Related papers: Data-scientific study of Kronecker coefficients
Zeros of many ensembles of polynomials with random coefficients are asymptotically equidistributed near the unit circumference. We give quantitative estimates for such equidistribution in terms of the expected discrepancy and expected…
In this chapter we explore the connection between mesoscopic physics and quantum computing. After giving a bibliography providing a general introduction to the subject of quantum information processing, we review the various approaches that…
A simplified Heisenberg spin model is studied in order to examine the idea of decoherence in closed quantum systems. For this purpose, we present a quantifiable definition to quantum coherence $\Xi$, and discuss in some detail a general…
Specifying a computational problem requires fixing encodings for input and output: encoding graphs as adjacency matrices, characters as integers, integers as bit strings, and vice versa. For such discrete data, the actual encoding is…
For a root system R, a field K and a "choice of coefficients in K" we define a category of graded spaces with operators and study some of its properties. Then we assume that the coefficients are given by quantum binomials. We use basic…
Observations or measurements taken of a quantum system (a small number of fundamental particles) are inherently random. If the state of the system depends on unknown parameters, then the distribution of the outcome depends on these…
Estimating the causal effects of an intervention from high-dimensional observational data is difficult due to the presence of confounding. The task is often complicated by the fact that we may have a systematic missingness in our data at…
We present a simple experimental scheme which can be used to demonstrate an all-or-nothing type contradiction between non-contextual hidden variables and quantum mechanics. The scheme, which is inspired by recent ideas by Cabello and…
The general scheme of data compression using the quantum noiseless coding theorem of Schumacher is dicussed for general quantum sources. When the Hilbert space of the quantum source is decomposable into orthogonal subspaces, one can first…
The problem of covariance estimation for replicated surface-valued processes is examined from the functional data analysis perspective. Considerations of statistical and computational efficiency often compel the use of separability of the…
Information-theoretical quantities such as statistical distinguishability typically result from optimisations over all conceivable observables. Physical theories, however, are not generally considered valid for all mathematically allowed…
We study the possibility of applying statistical mechanics to generally covariant quantum theories with a vanishing Hamiltonian. We show that (under certain appropiate conditions) this makes sense, in spite of the absence of a notion of…
In this work we study constant-coefficient first order systems of partial differential equations and give necessary and sufficient conditions for those systems to have a well posed Cauchy Problem. In many physical applications, due to the…
An apriori bound for the condition number associated to each of the following problems is given: general linear equation solving, minimum squares, non-symmetric eigenvalue problems, solving univariate polynomials, solving systems of…
We provide a unified framework for independence and mean independence tests based on the Hilbert-Schmidt independence criterion, extending some previous results in the literature to hold in general topological spaces. We also present a…
We perform a non-perturbative study of the Coleman-Weinberg phase transition in scalar QED. Our method permits a consistent treatment of the effective potential near the origin, a region not accessible to perturbation theory. As a result,…
Quantum computation with quantum data that can traverse closed timelike curves represents a new physical model of computation. We argue that a model of quantum computation in the presence of closed timelike curves can be formulated which…
Quantum information resources quantified by non-zero discord are ubiquitous for the continuous-variables bipartite systems. Complementary to this, we formally construct a model characterized by zero two-way discord for arbitrarily long time…
Signal processing of uniformly spaced data from stationary stochastic processes with missing samples is investigated. Besides randomly and independently occurring outliers also correlated data gaps are investigated. Non-parametric…
We introduce the concept of cloning for classes of observables and classify cloning machines for qubit systems according to the number of parameters needed to describe the class under investigation. A no-cloning theorem for observables is…