Related papers: Weaker quantization dimension results for self-sim…
We explore the relationship between symmetrisation and entanglement through measurements on few-particle systems in a multi-well potential. In particular, considering two or three trapped atoms, we measure and distinguish correlations…
We investigate the Hausdorff measure and content on a class of quasi self-similar sets that include, for example, graph-directed and sub self-similar and self-conformal sets. We show that any Hausdorff measurable subset of such a set has…
Many quantum paradoxes based on a realistic view of weak values were discussed in the last decades. They lead to astonishing conclusions such as the measurement of a spin component of a spin-1/2 particle resulting in $100\hbar$, the…
Coherent steering of a quantum state, induced by a sequence of weak measurements, has become an active area of theoretical and experimental study. For a closed steered trajectory, the underlying phase factors involve both geometrical and…
Motivated by quantum resource theories, we introduce a notion of incompatibility for quantum measurements relative to a reference basis. The notion arises by considering states diagonal in that basis and investigating whether probability…
We consider dimensional properties of limit sets of Moran constructions satisfying the finite clustering property. Just to name a few, such limit sets include self-conformal sets satisfying the weak separation condition and certain…
In a variety of applications it is important to extract information from a probability measure $\mu$ on an infinite dimensional space. Examples include the Bayesian approach to inverse problems and possibly conditioned) continuous time…
We prove general results about separation and weak$^\#$-convergence of boundedly finite measures on separable metric spaces and Souslin spaces. More precisely, we consider an algebra of bounded real-valued, or more generally a $*$-algebra…
We examine Frostman-type characterisations and other extremal measure criteria for a range of fractal dimensions of sets. In particular we derive properties of the less familiar modified lower box dimension and upper correlation dimension.…
We introduce a measure of average dimensionality (or coherence) for high-dimensional quantum devices. This includes sets of quantum measurements, steering assemblages, and quantum channels. For measurements and channels, our measure…
For a given $r \in (0, +\infty)$, the quantization dimension of order $r$, if it exists, denoted by $D_r(\mu)$, represents the rate at which the $n$th quantization error of order $r$ approaches to zero as the number of elements $n$ in an…
Self-testing was originally introduced as a device-independent method of certification of entangled quantum states and local measurements performed on them. Recently, in [F. Baccari \textit{et al.}, arXiv:2003.02285] the notion of state…
The study of Fourier transforms of probability measures on fractal sets plays an important role in recent research. Faster decay rates are known to yield enhanced results in areas such as metric number theory. This paper focuses on…
We study self-similar measures in $\mathbb{R}$ satisfying the weak separation condition along with weak technical assumptions which are satisfied in all known examples. For such a measure $\mu$, we show that there is a finite set of concave…
In this paper, we focus on the packing measure of self-similar sets. Let $K$ be a self-similar set whose Hausdorff dimension and packing dimension equal $s$, we state that if $K$ satisfies the strong open set condition with an open set…
In a metric space $(X,d)$ we reconstruct an approximation of a Borel measure $\mu$ starting from a premeasure $q$ defined on the collection of closed balls, and such that $q$ approximates the values of $\mu$ on these balls. More precisely,…
If $X$ is a set with finite Assouad dimension, it is known that the Assouad dimension of $X-X$ does not necessarily obey any non-trivial bound in terms of the Assouad dimension of $X$. In this paper, we consider self-similar sets on the…
We suggest two metrics for assessing the quality of atomistic configurations of disordered materials, both of which are based on quantifying the orientational distribution of neighbours around each atom in the configuration. The first…
Minimizing divergence measures under a constraint is an important problem. We derive a sufficient condition that binary divergence measures provide lower bounds for symmetric divergence measures under a given triangular discrimination or…
The usual notion of separability has to be reconsidered when applied to states describing identical particles. A definition of separability not related to any a priori Hilbert space tensor product structure is needed: this can be given in…