相关论文: The Chernoff lower bound for symmetric quantum hyp…
Although the assumption of elliptical symmetry is quite common in multivariate analysis and widespread in a number of applications, the problem of testing the null hypothesis of ellipticity so far has not been addressed in a fully…
Recently, many fundamental and important results in statistical decision theory have been extended to the quantum system. Quantum Hunt-Stein theorem and quantum locally asymptotic normality are typical successful examples. In the present…
Given a mixture of states, finding a way to optimally discriminate its elements is a prominent problem in quantum communication theory. In this paper, we will address mixtures of density operators that are unitarily equivalent via elements…
Recently, Samorodnitsky proved a strengthened version of Mrs. Gerber's Lemma, where the output entropy of a binary symmetric channel is bounded in terms of the average entropy of the input projected on a random subset of coordinates. Here,…
For the zone of moderate deviation probabilities the local asymptotic minimax lower bound of asymptotic efficiency of estimators is established. The estimation parameter is multidimensional. The lower bound admits the interpretation as the…
In recent years, the mathematical limits and algorithmic bounds for probabilistic group testing have become increasingly well-understood, with exact asymptotic thresholds now being known in general scaling regimes for the noiseless setting.…
We derive an asymptotic lower bound on the Shannon entropy $H$ of sums of $N$ arbitrary iid discrete random variables. The derived bound $H \geq \frac{r(X)}{2}\log(N) + {\it cst}$ is given in terms of the incommensurability rank $r(X)$ of…
We study the injective norm of random skew-symmetric tensors and the associated fermionic quantum states, a natural measure of multipartite entanglement for systems of indistinguishable particles. Extending recent advances on random quantum…
We introduce the problem of \emph{entropy equivalence testing} for probability distributions, a relaxation of the well-studied closeness testing problem, where the distribution testing algorithm is now only required to distinguish, given…
We undertake a detailed study of the performance of maximum likelihood (ML) estimators of the density matrix of finite-dimensional quantum systems, in order to interrogate generic properties of frequentist quantum state estimation. Existing…
We discuss our recent study of local quantum mechanical uncertainty relations in quantum many body systems. These lead to fundamental bounds for quantities such as the speed, acceleration, relaxation times, spatial gradients and the…
We consider the problem of estimating the proportion $\theta$ of true null hypotheses in a multiple testing context. The setup is classically modeled through a semiparametric mixture with two components: a uniform distribution on interval…
In this paper we present a new error bound on sampling algorithms for frequent itemsets mining. We show that the new bound is asymptotically tighter than the state-of-art bounds, i.e., given the chosen samples, for small enough error…
We prove a tight and close-to-optimal lower bound on the effectiveness of local quantum measurements (without classical communication) at discriminating any two bipartite quantum states. Our result implies, for example, that any two…
In this note, we investigate the performance of the PCM scheme with linear quantization rule for quantizing unit-norm tight frame expansions for ${\mathbb R}^d$ without the White Noise Hypothesis. In \cite{WX}, Wang and Xu showed that for…
A convenient framework for dealing with asymptotic limit problems of probabilistic nature is provided. These problems include questions such as finding the asymptotic proportion of terms of a sequence falling inside a given interval, or the…
Quantum hypothesis testing (QHT) has been traditionally studied from the information-theoretic perspective, wherein one is interested in the optimal decay rate of error probabilities as a function of the number of samples of an unknown…
We give bounds on the average fidelity achievable by any quantum state estimator, which is arguably the most prominently used figure of merit in quantum state tomography. Moreover, these bounds can be computed online---that is, while the…
No-signaling theories, which can contain nonlocal correlations stronger than classical correlations but limited by the no-signaling condition, have deepened our understanding of the quantum theory. In principle, the nonlocality of these…
We consider the optimal discrimination of bipartite quantum states and provide an upper bound for the maximum success probability of optimal local discrimination. We also provide a necessary and sufficient condition for a measurement to…