Related papers: Probability measure generated by the superfidelity

The magnitude of a metric space is a novel invariant that provides a measure of the 'effective size' of a space across multiple scales, while also capturing numerous geometrical properties, such as curvature, density, or entropy. We develop…

We investigate random density matrices obtained by partial tracing larger random pure states. We show that there is a strong connection between these random density matrices and the Wishart ensemble of random matrix theory. We provide…

The spectral density of various ensembles of sparse symmetric random matrices is analyzed using the cavity method. We consider two cases: matrices whose associated graphs are locally tree-like, and sparse covariance matrices. We derive a…

Software code complexity is a well-studied property to determine software component health. However, the existing code complexity metrics do not directly take into account the fault-proneness aspect of the code. We propose a metric called…

In recent years the ultrahigh dimensional linear regression problem has attracted enormous attentions from the research community. Under the sparsity assumption most of the published work is devoted to the selection and estimation of the…

A measure of complexity based on a probabilistic description of physical systems is proposed. This measure incorporates the main features of the intuitive notion of such a magnitude. It can be applied to many physical situations and to…

In the recent paper [17] the first experimental determination of the density matrix of a free electron beam has been reported. The employed method leads to a linear inverse problem with a positive semidefinite operator as unknown. The…

We introduce an approach to bias deep generative models, such as GANs and diffusion models, towards generating data with either enhanced fidelity or increased diversity. Our approach involves manipulating the distribution of training and…

Inspired by the theory of quantum information, I use two non-Hermitian random matrix models - a weighted sum of circular unitary ensembles and a product of rectangular Ginibre unitary ensembles - as building blocks of three new products of…

We construct ergodic probability measures with infinite metric entropy for typical continuous maps and homeomorphisms on compact manifolds. We also construct sequences of such measures that converge to a zero-entropy measure.

We analyze the convergence of probability density functions utilizing approximate models for both forward and inverse problems. We consider the standard forward uncertainty quantification problem where an assumed probability density on…

The spectral density of random matrices is studied through a quaternionic generalisation of the Green's function, which precisely describes the mean spectral density of a given matrix under a particular type of random perturbation. Exact…

Ensembles of random density matrices determined by various probability measures are analysed. A simple and efficient algorithm to generate at random density matrices distributed according to the Bures measure is proposed. This procedure may…

We discuss properties of two methods for ascribing probabilities to the shape of a probability distribution. One is based on the idea of counting the number of modes of a bootstrap version of a standard kernel density estimator. We argue…

This study intends to introduce kernel mean embedding of probability measures over infinite-dimensional separable Hilbert spaces induced by functional response statistical models. The embedded function represents the concentration of…

This paper proposes a novel method for testing observability in Gaussian models using discrete density approximations (deterministic samples) of (multivariate) Gaussians. Our notion of observability is defined by the existence of the…

Recent advances in deep generative models have led to impressive results in a variety of application domains. Motivated by the possibility that deep learning models might memorize part of the input data, there have been increased efforts to…

Spurious association arises from covariance between propensity for the treatment and individual risk for the outcome. For sensitivity analysis with stochastic counterfactuals we introduce a methodology to characterize uncertainty in causal…

We present an intrinsic metric that quantifies distances between power spectral density functions. The metric was derived by the author in a recent arXiv-report (math.OC/0607026) as the geodesic distance between spectral density functions…

We show on theoretical grounds that, even in the presence of noise, probabilistic measurement strategies (which have a certain probability of failure or abstention) can provide, upon a heralded successful outcome, estimates with a precision…