Related papers: Quantum Hellinger distances revisited
This short paper presents a general approach for computing robust Wasserstein barycenters of persistence diagrams. The classical method consists in computing assignment arithmetic means after finding the optimal transport plans between the…
Critical quantum systems are a promising resource for quantum metrology applications, due to the diverging susceptibility developed in proximity of phase transitions. Here, we assess the metrological power of parametric Kerr resonators…
The Generalized Hamming weights and their relative version, which generalize the minimum distance of a linear code, are relevant to numerous applications, including coding on the wire-tap channel of type II, $t$-resilient functions,…
For a simplicial complex $\Delta$ we study the effect of barycentric subdivision on ring theoretic invariants of its Stanley-Reisner ring. In particular, for Stanley-Reisner rings of barycentric subdivisions we verify a conjecture by Huneke…
A natural one-parameter family of K\"ahler quantizations of the cotangent bundle $T^*K$ of a compact Lie group $K$, taking into account the half-form correction, was studied in \cite{FMMN}. In the present paper, it is shown that the…
In this paper, we introduce a generalization of the Wasserstein barycenter, to a case where the initial probability measures live on different subspaces of R^d. We study the existence and uniqueness of this barycenter, we show how it is…
The notion of distance in Hilbert space is relevant in many scenarios. In particular, distances between quantum states play a central role in quantum information theory. An appropriate measure of distance is the quantum Jensen Shannon…
A family of logarithmic Sobolev inequalities on finite dimensional quantum state spaces is introduced. The framework of non-commutative $\bL_p$-spaces is reviewed and the relationship between quantum logarithmic Sobolev inequalities and the…
Extending hyperuniformity from classical to quantum fluctuations in electron systems yields a framework that identifies quantum phase transitions and reveals underlying gap structures through the quantum weight. We study long-wavelength…
A regularization renormalization method ($RRM$) in quantum field theory ($QFT$) is discussed with simple rules: Once a divergent integral $I$ is encountered, we first take its derivative with respect to some mass parameter enough times,…
The $\alpha$-divergences include the well-known Kullback-Leibler divergence, Hellinger distance and $\chi^2$-divergence. In this paper, we derive differential and integral relations between the $\alpha$-divergences that are generalizations…
We study quantum statistical inference tasks of hypothesis testing and their canonical variations, in order to review relations between their corresponding figures of merit---measures of statistical distance---and demonstrate the crucial…
We construct a generalised expression for the normal ordering of (a+a^{\dagger})^{m} for integral values of m and use the result to study the quantum anharmonic oscillator problem in the Heisenberg approach. In particular, we derive…
Given the growing quantity of proposals and works of basic hypergeometric functions in the scope of $q$-calculus, it is important to introduce a systematic classification of $q$-calculus. Our aim in this article is to investigate certain…
There are three classical divergence measures known in the literature on information theory and statistics. These are namely, Jeffryes-Kullback-Leiber \cite{jef} \cite{kul} \textit{J-divergence}. Sibson-Burbea-Rao \cite{sib} \cite{bur1,…
Quantum metrology is a science about quantum measurements and it plays a key role in precision of quantum parameter estimation. Meanwhile, quantum coherence is an important quantum feature and quantum Fisher information (QFI) is an…
The purpose of the present note is twofold. Firstly, we highlight the similarities between the ontologies of Kastner's possibilist transactional interpretation (PTI) of quantum mechanics - an extension of Cramer's transactional…
We propose Bell inequalities for discrete or continuous quantum systems which test the compatibility of quantum physics with an interpretation in terms of deterministic hidden-variable theories. The wave function collapse that occurs in a…
Classically the Harmonic Oscillator (HO) is the generic example for the use of angle and action variables phi in R mod 2 pi and I > 0. But the symplectic transformation (\phi,I) to (q,p) is singular for (q,p) = (0,0). Globally {(q,p)} has…
There has been much debate over the form of the quantum area spectrum for a black hole horizon, with the evenly spaced conception of Bekenstein having featured prominently in the discourse. In this letter, we refine a very recently proposed…