相关论文: The Chernoff lower bound for symmetric quantum hyp…

We provide new bounds for the rate of convergence of the multivariate Central Limit Theorem in Wasserstein distances of order $p \geq 2$. In particular, we obtain what we conjecture to be the asymptotically optimal rate whenever the density…

We consider a broad class of permutation invariant statistical problems by extending the standard decision theoretic definition to allow also selective inference tasks, where the target is specified only after seeing the data. For any such…

We prove a concise factor-of-2 estimate for the failure rate of optimally distinguishing an arbitrary ensemble of mixed quantum states, generalizing work of Holevo [Theor. Probab. Appl. 23, 411 (1978)] and Curlander [Ph.D. Thesis, MIT,…

A common statistical task lies in showing asymptotic normality of certain statistics. In many of these situations, classical textbook results on weak convergence theory suffice for the problem at hand. However, there are quite some…

We introduce a class of central symmetric infinitely divisible probability measures on compact Lie groups by lifting the characteristic exponent from the real line via the Casimir operator. The class includes Gauss, Laplace and stable-type…

The statistics and machine learning communities have recently seen a growing interest in classification-based approaches to two-sample testing. The outcome of a classification-based two-sample test remains a rejection decision, which is not…

It is well-known that density estimation on the unit interval is asymptotically equivalent to a Gaussian white noise experiment, provided the densities are sufficiently smooth and uniformly bounded away from zero. We show that a uniform…

Recent research has made significant progress on the problem of bounding log partition functions for exponential family graphical models. Such bounds have associated dual parameters that are often used as heuristic estimates of the marginal…

Lower and upper bounds are explored for the uniform (Kolmogorov) and $L^2$-distances between the distributions of weighted sums of dependent summands and the normal law. The results are illustrated for several classes of random variables…

We introduce a new quantum decoder based on a variant of the pretty good measurement, but defined via an alternative matrix quotient. We use this decoder to show new lower bounds on the error exponent both in the one-shot and asymptotic…

Information metrics give lower bounds for the estimation of parameters. The Cencov-Morozova-Petz Theorem classifies the monotone quantum Fisher metrics. The optimum bound for the quantum estimation problem is offered by the metric which is…

This paper considers the estimation of Shannon entropy for discrete distributions with countably infinite support. While minimax rates for finite-support distributions are established, infinite-support distributions present distinct…

We prove a lower bound on the relative entropy between two finite-dimensional states in terms of their entropy difference and the dimension of the underlying space. The inequality is tight in the sense that equality can be attained for any…

Symmetry is an important and unifying notion in many areas of physics. In quantum mechanics, it is possible to eliminate degrees of freedom from a system by leveraging symmetry to identify the possible physical transitions. This allows us…

We investigate the discrimination of two candidates of an unknown parameter in quantum systems with continuous weak measurement, inspired by the application of hypothesis testing in distinguish-ing two Hamiltonians [Kiilerich and M{\o}lmer,…

I propose a general quantum hypothesis testing theory that enables one to test hypotheses about any aspect of a physical system, including its dynamics, based on a series of observations. For example, the hypotheses can be about the…

This paper gives upper and lower bounds on the minimum error probability of Bayesian $M$-ary hypothesis testing in terms of the Arimoto-R\'enyi conditional entropy of an arbitrary order $\alpha$. The improved tightness of these bounds over…

We introduce and apply Hilbert's projective metric in the context of quantum information theory. The metric is induced by convex cones such as the sets of positive, separable or PPT operators. It provides bounds on measures for statistical…

The small sample universal hypothesis testing problem is investigated in this paper, in which the number of samples $n$ is smaller than the number of possible outcomes $m$. The goal of this work is to find an appropriate criterion to…

Estimating quantum entropies and divergences is an important problem in quantum physics, information theory, and machine learning. Quantum neural estimators (QNEs), which utilize a hybrid classical-quantum architecture, have recently…