Related papers: Multifractality beyond the Parabolic Approximation…
Quantitative characterization of different entanglement detection criteria for bipartite systems is presented. We review the implication sequence of these criteria and then numerically estimate volume ratios between criteria non-violating…
We present a new method for describing quantum measurements in relativistic systems that applies (i) to any QFT and for any field-detector coupling, (ii) to the measurement of any observable, and (iii) to arbitrary size, shape and motion of…
We calculate the limiting behavior of relative Renyi entropy when the first probability distribution is close to the second one in a non-regular location-shift family which is generated by a probability distribution whose support is an…
It is widely believed that combining the uncertainty principle with gravity will lead to an effective minimum length scale. A particular challenge is to specify this scale in a coordinate-independent manner so that covariance is not broken.…
Statistical properties of critical wave functions at the spin quantum Hall transition are studied both numerically and analytically (via mapping onto the classical percolation). It is shown that the index $\eta$ characterizing the decay of…
Recently, a concept of generalized multifractality, which characterizes fluctuations and correlations of critical eigenstates, was introduced and explored for all ten symmetry classes of disordered systems. Here, by using the non-linear…
The sample averaged longitudinal two-terminal conductance and the respective Kubo-conductivity are calculated at quantum critical points in the integer quantum Hall regime. In the limit of large system size, both transport quantities are…
We consider statistical methods based on finite samples of locally randomized measurements in order to certify different degrees of multiparticle entanglement in intermediate-scale quantum systems. We first introduce hierarchies of…
In this article we exploit the Bhattacharyya statistical divergence to determine the similarity of probability distributions of quantum observables. After brief review of useful characteristics of the Bhattacharyya divergence we apply it to…
We replace a Hamiltonian with a modular Hamiltonian in the spectral form factor and the level spacing distribution function. This study establishes a connection between quantities within Quantum Entanglement and Quantum Chaos. To have a…
In this paper we present a rigorous cost and error analysis of a multilevel estimator based on randomly shifted Quasi-Monte Carlo (QMC) lattice rules for lognormal diffusion problems. These problems are motivated by uncertainty…
We derive quantitative estimates proving the conditional propagation of chaos for large stochastic systems of interacting particles subject to both idiosyncratic and common noise. We obtain explicit bounds on the relative entropy between…
The concept of classical $f$-divergences gives a unified framework to construct and study measures of dissimilarity of probability distributions; special cases include the relative entropy and the R\'enyi divergences. Various quantum…
A numerical study is made of current distribution in small Hall bars with disorder. It is observed, in particular, that in the Hall-plateau regime the Hall current tends to concentrate near the sample edges while it diminishes on average in…
We show that different entropic measures of fluctuations lead to contradictory uncertainty relations for two complementary observables. We apply Tsallis and R\'{e}nyi entropies to the joint distribution emerging from a noisy simultaneous…
We study the multifractal spectrum of the current in the two-dimensional random resistor network at the percolation threshold. We consider two ways of applying the voltage difference: (i) two parallel bars, and (ii) two points. Our…
Some of the most popular ways to treat quantum critical materials, that is, materials close to a magnetic instability, are based on the Landau functional. The central quantity of such approaches is the average magnitude of spin…
We consider Gaussian quantum circuits that alternate unitary gates and post-selected weak measurements, with spatial translation symmetry and time periodicity. We show analytically that such models can host different kinds of…
Entropy is useful in statistical problems as a measure of irreversibility, randomness, mixing, dispersion, and number of microstates. However, there remains ambiguity over the precise mathematical formulation of entropy, generalized beyond…
Outcomes of measurements are characterized by an infinite family of generalized uncertainties, or cumulants, which provide information beyond the mean and variance of the observable. Here, we investigate the cumulants of a conserved charge…