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Consider a fixed universe of $N=2^n$ elements and the uniform distribution over elements of some subset of size $K$. Given samples from this distribution, the task of complement sampling is to provide a sample from the complementary subset.…

Strictly proper kernel scores are well-known tool in probabilistic forecasting, while characteristic kernels have been extensively investigated in the machine learning literature. We first show that both notions coincide, so that insights…

Generalised dichotomic quantum measurements are fully characterised by two real parameters, dubbed as sharpness parameter and biasedness parameter. The trade-off between the degree of joint measurability, sharpness and biasedness of…

We consider compound as well as arbitrarily varying classical-quantum channel models. For classical-quantum compound channels, we give an elementary proof of the direct part of the coding theorem. A weak converse under average error…

Variational quantum circuits (VQCs) are a central component of many quantum machine learning algorithms, offering a hybrid quantum-classical framework that, under certain aspects, can be considered similar to classical deep neural networks.…

We derive simple practical procedures revealing the quantum behavior of angular momentum variables by the violation of classical upper bounds on the statistics. Data analysis is minimum and definite conclusions are obtained without…

We give a short, critical review of the issue of decoherence. We establish the most general framework in which decoherence can be discussed, how it can be quantified and how it can be measured. We focus on environment induced decoherence…

We establish an operational connection between discrete rounds of generalized measurements and continuous-time decoherence, with an explicit correspondence between the number of measurement rounds and the evolution time. Operationally, we…

A new class of weighted spectral geometric means has recently been introduced. In this paper, we present its inequalities in terms of the L\"{o}wner order, operator norm, and trace. Moreover, we establish a log-majorization relationship…

One of the basic distinctions between classical and quantum mechanics is the existence of fundamentally incompatible quantities. Such quantities are present on all levels of quantum objects: states, measurements, quantum channels, and even…

Surprisingly often decoherence is due to classical fluctuations of ambient fields and may thus be described in terms of random unitary (RU) dynamics. However, there are decoherence channels where such a representation cannot exist. Based on…

Since the uncertainty about an observable of a system prepared in a quantum state is usually described by its variance, when the state is mixed, the variance is a hybrid of quantum and classical uncertainties. Besides that, complementarity…

The study of multivariate extremes is dominated by multivariate regular variation, although it is well known that this approach does not provide adequate distinction between random vectors whose components are not always simultaneously…

We use a master equation to study the dynamics of two coupled macroscopic quantum systems (e.g.\ a Josephson junction made of two Bose-Einstein condensates or two spin states of an ensemble of trapped ions) subject to a weak continuous…

Quantum f-divergences are a quantum generalization of the classical notion of f-divergences, and are a special case of Petz' quasi-entropies. Many well known distinguishability measures of quantum states are given by, or derived from,…

By wavelets approach we estimate densities. Then by means of mean value theorem we establish asymptotic consistency and normality for special divergence measures and construct their consistency bands.

Categorical variables are of uttermost importance in biomedical research. When two of them are considered, it is often the case that one wants to test whether or not they are statistically dependent. We show weaknesses of classical methods…

We perform an experimental test where we directly observe light-induced electron transitions with a macroscopic spatial discontinuity. The effect is related to the fundamental indivisibility of macroscopic orbit-like quantum states…

We analyze the classical and quantum properties of the integrable dimer problem. The classical version exhibits exactly one bifurcation in phase space, which gives birth to permutational symmetry broken trajectories and a separatrix. The…

Contextuality is regarded as a non-classical feature, challenging our everyday intuition; quantum contextuality is currently seen as a resource for many applications in quantum computation, being responsible for quantum advantage over…