model is unitarily isomorphic to the minimal Stinespring dilation space of the…

These three topics are an attempt to explicate some curiosities of the inverse problem of representation theory (i.e. having a set of operators to describe the "correct" algebraic object, which is represented by them) on simple examples…

The notion of polarity between sets, well-known from convex geometry, is a geometric version of the Fourier transform. We exploit this analogy to propose a new simple definition of quantum indeterminacy, using what we call "hbar-polar…