相关论文: Jensen-Shannon divergence, Fisher information, and…

It is widely accepted that the states of any quantum system are vectors in a Hilbert space. Not everyone agrees, however. The recent paper ``The unphysicality of Hilbert spaces'' by Carcassi, Calder\'on and Aidala is a thoughtful dissection…

Comparing probability distributions is an indispensable and ubiquitous task in machine learning and statistics. The most common way to compare a pair of Borel probability measures is to compute a metric between them, and by far the most…

Incompatible observables can be approximated by compatible observables in joint measurement or measured sequentially, with constrained accuracy as implied by Heisenberg's original formulation of the uncertainty principle. Recently, Busch,…

We study the statistical geometry of random chords on n-dimensional spheres by deriving explicit analytical expressions for the chord length distribution and its associated structural properties. A critical threshold emerges at dimension…

There are many information and divergence measures exist in the literature on information theory and statistics. The most famous among them are Kullback-Leiber relative information and Jeffreys J-divergence. The measures like, Bhattacharya…

Feature selection is a key step when dealing with high dimensional data. In particular, these techniques simplify the process of knowledge discovery from the data by selecting the most relevant features out of the noisy, redundant and…

Combining gravity with quantum theory is still work in progress. On the one hand, classical gravity, is the geometry of space-time determined by the energy-momentum tensor of matter and the resulting nonlinear equations; on the other hand,…

Bell's inequality plays an important role with respect to the Einsteinian question about the physical reality of quantum theory. While Bell's inequality is usually viewed within the geometric framework of a Hilbert space quantum model, the…

There are three classical divergence measures exist in the literature on information theory and statistics. These are namely, Jeffryes-Kullback-Leiber J-divergence. Sibson-Burbea-Rao Jensen-Shannon divegernce and Taneja arithemtic-geometric…

Skew-symmetric densities recently received much attention in the literature, giving rise to increasingly general families of univariate and multivariate skewed densities. Most of those families, however, suffer from the inferential drawback…

In quantum metrology, the parameter estimation accuracy is bounded by quantum Fisher information. In this paper, we present coherence measures in terms of (quantum) Fisher information by directly considering the post-selective non-unitary…

Fisher Information (FI) is a quantity ubiquitously measured in such varied areas like metrology, machine learning, and biological complexity. Mathematically, it represents a lower bound in the variance of unknown parameters that are related…

We discuss that there is a crucial contradiction within quantum mechanics. We derive a proposition concerning a quantum expectation value under the assumption of the existence of the directions in a spin-1/2 system. The quantum predictions…

In this paper we investigate the Erd\"os/Falconer distance conjecture for a natural class of sets statistically, though not necessarily arithmetically, similar to a lattice. We prove a good upper bound for spherical means that have been…

The density matrix in quantum mechanics parameterizes the statistical properties of the system under observation, just like a classical probability distribution does for classical systems. The expectation value of observables cannot be…

Local information objectivity, that local, independent observers can infer the same information about a model upon exchange of independently acquired experimental data, is fundamental to science. It is mathematically encoded via Cencov's…

We obtain an estimate for the expected subspace robust Wasserstein distance between any probability measure on the unit ball of a separable Hilbert space, and its empirical distribution from $n$ i.i.d. samples.

The quantum Fisher information represents the continuous family of metrics on the space of quantum states and places the fundamental limit on the accuracy of quantum state estimation. We show that the entire family of the quantum Fisher…

In the general theory of quantum measurement, one associates a positive semidefinite operator on a $d$-dimensional Hilbert space to each of the $n$ possible outcomes of an arbitrary measurement. In the special case of a projective…

For statistical inference on an infinite-dimensional Hilbert space $\H $ with no moment conditions we introduce a new class of energy distances on the space of probability measures on $\H$. The proposed distances consist of the integrated…