Related papers: Hilbert-Schmidt Separability Probabilities and Non…
We prove that kernel covariance embeddings lead to information-theoretically perfect separation of distinct continuous probability distributions. In statistical terms, we establish that testing for the \emph{equality} of two non-atomic…
In Bayesian multilevel models, the data are structured in interconnected groups, and their posteriors borrow information from one another due to prior dependence between latent parameters. However, little is known about the behaviour of the…
The principle of complementarity is quantified in two ways: by a universal uncertainty relation valid for arbitrary joint estimates of any two observables from a given measurement setup, and by a general uncertainty relation valid for…
We propose an approach to rapidly find the upper limit of separability between datasets that is directly applicable to HEP classification problems. The most common HEP classification task is to use $n$ values (variables) for an object…
Computing accessible information for an ensemble of quantum states is a basic problem in quantum information theory. We show that the recently obtained optimality criterion (A.S. Holevo, Lobachevskii J. Math., \textbf{43}:7 (2022),…
We employ conditional Tsallis q entropies to study the separability of symmetric one parameter W and GHZ multiqubit mixed states. The strongest limitation on separability is realized in the limit q-->infinity, and is found to be much…
A Hilbert space embedding for probability measures has recently been proposed, with applications including dimensionality reduction, homogeneity testing, and independence testing. This embedding represents any probability measure as a mean…
Predicting the outcomes of quantum measurements is a cornerstone of quantum information theory and a key resource for quantum technologies. Here, we introduce a comprehensive framework for quantifying the predictability of measurements on a…
In a smooth semiparametric estimation problem, the marginal posterior for the parameter of interest is expected to be asymptotically normal and satisfy frequentist criteria of optimality if the model is endowed with a suitable prior. It is…
We use a generalised procedure for the combined likelihood analysis of different cosmological probes, the `Hyper-Parameters' method, that allows freedom in the relative weights of the raw measurements. We perform a joint analysis of the…
We give a polynomial-time algorithm to sample from the Gibbs measure of the Sherrington-Kirkpatrick model with negligible total-variation distance (TVD) error up to inverse temperature $\beta < 1/2$. Prior work obtained TVD error guarantees…
Propagation of error is a widely used estimation tool in experiments, where the estimation precision of the parameter depends on the fluctuation of the physical observable. Thus which observable is chosen will greatly affect the estimation…
We recall some of the history of the information-theoretic approach to deriving core results in probability theory and indicate parts of the recent resurgence of interest in this area with current progress along several interesting…
The Heisenberg uncertainty principle is one of the most famous features of quantum mechanics. However, the non-determinism implied by the Heisenberg uncertainty principle --- together with other prominent aspects of quantum mechanics such…
The theory of a two-level $\eta$-Hermitian Hamiltonian with $\mathcal{PT}$ symmetry is reviewed and extended to include open system dynamics. A first-principles derivation of the generalized Gorini-Kossakowski-Sudarshan-Lindblad master…
Given a positive definite, bounded linear operator $A$ on the Hilbert space $\mathcal{H}_0:=l^2(E)$, we consider a reproducing kernel Hilbert space $\mathcal{H}_+$ with a reproducing kernel $A(x,y)$. Here $E$ is any countable set and…
A definition of the nonadditive (nonextensive) conditional entropy indexed by q is presented. Based on the composition law in terms of it, the Shannon-Khinchin axioms are generalized and the uniqueness theorem is established for the Tsallis…
We consider the analysis of probability distributions through their associated covariance operators from reproducing kernel Hilbert spaces. We show that the von Neumann entropy and relative entropy of these operators are intimately related…
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,…
The generic real (b=1) and complex (b=2) two-qubit states are 9-dimensional and 15-dimensional in nature, respectively. The total volumes of the spaces they occupy with respect to the Hilbert-Schmidt and Bures metrics are obtainable as…