相关论文: Local asymptotic normality in quantum statistics

In this paper we consider the construction of optimal tests of equivalence hypotheses. Specifically, assume X_1,..., X_n are i.i.d. with distribution P_{\theta}, with \theta \in R^k. Let g(\theta) be some real-valued parameter of interest.…

We uncover the quantum fluctuation-response inequality, which, in the most general setting, establishes a bound for the mean difference of an observable at two different quantum states, in terms of the quantum relative entropy. When the…

We study the central limit theorem in the non-normal domain of attraction to symmetric $\alpha$-stable laws for $0<\alpha\leq2$. We show that for i.i.d. random variables $X_i$, the convergence rate in $L^\infty$ of both the densities and…

Nonlocality exhibited by ensembles of composite quantum states, wherein local operations and classical communication (LOCC) yield suboptimal discrimination probabilities compared to global strategies, is one of the striking nonclassical…

In quantum measurement theory, a measurement scheme describes how an observable of a given system can be measured indirectly using a probe. The measurement scheme involves the specification of a probe theory, an initial probe state, a probe…

Local available quantum correlations (LAQC), as defined by Mundarain et al., are analyzed for non-symmetric 2-qubit X states, that is, X-states that are not invariant under the exchange of subsystems and therefore have local Bloch vectors…

Asymptotics of maximum likelihood estimation for $\alpha$-stable law are analytically investigated with a continuous parameterization. The consistency and asymptotic normality are shown on the interior of the whole parameter space. Although…

We develop a general theoretical framework for measurement protocols employing statistical correlations of randomized measurements. We focus on locally randomized measurements implemented with local random unitaries in quantum lattice…

Conventional scattering theory is incomplete in that it does not adequately describe the behaviour of the wave function at macroscopic distances from the scattering reaction volume. In scattering experiments particles are incident from…

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…

We consider a general class of statistical experiments, in which an $n$-dimensional centered Gaussian random variable is observed and its covariance matrix is the parameter of interest. The covariance matrix is assumed to be…

We show that quantum mechanics can be represented as an asymptotic projection of statistical mechanics of classical fields. Thus our approach does not contradict to a rather common opinion that quantum mechanics could not be reduced to…

We prove that the correlations present in a multipartite quantum state have an \emph{operational} quantum character as soon as the state does not simply encode a multipartite classical probability distribution, i.e. does not describe the…

Solutions for a class of wave equations with effective potentials are obtained by a method of a Laplace-transform. Quasinormal modes appear naturally in the solutions only in a spatially truncated form; their coefficients are uniquely…

Quantum entanglement and nonlocality are inequivalent notions: There exist entangled states that nevertheless admit local-realistic interpretations. This paper studies a special class of local-hidden-variable theories, in which the linear…

The question of the local stability of the (replica-symmetric) amorphous solid state is addressed for a class of systems undergoing a continuous liquid to amorphous-solid phase transition driven by the effect of random constraints. The…

We establish the asymptotic theory in quantile autoregression when the model parameter is specified with respect to moderate deviations from the unit boundary of the form (1 + c / k) with a convergence sequence that diverges at a rate…

This paper is concerned with two questions in the decoherent histories approach to quantum mechanics: the emergence of approximate classical predictability, and the fluctuations about it necessitated by the uncertainty principle. We…

This work develops analytic methods to quantitatively demarcate quantum reality from its subset of classical phenomenon, as well as from the superset of general probabilistic theories. Regarding quantum nonlocality, we discuss how to…

We rigorously derive explicit formulae for the pair correlation function of the ground state of the free Fermi gas in the thermodynamic limit for general geometries of the macroscopic regions occupied by the particles and arbitrary…