相关论文: Barycentric decompositions for extensive monotone …

Samplets are data adapted multiresolution analyses of localized discrete signed measures. They can be constructed on scattered data sites in arbitrary dimension such that they exhibit vanishing moments with respect to any prescribed set of…

A defining signature of classical systems is "in principle measurability" without disturbance: a feature manifestly violated by quantum systems. We describe a multi-interferometer experimental setup that can, in principle, reveal the…

The transition between distinct phases of matter is characterized by the nature of fluctuations near the critical point. We demonstrate that noise spectroscopy can not only diagnose the presence of a phase transition, but can also determine…

In modern data analysis, nonparametric measures of discrepancies between random variables are particularly important. The subject is well-studied in the frequentist literature, while the development in the Bayesian setting is limited where…

We analyze a supersymmetric system with four flat directions. We observe several interesting properties, such as the coexistence of the discrete and continuous spectrum in the same range of energies. We also solve numerically the classical…

It is well known that many operations in quantum information processing depend largely on a special kind of quantum correlation, that is, entanglement. However, there are also quantum tasks that display the quantum advantage without…

Measurement error occurs when a covariate influencing a response variable is corrupted by noise. This can lead to misleading inference outcomes, particularly in problems where accurately estimating the relationship between covariates and…

We give systematic ways of defining monotone quantum relative entropies and (multi-variate) quantum R\'enyi divergences starting from a set of monotone quantum relative entropies. Despite its central importance in information theory, only…

The term moderate deviations is often used in the literature to mean a class of large deviation principles that, in some sense, fills the gap between a convergence in probability of some random variables to a constant and a weak convergence…

How much information do we need about a process' past to faithfully simulate its future? The statistical complexity is a prominent quantifier of structure for stochastic processes. Quantum machines, however, can simulate classical…

An understanding of quantum theory in terms of new, underlying descriptions capable of explaining the existence of non-classical correlations, non-commutativity of measurements and other unique and counter-intuitive phenomena remains still…

Divergence is not only an important mathematical concept in information theory, but also applied to machine learning problems such as low-dimensional embedding, manifold learning, clustering, classification, and anomaly detection. We…

Generalized quantum instruments correspond to measurements where the input and output are either states or more generally quantum circuits. These measurements describe any quantum protocol including games, communications, and algorithms.…

We consider two interacting systems when one is treated classically while the other system remains quantum. Consistent dynamics of this coupling has been shown to exist, and explored in the context of treating space-time classically. Here,…

The classical multivariate extreme-value theory concerns the modeling of extremes in a multivariate random sample, suggesting the use of max-stable distributions. In this work, the classical theory is extended to the case where aggregated…

Quantum correlations arising in Bell experiments, involving a physical source that emits a quantum state to a number of observers, have been intensively studied over the last decades. Much less is known about the nature of quantum…

Recently some authors have pointed out that there exist nonclassical correlations which are more general, and possibly more fundamental, than entanglement. For these general quantum correlations and their classical counterparts, under the…

Bargmann invariants of order $n$, defined as multivariate traces of quantum states $\text{Tr}[\rho_1\rho_2 \ldots \rho_n]$, are useful in applications ranging from quantum metrology to certification of nonclassicality. A standard quantum…

A minimal approach to the measurement problem and the quantum-to-classical transition assumes a universally valid quantum formalism, i.e. unitary time evolution governed by a Schr\"odinger-type equation. As had been pointed out long ago, in…

Superposition is the core feature that sets quantum theory apart from classical physics. Here, we investigate whether sets of quantum measurements can be modelled by using only devices that are operationally classical, in the sense that…